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Smooth Bilevel Programming for Sparse Regulari...

Smooth Bilevel Programming for Sparse Regularization

Talk given at the SMAI-SIGMA workshop in Paris.

Gabriel Peyré

October 19, 2021
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  1. Smooth Bilevel Programming for Sparse Regularization Gabriel Peyré É C

    O L E N O R M A L E S U P É R I E U R E RESEARCH UNIVERSITY PARIS Joint work with: Clarice Poon 
 (Bath University)
  2. k2 with > 0. P i ⌘ i . Quadratic

    Variational Forms Bilevel VarPro
  3. Sparse Regularization <latexit 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A 2 Rn⇥d <latexit 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min

    x2Rd 1 2 kAx yk2 + kxk1 <latexit 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min Ax=y kxk1 <latexit 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Ax ⇡ y <latexit 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over-determined + noise <latexit sha1_base64="KP+hZOSsydxfXbMgjqAFx8TV0IU=">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</latexit> under-determined <latexit sha1_base64="nCIFL0QNopmQRSBhYa6iV/R4B74=">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</latexit> regularize
  4. Sparse Regularization <latexit 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A 2 Rn⇥d <latexit 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min

    x2Rd 1 2 kAx yk2 + kxk1 <latexit 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min Ax=y kxk1 <latexit 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Ax ⇡ y <latexit 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over-determined + noise <latexit sha1_base64="KP+hZOSsydxfXbMgjqAFx8TV0IU=">AABB03ictVzdchTHFW6cHxvyY0guczOJTAqnMBYyFcflSpWFJISMAMGuBLYF1P6MloXZnWVmVwLWuknlNo+Q2+Qx8hx5g+Qqr5Dz0z3ds9szp0chdEnq6e3vnNNnuk+fc7qX7iQZ5tPV1X+ee+8HP/zRj9//4PyFn/z0Zz//8OKlXxzk6Szrxfu9NEmzx91OHifDcbw/HU6T+PEkizujbhI/6r7cwM8fHcdZPkzH7embSfxk1BmMh0fDXmcKTc8uXpqN+3H2ST+extkIaPSjZxdXVq+t0r9ouXJdV1aU/reXXor21aHqq1T11EyNVKzGagr1RHVUDuU7dV2tqgm0PVFzaMugNqTPY3WqLgB2Br1i6NGB1pfwewBP3+nWMTwjzZzQPeCSwE8GyEhdBkwK/TKoI7eIPp8RZWytoj0nmijbG/jb1bRG0DpVz6FVwpmeoTgcy1QdqT/QGIYwpgm14Oh6msqMtIKSR86opkBhAm1Y78PnGdR7hDR6jgiT09hRtx36/F/UE1vxuaf7ztS/ScrLUCLV0qNPCwoddUz0I3qbM/iM5UmA8wAoxHqMWDshXY9o9GPoP4f2e1BOqWZ00oUyp9bTWuQGFB9yQ0RuQ/Eht0XkLhQfcldE7kHxIfc0ErEZ6dyPb0Hx4Vsi5wdQfMgHIvIhFB/yoYg8gOJDHojIb6H4kN+KyFtQfMhbIvIOFB/yjohsQ/Eh2yJyH4oPuS8it6D4kFsaWb1SMygp0RkKq3Id6mUeaCkSaFkX5btJ1tGHvRmwpnsVWHlVb8JfP3YzQKdxBXYrYN4dVWDlmbcNNtKPlW3RbdpNfNjbInYHZoAfuyNiv1YvKrBfB6y0lxVYea3tQj8/Vra+d+HJj70rYu9BzY+V96j70OLH3g/YMSYV2D0R+0C9qsCGWP2sAivb/RbYFT9W3qfa0N+PDbGmswqsbE8PwIPxY+Xd6hG0+rGPROxj9boC+1jEfgPW3Y/9JmCHfVuBNXvsBdpBBuSPxLBi66h1ilWJtQlQ6wj8k2JvScg37kK7hBkUmAFhRiJiu0BsByJ2C8RusFx5YUdz8ndlLq0C0QpEdIu9CWtTsX+/6I+1JACxWSA2FxB1Him+azOWY/IuTIuEnBY7F9ZCxpQW9htrsZ4P9ZbXIO6XEDy3n9PMv0rREkZQqKk6as+LPZ6RET3XIU4oejOjNDxk3LSwCi7qtYjqelBdEfXGg3ojomYe1ExEHXtQxyLKrnwXdxgwA6z+8V3M6YlnAPvI1SUCr2Addp3bsEYjmD974AU+pJb78LdFsbdU6iTDaB73ScxyPClZ4gxqc7UC7TYq3KT4OqEVFoNk3PO+jvHxCXMbc73m2AqfFjt5VGRMwukMSZ5BQQe9xYjWUzM6d6jllLw7rjXD3y7Wvak1w2+Rxk/Ji+daM/xUSz89g+xtjW2fAduC1TTR2rf1pjQ4/8I0TP0C7bpocfGtjvScQXqvG9Lf0W9m5wzvZYNqrB9bb0Yjd8aXl8bXhIbVc+7ouRkV9J7Y6zW1qPFIxjrutfWmMqS0i461HPap6ZvBPn39Zky9GY098Lg2KOaeO/Wms3dSjMbWm9E4UJz3PCVP3tSb0RjQM+vD1pvRwGxLR8f5tt7UsqMGOHa29aZWfUxZYMwB8ZznFusVZeQnzTS1IfkH9dka1+df3scwZ/O0iBHqKVnftppOt9jL6iUy/kIMVm3aUA70L2aOD1amMVdrYnzFMkxL+/syHbvHo+Z3QYsRrH4+A5By5glIaHISaL0ToHhdjLrKIzO4NRGHs+RoAXWoW6eit2j5ctao3PaMWqW4zI7W6vGQ7HVOc29CPuEuaVbSw27lG66iKGlot6QhmV4T3b3V67Ws/VURN1lATIqZ1qMTIT5Jq49TfVpvOTq+rE95plD4zMfOX8w2H2lrgzFPSrYIZanj6fYzeSS3DffVq8rmuPmziN4o2qtjshpDOpHKxSjUZIvZG5/Ts6W9T2dyyINp9OA9RprKRPGpGWbRMZ8ekUV17a3EG/VlMnRcz8nqGntcjx446IEH3TzG2YAd4x7U2hAz7MNTOyDKuVDoKiWNZ+qT4nQ0pTdYH9EnJQtpaLC9iUsWsi7Kfl6icgJonA0cpYfTWKRj8IdLlOSo3yePjV3Llv8yndya8+0OzfHq2VydiekT1zXiGtGq4VNdflrkwBLMvZ+skf9aP0rk14Qj2lCJ61OHM+tlTCf+MUWwE/KME1pt0uoo93bzU4ufGE57ypyd42l2ShYyIvsXwf6U0pyM6Me9O2BO0NkiJGQjQ+zOsPBufL7OUJxj1o8bKr7VYOdbTLZsRvwNXXd15TQXOWLgfeB0YW4bneySLxgT10xbd7u263cfRNp7Eu4sYYp2rlwh/h/Tb/Nj5snK0oxADeMbyLWt872PlGIW1FGHdvl6G2T6ulJ+VMjwVEtt9z8r00clyTYp4kJ5cLfuA+cePTMvnCUZyZ0v9eF9tC6bi5QnC3rE0R5RFM92f6B3YJT7Ku2SK7TmDmmWDGAWTIsowvSVssiLfOt5lamH0c7/L9StrstaQ4qRshlc1pCU348pWnOlTGBW8/x9SavJr/VsoVc9nzHNxZGzlr+H1l/DbyO3eQ6j0y1ZhZs0B5iCfbIa4ZZoqUcYr5slXmZmGlr22fKzc9L0clvOEl+zdbMx9nFjKns0a17rrIWpn4XGC4fGi0Adtums0WrRtBtL9EyMLdr6tDKUXxNu7QaUZyJl2SMzqGGAlG4sFUa1L1KVY3yDeivSWhVpdWC1uqcB7poPQfrX+uLq/r7Y3SN1i3ybHnlgHL/0aZUOyecyrfWRGlNAzje0fXVX/yG1IPcuWVCkzPc4ccXwqVOPymkh6W/1zpaSnbcWwdxbOtF9jI09pPpnS8gRrYmc1qVB3KAesZbflSNasEjXHJ8josx/h3wq9jvqY2a3t30nUcmfsPEmryrLiyOFMelfyrztLEWvO078GlFMONPedRdoNX/DSIExJpPg9yxzekO4y/FJAnu0XbKfy3aKT/HGjkTXSOq5+mOAjeGo1851d26ZEZux/Q56otbtW/f1kPklwRwlfmc50evQrjbSPup84flstDp6lys/1+lhtsDX6mNGfdzIwkZ5Zcyh+jKYC0vUjAtjQrg0G0UT+ZtJ3kRmPp0KpWx6G8rlTAPbmOcUL0n3QBHh8+6ueL25j4VxdJfodQnrUuMWiRJm41KdH3AtLWalzi/tQ9x6vnY3SpydqGqnMNTd3cLab7aQMVm/REk5G+7tyn5YilLkLAxT6Cm+0VsVH7o0v4SCvyPliw4Nx5DcYQv823W1obbewW2IV7rOGc2IWtAW9Bdi744eZ7lHvY5eOdRd+iEcwnkMQdeS9EPaSZvKzpRlyV3q4fRPyApkKhaltz2bj8HlIo9kmVOT8QzJssmjGSrzXZymYzEcQkZS5hLOh881pFEcKfOdpmZjMNTlEZQ5NOFh7jGEvXPbuzkvl1O9vpa5hPLgXcCcuBgcnvxVxyq2X4iFypw38u45oHU4qqFudov/dRyGj+XUnFcot5y+a/Yi4K1zv1hnZNEfbr5mLLeQ2VzNMZxnWozOekt+fuz3RY3eVOqM5t3TR3/UzgHDa644DypLx3h3Fll5Q6nguYBPhlT9R/3jnPxthFcFjSo5mlAy5xTV1EwPmZr5xqVvdOazEJksnSqZytRsHNGiG7Ebakfdgp+NwgNsejuUv0vJfxHr//5sH1qPyHqYLDpnDg6pLabshz1F69OzvT9bJTHe5eW7vW1owbPwXWrFe773qD/e9W2Xxlb9DRJe63dVqvqliGTxdM+uqy6MoHzyxjkg8z3fiO7ScxaLb56NAs4Wzf2pRYnm9Il8s6Bbie86UvZork70WT2eHOAN+06RH4rUp9TW0XYe91yJ814l570Fzjlpp8zhtfNZ/d2sKi4bDpd+kTs71v1SirPteV59bnSzkgvfQa/HD2rwA0fKFmn/JUXCmarP5s1qaM60TO4J61iZTCTrAePMTvG+6yPb4xpexwHjv1OJvuNIug2ydCn/HdEJW0b0Eq2bLZKebzrWZ1Jv10irv0dJ/7vBF/Qv4srnN3Tli+vF/25wsHbt+u+vffZgbeWrm/r/OfhA/Ur9Rl2BNf65+gqo7al94HCi/qr+pv6+vr8+X//T+p+563vnNOaXqvRv/S//BSovqBc=</latexit> under-determined <latexit sha1_base64="nCIFL0QNopmQRSBhYa6iV/R4B74=">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</latexit> regularize <latexit 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Spike deconvolution: <latexit 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Ax = a ? x <latexit 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x0 <latexit 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y = x ? a + " <latexit 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x
  5. Sparse Regularization <latexit 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A 2 Rn⇥d <latexit 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min

    x2Rd 1 2 kAx yk2 + kxk1 <latexit 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min Ax=y kxk1 <latexit 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Ax ⇡ y <latexit 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over-determined + noise <latexit sha1_base64="KP+hZOSsydxfXbMgjqAFx8TV0IU=">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</latexit> under-determined <latexit sha1_base64="nCIFL0QNopmQRSBhYa6iV/R4B74=">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</latexit> regularize <latexit 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Spike deconvolution: <latexit 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Ax = a ? x <latexit 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x0 <latexit 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y = x ? a + " <latexit 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x <latexit 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<latexit sha1_base64="DvsYbo9hB8zeOFMxhW8tXI1kFTY=">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</latexit> Data (ai, yi)n i=1 <latexit sha1_base64="YHdOt0d069yYdxf084ppd3pbpyY=">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</latexit> Model selection: <latexit 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yi ⇡ hai, xi <latexit 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Lasso: ||x||1 <latexit 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Ridge: ||x||2 2
  6. 2⌧ 2 Forward-Backward splitting • ˆ k+1 = k ⌧X>

    rLy (X k ) • k+1 = ˆ k+1 ⌧rR (ˆ k+1 ) and its siblings: FISTA, FISTA with restarts, variab metric/quasi-Newton proximal methods. Forward-Backward <latexit sha1_base64="iaP8TP8Hzy0Jg9H0z5MLH35sX2Y=">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</latexit> xk+1 = Prox⌧ ||·||1 (y ⌧A>(Axk y)) <latexit sha1_base64="F951Nm+rra9ve6UDYp3LMnIQF58=">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</latexit> Prox ||·||1 (x) = (sign(xi)(|xi | )+)i <latexit 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⌧ < 2 kAk <latexit 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k <latexit 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min x2Rd f(x) , 1 2 kAx yk2 + kxk1 <latexit 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x <latexit 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<latexit 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Prox ||·||1
  7. 2⌧ 2 Forward-Backward splitting • ˆ k+1 = k ⌧X>

    rLy (X k ) • k+1 = ˆ k+1 ⌧rR (ˆ k+1 ) and its siblings: FISTA, FISTA with restarts, variab metric/quasi-Newton proximal methods. Forward-Backward <latexit sha1_base64="iaP8TP8Hzy0Jg9H0z5MLH35sX2Y=">AABCEXictVxfcxu3EYfTf7H7z2kf+4JWccdubVdSPE0zmcyElmRZMW3RJiU7CW3NkTzRtI48+u4oS2b4KfpZ+tCndvraT9DpazvTPvUrdHcBHHAk7oBTXWMk4UD8dhd7wGJ3Abo3jUZptr7+t0vvfevb3/nu996/fOX7P/jhj3589YOfHKbxLOmHB/04ipNnvSANo9EkPMhGWRQ+myZhMO5F4dPeyRZ+/vQ0TNJRPOlk59Pw+TgYTkbHo36QQdPR1f2zo/nJrzcW/DPezcKzbN5K4rPF0bybBTPejYDQIODdSZyM593+IM4WRxuL6/yc3+LUo/Gim8VTfr1xdnRy6/wGv3F0dW399jr946uVDVlZY/JfK/6AH7AuG7CY9dmMjVnIJiyDesQClkL5mm2wdTaFtudsDm0J1Eb0ecgW7ApgZ9ArhB4BtJ7A7yE8fS1bJ/CMNFNC94FLBD8JIDm7BpgY+iVQR26cPp8RZWwtoz0nmijbOfztSVpjaM3YS2h14VRPXxyOJWPH7Hc0hhGMaUotOLq+pDIjraDk3BhVBhSm0Ib1AXyeQL1PSKVnTpiUxo66Dejzf1FPbMXnvuw7Y/8mKa9B4awtRx/nFAJ2SvQ5vc0ZfCbkiYDzECiEcoxYe0O6HtPoJ9B/Du2PoCyopnTSgzKn1kUlcguKDbnlRO5CsSF3ncgmFBuy6US2oNiQLYlEbEI6t+PbUGz4tpPzYyg25GMn8gkUG/KJE3kIxYY8dCK/gmJDfuVE3oNiQ95zIh9AsSEfOJEdKDZkx4k8gGJDHjiRO1BsyB2JLF+pCZSY6Iwcq7IB9SIPtBQRtDSc8t0l62jD3vVY0/0SrHtVb8NfO3bbQ6dhCXbHY94dl2DdM28XbKQd67ZF92k3sWHvO7F7MAPs2D0n9gv2qgT7hcdKOynButdaE/rZsW7r+xCe7NiHTuwjqNmx7j1qH1rs2H2PHWNagm05sY/Z6xKsj9VPSrBuu98Gu2LHuvepDvS3Y32s6awE67anh+DB2LHu3eoptNqxT53YZ+ysBPvMif0SrLsd+6XHDvu2BKv22Cu0gwzJHwlhxVZRC/JVibUpUAsc/KN8b4nIN+5BuwszzDFDwoydiN0cseuJaOaIprdcaW5HU/J33VzaOaLtiejlexPWMmf/Qd4fa5EHYjtHbC8hqjxSfNdqLKfkXagWFzLLdy6s+Ywpzu031kI5H6otr0LsFxBibr+kmX+ToiWMoFBTVdRe5nu8QHJ6rkK8oehNjVLxcOOy3CqYqDMnqmdB9Zyocwvq3ImaWVAzJ+rUgjp1ovTKN3Fdjxmg9Y/vYk5PYgYIH7m8cPAKGrDr3Ic1ymH+tMALfEIt+/C3TbG3q1RJhtE87pOY5XhesMQJ1OZsDdp1VLhN8XVEKywEyUTPfRnj4xPmNuZyzQkrvMh3cp5nTPzpjEieYU4HvUVO66kenQfUsiDvTtTq4e/n617V6uF3SOML8uJFrR4+k9JnF5C9I7GdC2DbsJqmUvu6XpeGyL8IGqp+hXZdtLj4VsdyziC9s5r09+Sb2bvAe9mimtCPrtejkRrjSwvjq0ND6zk19FyPCnpPwutVNV57JBMZ9+p6XRli2kUnUg79VPfNYJ+BfDOqXo9GCzyuLYq550a97uyd5qPR9Xo0DpnIey7Ik1f1ejSG9Cz0oev1aGC2JZBxvq7XteyoARE763pdqz6hLDDmgMScFy3aK0rIT5pJaiPyD6qzNabPv7qPYc7mRR4jVFPSvm05nV6+l1VLpPyFEKxaVlMO9C9mhg9WpDFnm874SsiQFfb3VTp6j0fNN0GLHFa/OANw5cwjkFDlJNB6R0Bxwxl1FUemcJtOHM6S4yVUV7ZmTm9R8xVZo2LbEbW64jI9Wq3HLtnrlObelHzCJmnWpYdm6Rsuo+jSULOgITe9Orp7K9drUfvrTtx0CTHNZ1qfToTESVp1nGrTetvQ8TV5ypNBEWc+ev5itvlYWhuMeWKyRShLFU+zn8ojmW24r95kOsctPuP0RtFenZLVGNGJVOqMQlW2WHjjc3rWtA/oTA55CBp9eI9cUpkycWqGWXTMp3OyqKa9dfFGfakMnainZHWVPa5GDw300IKuH+NswY7xCGodiBkO4KnjEeVcyXUVk8YTdis/HY3pDVZH9FHBQioawt6EBQtZFWW/LFB5A2icDSJK96exTEfhuyuU3FG/TR4duxYt/zU6uVXn2wHN8fLZXJ6JGRDXTeLKadWIU13xtMxBSDC3frJJ/mv1KJFfHY5oQ11cXxichV4mdOIfUgQ7Jc84otXmWh3F3mZ+avkTxanF1Nk5nmbHZCE52T8O+1NMc5LTj3l3QJ2gC4sQkY30sTuj3Lux+Toj5xzTftyIiVsNer6FZMtmxF/RNVdXSnNRRAxiH1gszW2lkyb5giFxTaR112u7evdBpL4nYc4SQVHPlevE/wb9Vj9qnqytzAjUML6BVNo62/uIKWZBHQW0y1fbINXXlPLDXIYXUmq9/2mZPixItk0RF8qDu/UAOPfpWfDCWZKQ3OlKH7GPVmVzkfJ0SY842mOK4oXdH8odGOW+SbvkGq25Ls2SIcyCLI8iVF9XFnmZbzWvInU/2un/hbrWdVFrSJEzncEVGnLl90OK1kwpI5jVYv6e0Gqyaz1Z6lXNZ0JzcWys5W+g9efwW8mtnv3o9ApW4S7NAUFBP2mNiBa+0sOP190CLzUzFS39rPnpOal6mS0Xia+FddMx9mltKi2aNWcya6HqF6HxyqDxylOHHTpr1FpU7coSHTlji448rfTlV4dbpwblmZOy2yNTqJGHlGYs5Ud14KTqjvEV6q2T1rqTVgCr1TwNMNe8D9K+1pdX9zf57s7ZPfJt+uSBifhlQKt0RD6Xaq2O1AQF5HxH2ldz9XepBbn3yIIiZXGPE1eMOHXqU1nkkv5S7mwx2XltEdS9pTeyj7KxXap/tIIc05pIaV0qxB3qEUr5TTn4kkW6bfgcnDL/AflUwu+ojpnN3vqd8II/oeNNsao0LxEpTEj/rszb3kr0umfEr5xiwpn0rntAq/4bRgoCozIJds8ypTeEu5w4SRAebY/s56qdEqd4E0Oi2yT1nH3mYWNE1Kvnujm31IjV2H4FPVHr+q3berj5Rd4cXfwucqIX0K42lj7qfOn5YrQCucsVn6v0MFviq/Uxoz5mZKGjvCKmyz715iIkqsdFYHy41BtFHfnrSV5HZnE65UtZ9VaUi5kGYWNeUrzkugeKCJt3d93qzd1wjKO3Qq9HWJOaaHFRwmxcLPMDpqXFrNTllX1ItF6u3I0iYycq2ykUdXO30PZbWMiQrF/EXDkb0duUvVuIUtxZGEGhz8SN3rL40KT5KRT8zZktOlQcfXKHbfBvG2yL7byD2xCvZV1kNDm1oC0YLMXegRxnsUe1jl4b1E36Phz8eYxA1y7pR7ST1pVdUHZLblL3p/+GrEDCQqf0umf9MZhc3CNZ5VRnPCOybO7RjJj6Lk7dsSgOPiMpcvHnI841XKM4Zuo7TfXGoKi7R1DkUIeHusfg98517/q8TE7V+lrl4stD7ALqxEXh8OSvPFbR/XwsVGK8kXfPAa3DcQV1tVv8r+NQfDSn+rx8uaX0XbNXHm9d9AtlRhb94fprRnPzmc3lHP15xvnotLdk5yf8Pl7rTcXGaN49ffRH9RxQvOZM5EHd0gm8OYu0vL5U8FzAJkPM/sP+dMn9bYTXOY0yOepQUucU5dRUDzc19Y1L2+jUZz4yaTplMhWp6TiiTTdit9geuwc/W7kHWPd2qPgupfiLWPv3ZwfQekzWQ2XRReagS20hZT/0KdqAnvX92TKJ8S6vuNvbgRY8C29SK97zfUT98a5vpzC28m+QiLX+kMVsUIhIlk/39LrqwQiKJ28iB6S+58vpLr3IYombZ2OPs0V1f2pZojl94r5Z0CvF9wwp+zRXp/KsHk8O8IZ9kOeHOPsNtQXSzuOe6+LcKuXcWuKcknaKHM6Mz6rvZpVx2TK4DPLc2ansF1Ocrc/zqnOj26VcxB30avywAj80pGyT9k8oEk5YdTZvVkFzJmUyT1gnTGUihR4wzgzy910d2Z5W8Dr1GP+DUvQDQ9JdkKVH+W9OJ2wJ0YukbnZIenHTsTqTer9CWvk9SvrfDT6hf1xUPr4jK59s5P+7weHm7Y3f3v7o8Z21z+/K/+fgffYz9gt2Hdb4x+xzoNZiB8DhD+zv7B/sn43fN/7Y+HPjL6Lre5ck5qes8K/x1/8CZxq/kw==</latexit> xk+1 = Prox⌧ ||·||1 (y ⌧A>(Axk y)) <latexit sha1_base64="F951Nm+rra9ve6UDYp3LMnIQF58=">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</latexit> Prox ||·||1 (x) = (sign(xi)(|xi | )+)i <latexit 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⌧ < 2 kAk <latexit 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k <latexit 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min x2Rd f(x) , 1 2 kAx yk2 + kxk1 <latexit 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x <latexit 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Prox ||·||1 <latexit 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f(xk) min f 6 Cn,d k <latexit sha1_base64="rD2uViTq2LCt//2OHuuLL1eGPaA=">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</latexit> Theorem: <latexit sha1_base64="VltScW0qieg47mBCbdXDqVZez6c=">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</latexit> Nesterov, FISTA accelerations: 1/k2 rates.
  8. 2⌧ 2 Forward-Backward splitting • ˆ k+1 = k ⌧X>

    rLy (X k ) • k+1 = ˆ k+1 ⌧rR (ˆ k+1 ) and its siblings: FISTA, FISTA with restarts, variab metric/quasi-Newton proximal methods. Forward-Backward <latexit sha1_base64="iaP8TP8Hzy0Jg9H0z5MLH35sX2Y=">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</latexit> xk+1 = Prox⌧ ||·||1 (y ⌧A>(Axk y)) <latexit sha1_base64="F951Nm+rra9ve6UDYp3LMnIQF58=">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</latexit> Prox ||·||1 (x) = (sign(xi)(|xi | )+)i <latexit 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⌧ < 2 kAk <latexit 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k <latexit 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min x2Rd f(x) , 1 2 kAx yk2 + kxk1 <latexit 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x <latexit 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Prox ||·||1 <latexit 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f(xk) min f 6 C k 4 4+dim <latexit 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(deconvolution + min-separation) <latexit 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Grid-free rates [L´ eger, Chizat]: <latexit sha1_base64="oORH+79GGWu2NX9Kh4QXoFA0ncM=">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</latexit> f(xk) min f 6 Cn,d k <latexit sha1_base64="rD2uViTq2LCt//2OHuuLL1eGPaA=">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</latexit> Theorem: <latexit sha1_base64="VltScW0qieg47mBCbdXDqVZez6c=">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</latexit> Nesterov, FISTA accelerations: 1/k2 rates.
  9. 1 2 2 Quadratic variational formulation: k k1 = inf⌘>0

    1 2 P i ⌘ 1 i | i | 2 + 1 2 P i ⌘ i . 7 / 49 <latexit 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“⌘-trick” Iterative Reweighted Least Squares <latexit 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|x| = inf ⌘>0 1 2 x2 ⌘ + 1 2 ⌘ <latexit 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⌘? = |x|
  10. 1 2 2 Quadratic variational formulation: k k1 = inf⌘>0

    1 2 P i ⌘ 1 i | i | 2 + 1 2 P i ⌘ i . 7 / 49 <latexit 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“⌘-trick” Iterative Reweighted Least Squares <latexit sha1_base64="snzG/SUNhxJOSDZedYIkBqAlzNM=">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</latexit> |x| = inf ⌘>0 1 2 x2 ⌘ + 1 2 ⌘ <latexit sha1_base64="SaxMCG/AIDgBrgxMVRkSten/UyU=">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</latexit> min x2Rd 1 2 kAx yk2 + kxk1 <latexit sha1_base64="lLsRnvUWJkY/RQ0TaBM4L4cAAjc=">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</latexit> Jointly convex <latexit 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over <latexit 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parameterization <latexit 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min x2Rd,⌘2Rd + 1 2 ||Ax y||2 + 1 2 X i x2 i ⌘i + ⌘i <latexit 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⌘? = |x|
  11. 1 2 2 Quadratic variational formulation: k k1 = inf⌘>0

    1 2 P i ⌘ 1 i | i | 2 + 1 2 P i ⌘ i . 7 / 49 <latexit 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“⌘-trick” Iterative Reweighted Least Squares <latexit sha1_base64="snzG/SUNhxJOSDZedYIkBqAlzNM=">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</latexit> |x| = inf ⌘>0 1 2 x2 ⌘ + 1 2 ⌘ <latexit sha1_base64="SaxMCG/AIDgBrgxMVRkSten/UyU=">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</latexit> min x2Rd 1 2 kAx yk2 + kxk1 <latexit sha1_base64="lLsRnvUWJkY/RQ0TaBM4L4cAAjc=">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</latexit> Jointly convex <latexit 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over <latexit 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parameterization <latexit 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min x2Rd,⌘2Rd + 1 2 ||Ax y||2 + 1 2 X i x2 i ⌘i + ⌘i <latexit 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Minimization on ⌘: <latexit sha1_base64="+2GPREQpEwIVrYJm4P1duouGq8A=">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</latexit> Minimization on x: <latexit sha1_base64="XoMHG/upk4SQvsnTOC9fMQMDdXI=">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</latexit> ⌘ |x| <latexit 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x (A>A + diag(⌘ 1)) 1A>y <latexit 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⌘? = |x|
  12. 1 2 2 Quadratic variational formulation: k k1 = inf⌘>0

    1 2 P i ⌘ 1 i | i | 2 + 1 2 P i ⌘ i . 7 / 49 <latexit 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“⌘-trick” Iterative Reweighted Least Squares <latexit sha1_base64="snzG/SUNhxJOSDZedYIkBqAlzNM=">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</latexit> |x| = inf ⌘>0 1 2 x2 ⌘ + 1 2 ⌘ <latexit sha1_base64="SaxMCG/AIDgBrgxMVRkSten/UyU=">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</latexit> min x2Rd 1 2 kAx yk2 + kxk1 <latexit sha1_base64="lLsRnvUWJkY/RQ0TaBM4L4cAAjc=">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</latexit> Jointly convex <latexit 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over <latexit 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parameterization <latexit 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min x2Rd,⌘2Rd + 1 2 ||Ax y||2 + 1 2 X i x2 i ⌘i + ⌘i <latexit 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Minimization on ⌘: <latexit sha1_base64="+2GPREQpEwIVrYJm4P1duouGq8A=">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</latexit> Minimization on x: <latexit sha1_base64="XoMHG/upk4SQvsnTOC9fMQMDdXI=">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</latexit> ⌘ |x| <latexit 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x (A>A + diag(⌘ 1)) 1A>y <latexit sha1_base64="i/Ola8a7r4H3a3v882xa+1W4QCI=">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</latexit> Problem: does not converge (F non-smooth). <latexit 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Regularisation: <latexit 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Minimization on ⌘: <latexit 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⌘? = |x|
  13. Variational Representation <latexit sha1_base64="LvhqKSr3hik5zgcAuhWUDO43Vis=">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</latexit> convex <latexit 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non-smooth <latexit 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    smooth <latexit sha1_base64="wUonO5puT+guKFuVkv+9v7DNgFg=">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</latexit> non-convex <latexit sha1_base64="7xh8rA8zANqdhqPchx9bfdGk53k=">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</latexit> |x| = min uv=x u2 + v2 2 <latexit sha1_base64="sYSTv3M6+H+nMT9S9CDXT7t+qxY=">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</latexit> u? = sign(x)v? = p |x| <latexit sha1_base64="snzG/SUNhxJOSDZedYIkBqAlzNM=">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</latexit> |x| = inf ⌘>0 1 2 x2 ⌘ + 1 2 ⌘ <latexit 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⌘? = |x| <latexit 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u , p ⌘ <latexit 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v , x/ p ⌘
  14. Variational Representation <latexit sha1_base64="LvhqKSr3hik5zgcAuhWUDO43Vis=">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</latexit> convex <latexit 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non-smooth <latexit 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    smooth <latexit sha1_base64="wUonO5puT+guKFuVkv+9v7DNgFg=">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</latexit> non-convex <latexit sha1_base64="7xh8rA8zANqdhqPchx9bfdGk53k=">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</latexit> |x| = min uv=x u2 + v2 2 <latexit sha1_base64="sYSTv3M6+H+nMT9S9CDXT7t+qxY=">AABC9XictVxLcxvHER45L0t5yckxl01opaQUzVCyHNvlcpXFhyhalEQJICVbkFR4LCFIIBbCAiAlCL8hvyC3VK455Rr/juQXJKf8hfRjZmcWmN2eZRRugZydna+7p3emp7tnwNaw30vH6+v/OPfe977/gx/+6P3zF378k5/+7OcXP/jFYZpMRu34oJ30k9GjVjON+71BfDDujfvxo+Eobh63+vHD1stNfP5wGo/SXjKoj18P4yfHze6gd9RrN8dQ9ezilcbkaSMdN0fRl1Ej7XUHl0+vRI2pU/dqNJ69PX07f3ZxZX1tnX6i5cJVXVhR+mc/+SD6p2qojkpUW03UsYrVQI2h3FdNlcL1WF1V62oIdU/UDOpGUOrR81jN1QXATqBVDC2aUPsSfnfh7rGuHcA90kwJ3QYuffiMABmpS4BJoN0IysgtoucTooy1RbRnRBNlew1/W5rWMdSO1XOolXCmZSgO+zJWR+oz6kMP+jSkGuxdW1OZkFZQ8sjp1RgoDKEOyx14PoJym5BGzxFhUuo76rZJz/9FLbEW79u67UT9m6S8BFekarr3SUahqaZEP6K3OYFnLE8fOHeBQqz7iKUT0vUx9X4A7WdQfxeuOZWMTlpwzah2XorchMuH3BSRO3D5kDsicg8uH3JPRO7D5UPuayRiR6RzP74Glw9fEznfh8uHvC8iH8DlQz4QkYdw+ZCHIvJbuHzIb0XkTbh8yJsi8jZcPuRtEVmHy4esi8gDuHzIAxG5DZcPua2RxTN1BFdCdHrCrLwB5TwPtBR9qLkhyrdB1tGH3QiY0+0CrDyrt+CvH7sVoNO4ALsdMO6OCrDyyNsBG+nHyrboFq0mPuwtEbsLI8CP3RWxX6sXBdivA2baywKsPNf2oJ0fK1vfO3Dnx94RsXeh5MfKa9Q9qPFj7wWsGMMC7L6Iva9eFWBDrP6oACvb/RrYFT9WXqfq0N6PDbGmkwKsbE8PwYPxY+XV6iHU+rEPRewjdVqAfSRivwHr7sd+E7DCvinAmjX2Aq0gXfJHYpixZdSa2azE0hCoNQX+/Wxt6ZNv3IJ6CdPNMF3CHIuInQyxE4jYyxB7wXKlmR1Nyd+VudQyRC0Q0crWJiyNxfadrD2W+gGIrQyxtYAo80jxXZu+TMm7MDUScpytXFgK6VOS2W8sxXo8lFteg7iXQ/DYfk4jf5WiJYygUFNl1J5nazwjI7ovQ5xQ9GZ6aXjIuHFmFVzUqYhqeVAtEfXag3otoiYe1ERETT2oqYiyM9/FNQJGgNU/vosZ3fEIYB+5+IrAK7gBq84tmKMRjJ998AIfUM09+Fuj2Fu6yiTDaB7XScxyPMlZ4hGUZmoF6m1UuEXxdZ9mWAyScct7OsbHO8xtzPScYys8z1byKMuYhNPpkTzdjA56ixHNp2p0blPNnLw7LlXD38rmvSlVw2+TxufkxXOpGn6spR+fQfa6xtbPgK3BbBpq7dtyVRqcf2EapnyBVl20uPhWj/WYQXqnFenv6jeze4b3skkl1o8tV6OROv1Lc/2rQsPqOXX0XI0Kek/s9ZpSVLknAx332nJVGRJaRQdaDntX9c1gm45+M6ZcjcY+eFybFHPPnHLV0TvMemPL1WgcKs57zsmTN+VqNLp0z/qw5Wo0MNvS1HG+LVe17KgBjp1tuapVH1AWGHNAPOa5xnpFI/KTJppaj/yD8myN6/Mvr2OYs3maxQjllKxvW0ynla1l5RIZfyEGqzauKAf6FxPHB8vTmKlrYnzFMoxz6/syHbvGo+b3QIsRzH7eA5By5n2Q0OQk0Hr3geJVMerK98zgrok4HCVHC6iGrh2L3qLly1mjfN0zqpXiMttbq8cG2euUxt6QfMI90qykh73CN1xEUdLQXk5DMr0qunuj52te++sibriAGGYjrU07QryTVh6n+rRec3R8Se/yjOHiPR87fjHbfKStDcY8CdkilKWMp9vO5JHcOlxXV5XNcfOziN4o2qspWY0e7UilYhRqssXsjc/o3tI+oD055ME02vAeI01lqHjXDLPomE+PyKK69lbijfoyGToup2R1jT0uR3cddNeDrh7jbMKKcRdKdYgZDuCuHhDlXMh0lZDGR+qjbHc0oTdYHtH3cxbS0GB7E+csZFmU/TxH5QTQOBo4Sg+nsUjH4BtLlOSo3yePjV3zlv8S7dya/e0mjfHi0VyciekQ12vENaJZw7u6fLfIgSWYeZ9cI/+1vJfIrwpHtKES16cOZ9bLgHb8Y4pgh+QZ92m2SbMj39rNTy0+MZz2ldk7x93shCxkRPYvgvUpoTEZ0cc9O2B20Nki9MlGhtidXubd+HydnjjGrB/XU3yqwY63mGzZhPgbuu7sSmkscsTA68B8YWwbneyRLxgT15G27nZul68+iLTnJNxRwhTtWLlM/K/Qb/Mx42RlaUSghvENpNrW+d5HQjEL6qhJq3y5DTJtXSk/zGR4qqW265+V6cOcZFsUcaE8uFp3gHOb7pkXjpIRyZ0uteF1tCybi5SHC3rE3h5RFM92v6tXYJR7lVbJFZpzDRolXRgF4yyKMG2lLPIi33JeeephtNP/C3Wr67zWkGKkbAaXNSTl92OK1lwp+zCqefy+pNnk1/pooVU5nwGNxWNnLr+F2l/DbyO3uQ+j08pZhQ0aA0zB3lmNcE201CKM10aOlxmZhpa9t/zsmDSt3JqzxNds3WyMPa1MZZ9GzanOWpjyWWi8cGi8CNRhnfYarRZNvbFEz8TYoq53K0P5VeFWr0B5IlKWPTKD6gVI6cZSYVQ7IlU5xjeoNyKtdZFWE2aruxvgzvkQpH+uL87ut9nqHqmb5Nu0yQPj+KVDs7RHPpepLY/UmAJyvq7tqzv7G1SD3FtkQZEyn+PEGcO7Tm265pmkv9UrW0J23loEc27pRLcxNrZB5Y+XkMc0J1KalwZxnVrEWn5XjmjBIq05PkdEmf8m+VTsd5THzG5r+06inD9h402eVZYXRwoD0r+Uedtdil53nfg1ophwor3rFtCq/oaRAmNMJsHvWab0hnCV450E9mhbZD+X7RTv4g0cidZI6pn6MsDGcNRrx7o7tkyPTd9+By1R6/at+1rI/PrBHCV+Z9nRa9Kqdqx91NnC/dloNfUql78v08Nkga/Vx4TauJGFjfLymIb6IpgLS1SNC2NCuFTrRRX5q0leRWbenQqlbFobyvlMA9uY5xQvSedAEeHz7i57vbkrQj9aS/RahHWpcY1ECbNxic4PuJYWs1Lnl9Yhrj1fuhr1nZWoaKUw1N3VwtpvtpAxWb++knI23NqVvZGLUuQsDFNoKz7RWxQfujS/gAt/R8oXHRqOIbnDGvi3N9Sm2n4HpyFe6TJnNCOqQVvQWYi9m7qf+RblOnrlUHfph3AI59EDXUvS92glrSo7U5Yld6mH0z8hKzBSsSi9bVm9Dy4XuSfLnKr0p0eWTe5NT5nv4lTti+EQ0pM8l3A+vK8h9eJIme80VeuDoS73IM+hCg9zjiHsndvW1Xm5nMr1tcwllAevAmbHxeBw5684VrHtQizUyHkj754DWoejEupmtfhf+2H4WE7VeYVyS+m7Zi8C3jq3i3VGFv3h6nPGcgsZzcUcw3kmWe+st+Tnx35fVOlNJU5v3j199EftGDC8ZorzoLJ0jHdHkZU3lAruC/hkSNR/1Hfn5G8jvMpoFMlRhZLZpyimZlrI1Mw3Ln29M89CZLJ0imTKU7NxRI1OxG6qXXUTPpuZB1j1dCh/l5L/Itb//dkO1B6R9TBZdM4cNKgupuyH3UXr0L09P1skMZ7l5bO9dajBvfA9qsVzvnepPZ71ref6VvwNEp7rd1SiOrmIZHF3z86rFvQgv/PGOSDzPd+IztJzFotPnh0H7C2a81OLEs3oiXyyoFWIbzlStmmsDvVePe4c4An7ZpYfitTvqa6p7TyuuRLn/ULO+wucU9JOnsOp86z8bFYRl02HSyfLnU11u4TibLufV54b3SrkwmfQy/HdEnzXkbJG2n9JkfBIlWfzJiU0J1omd4d1oEwmkvWAcWYze9/lke20hNc0oP+3C9G3HUl3QJYW5b8j2mEbEb2+1s02Sc8nHcszqbdKpDXfo5TGLn8fgvMS5n8NPKa8VIuswLpapc+a+gxaToJm4lSgibRWNeW51qt8MsKcsCyj+0km7Sdq7qCAPv2fh8/pJ+LCp9d14fOr2f95OLy2dvUPax/fv77y1Yb+jw/vq1+p36jLYO0+VV+BXvfVAfD/o/qb+rv6buNk408bf974Czd975zG/FLlfjb++l+a/OSs</latexit> u? = sign(x)v? = p |x| <latexit sha1_base64="snzG/SUNhxJOSDZedYIkBqAlzNM=">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</latexit> |x| = inf ⌘>0 1 2 x2 ⌘ + 1 2 ⌘ <latexit 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⌘? = |x| <latexit 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Alternate form: <latexit sha1_base64="npZo7/vkol/v8V2t/Lnba4nbquk=">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</latexit> ! not amenable to alternate minimization. <latexit sha1_base64="ykevw/cChS0JUUVK7j+Mz5LLXmM=">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</latexit> |x| = min u2 v2=x u2 + v2 <latexit 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u , p ⌘ <latexit 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v , x/ p ⌘
  15. Variational Representation <latexit sha1_base64="LvhqKSr3hik5zgcAuhWUDO43Vis=">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</latexit> convex <latexit 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non-smooth <latexit 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    smooth <latexit sha1_base64="wUonO5puT+guKFuVkv+9v7DNgFg=">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</latexit> non-convex <latexit sha1_base64="7xh8rA8zANqdhqPchx9bfdGk53k=">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</latexit> |x| = min uv=x u2 + v2 2 <latexit sha1_base64="sYSTv3M6+H+nMT9S9CDXT7t+qxY=">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</latexit> u? = sign(x)v? = p |x| <latexit sha1_base64="snzG/SUNhxJOSDZedYIkBqAlzNM=">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</latexit> |x| = inf ⌘>0 1 2 x2 ⌘ + 1 2 ⌘ <latexit 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⌘? = |x| <latexit 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Alternate form: <latexit sha1_base64="npZo7/vkol/v8V2t/Lnba4nbquk=">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</latexit> ! not amenable to alternate minimization. <latexit sha1_base64="ykevw/cChS0JUUVK7j+Mz5LLXmM=">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</latexit> |x| = min u2 v2=x u2 + v2 <latexit sha1_base64="SaxMCG/AIDgBrgxMVRkSten/UyU=">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</latexit> min x2Rd 1 2 kAx yk2 + kxk1 <latexit 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min u,v 1 kA(u v) yk2 + kuk2 2 + kvk2 2 <latexit sha1_base64="VwU4bjbjAw/6TPQPDVxdaVZJlKI=">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</latexit> x = u v <latexit 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, (uivi)d i=1 <latexit 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u , p ⌘ <latexit 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v , x/ p ⌘
  16. Variational Representation <latexit sha1_base64="LvhqKSr3hik5zgcAuhWUDO43Vis=">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</latexit> convex <latexit 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non-smooth <latexit 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    smooth <latexit sha1_base64="wUonO5puT+guKFuVkv+9v7DNgFg=">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</latexit> non-convex <latexit sha1_base64="7xh8rA8zANqdhqPchx9bfdGk53k=">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</latexit> |x| = min uv=x u2 + v2 2 <latexit sha1_base64="sYSTv3M6+H+nMT9S9CDXT7t+qxY=">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</latexit> u? = sign(x)v? = p |x| <latexit sha1_base64="snzG/SUNhxJOSDZedYIkBqAlzNM=">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</latexit> |x| = inf ⌘>0 1 2 x2 ⌘ + 1 2 ⌘ <latexit 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⌘? = |x| <latexit 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Alternate form: <latexit sha1_base64="npZo7/vkol/v8V2t/Lnba4nbquk=">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</latexit> ! not amenable to alternate minimization. <latexit sha1_base64="ykevw/cChS0JUUVK7j+Mz5LLXmM=">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</latexit> |x| = min u2 v2=x u2 + v2 <latexit sha1_base64="SaxMCG/AIDgBrgxMVRkSten/UyU=">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</latexit> min x2Rd 1 2 kAx yk2 + kxk1 <latexit 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min u,v 1 kA(u v) yk2 + kuk2 2 + kvk2 2 <latexit sha1_base64="VwU4bjbjAw/6TPQPDVxdaVZJlKI=">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</latexit> x = u v <latexit sha1_base64="dYUkH7hnSlfCBXN1uYbi20DFxq0=">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</latexit> , (uivi)d i=1 <latexit sha1_base64="my0E+vgeJWmKlzNLs9Rdhsorp4U=">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</latexit> (Sherman–Morrison formula) <latexit sha1_base64="83eKHl+qCDf6euBpfa9tc5tvDvM=">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</latexit> Alternating mimization: <latexit sha1_base64="+8lThvl9GuWuxQI5dWUydgORXrw=">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</latexit> Empirical finding: works better than IRLS (despite non-convex). <latexit 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u (diag(v)A>Adiag(v) + Idd) 1(v A>y) <latexit 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= v A>(Adiag(v2)A> + Idn) 1y <latexit 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v (diag(u)A>Adiag(u) + Idd) 1(u A>y)u <latexit 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u , p ⌘ <latexit 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v , x/ p ⌘
  17. Lasso illustration Evolution of 10 coe cients via ISTA and

    gradien ISTA Noncvx- ISTA : k+1 = SoftThresh k ⌧X > Noncvx-Pro: k+1 = k ⌧rf ( k ). Lasso illustration Evolution of 10 coe cients via ISTA and gradient descent of f . ISTA Noncvx-Pro ISTA : k+1 = SoftThresh k ⌧X >(X k y), ⌧ Noncvx-Pro: k+1 = k ⌧rf ( k ). 12 / 49 . Quadratic For Lasso Numerical
  18. VarPro General Idea <latexit 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Envelope theorem: <latexit sha1_base64="SYQDeQ1yH+gNfM+oH9y/AsAnH/8=">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</latexit> Variational

    Projection: Gene Golub Victor Pereyra <latexit sha1_base64="T67g3m5D/nIqeo47Q/RS6LTWYlE=">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</latexit> f(v) , F(u?(v), v) = min u F(u, v) <latexit sha1_base64="giqx4/bBN97akGvg1+7OscAW2Xs=">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</latexit> rf(v) = rvF(u?(v), v)
  19. VarPro General Idea <latexit 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Envelope theorem: <latexit sha1_base64="SYQDeQ1yH+gNfM+oH9y/AsAnH/8=">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</latexit> Variational

    Projection: Gene Golub Victor Pereyra <latexit 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f(v) , F(u?(v), v) = min u F(u, v) <latexit sha1_base64="giqx4/bBN97akGvg1+7OscAW2Xs=">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</latexit> rf(v) = rvF(u?(v), v) <latexit 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Implicit di↵erentiation: <latexit sha1_base64="i9gJ4a40lkR4zipG4FoVdDE02ro=">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</latexit> @u?(v) = @2 u F(u?, v) 1@2 u,v F(u?, v) <latexit 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@2f(v) = @2 v F(u?, v) @2 u,v F(u?, v)@2 u F(u?, v) 1@2 u,v F(u?, v)
  20. VarPro General Idea <latexit 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Envelope theorem: <latexit sha1_base64="SYQDeQ1yH+gNfM+oH9y/AsAnH/8=">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</latexit> Variational

    Projection: Gene Golub Victor Pereyra <latexit 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f(v) , F(u?(v), v) = min u F(u, v) <latexit sha1_base64="giqx4/bBN97akGvg1+7OscAW2Xs=">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</latexit> rf(v) = rvF(u?(v), v) <latexit 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Implicit di↵erentiation: <latexit sha1_base64="i9gJ4a40lkR4zipG4FoVdDE02ro=">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</latexit> @u?(v) = @2 u F(u?, v) 1@2 u,v F(u?, v) <latexit 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@2f(v) = @2 v F(u?, v) @2 u,v F(u?, v)@2 u F(u?, v) 1@2 u,v F(u?, v) <latexit 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=) <latexit 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@F 1 = ✓ @2 u F @2 u,v F @2 u,v F @2 v F ◆ 1 = ✓ · · · · · · · · · [@2 v f] 1 ◆ <latexit sha1_base64="tSKv0HuS2kfO5eAwU+AMxohUOqY=">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</latexit> @2 v f is better conditionned than @2 u,v F
  21. Lasso VarPro <latexit sha1_base64="SaxMCG/AIDgBrgxMVRkSten/UyU=">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</latexit> min x2Rd 1 2 kAx yk2

    + kxk1 <latexit sha1_base64="VwU4bjbjAw/6TPQPDVxdaVZJlKI=">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</latexit> x = u v <latexit sha1_base64="A1ZAtxlBHppeP9b83aQLRqnZxYA=">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</latexit> min u,v F(u, v) , 1 kA(u v) yk2 + kuk2 2 + kvk2 2 <latexit sha1_base64="RQJ60M8EfK4pJ9HxTAIUZXby20s=">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</latexit> min v f(v) , min u 1 kA(u v) yk2 + kuk2 2 + kvk2 2
  22. Lasso VarPro <latexit sha1_base64="SaxMCG/AIDgBrgxMVRkSten/UyU=">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</latexit> min x2Rd 1 2 kAx yk2

    + kxk1 Lasso illustration Evolution of 10 coe cients via ISTA ISTA : k+1 = SoftT Lasso illustration Evolution of 10 coe cients via ISTA and gradient descent <latexit 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Forward-backward <latexit 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Lasso VarPro <latexit 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Descend <latexit sha1_base64="VwU4bjbjAw/6TPQPDVxdaVZJlKI=">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</latexit> x = u v <latexit sha1_base64="A1ZAtxlBHppeP9b83aQLRqnZxYA=">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</latexit> min u,v F(u, v) , 1 kA(u v) yk2 + kuk2 2 + kvk2 2 <latexit sha1_base64="RQJ60M8EfK4pJ9HxTAIUZXby20s=">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</latexit> min v f(v) , min u 1 kA(u v) yk2 + kuk2 2 + kvk2 2 <latexit 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Proposition: f is smooth and <latexit sha1_base64="0J9DVzW8My87+/opFWIJ+xpB+3g=">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</latexit> Envelope theorem: <latexit sha1_base64="AnwYxDOZfN2O18xp53N3zZMHoBc=">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</latexit> u?(v) , argminu F(u, v) <latexit sha1_base64="3D9R8zXUx54CQI4IoCxqXDCym5s=">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</latexit> = v A>(Adiag(v2)A> + Idn) 1y <latexit sha1_base64="UIo+BlLZbS+w+U5uLc9U+0P0w58=">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</latexit> rf(v) = rvF(u?(v), v) <latexit 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= 1 u? A>(A(u? v) y) + v
  23. Lasso VarPro <latexit sha1_base64="SaxMCG/AIDgBrgxMVRkSten/UyU=">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</latexit> min x2Rd 1 2 kAx yk2

    + kxk1 Lasso illustration Evolution of 10 coe cients via ISTA ISTA : k+1 = SoftT Lasso illustration Evolution of 10 coe cients via ISTA and gradient descent <latexit 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Forward-backward <latexit 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Lasso VarPro <latexit 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Descend <latexit sha1_base64="VwU4bjbjAw/6TPQPDVxdaVZJlKI=">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</latexit> x = u v <latexit sha1_base64="A1ZAtxlBHppeP9b83aQLRqnZxYA=">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</latexit> min u,v F(u, v) , 1 kA(u v) yk2 + kuk2 2 + kvk2 2 <latexit sha1_base64="RQJ60M8EfK4pJ9HxTAIUZXby20s=">AABDPHictVxLcxy3EYZsJ7GYl5wcc0FCKyXFMkPScmyXK1UWH6Jo0RKlXUqyNRJrdne4Wmm4s9qXHqv9a8mfyCWVaw5JpVK55ZBT+gEMMLuYAYZROLUkBoOvu9EDNLobWLYGaW80Xl//87l33n3ve9//wfvnV374ox//5KcXPvjZvVE2GbaTo3aWZsMHrXiUpL1+cjTujdPkwWCYxKetNLnferaNz+9Pk+Gol/Wb41eD5NFp3O33TnrteAxVxxf60WmvfxxN5cmlaHpZRuNhL+530+S5pAezaDKXMjoZxu3ZxnwWpUC5E8+jN/LapWgio6yTjSUCP5avZPTm8eaKhJ+PoBhNojfHm483+Waqbo4vrK6vrdOPXC5sqMKqUD+H2QfyLyISHZGJtpiIU5GIvhhDORWxGMH1UGyIdTGAukdiBnVDKPXoeSLmYgWwE2iVQIsYap/B7y7cPVS1fbhHmiNCt4FLCp8hIKW4CJgM2g2hjNwkPZ8QZawtoz0jmijbK/jbUrROoXYsnkCtD6dbhuKwL2NxIj6nPvSgTwOqwd61FZUJaQUll1avxkBhAHVY7sDzIZTbhNR6loQZUd9RtzE9/xu1xFq8b6u2E/F3kvIiXFI0VO+znEIspkRf0tucwDOWJwXOXaCQqD5i6QXp+pR634f2M6i/BdecSlonLbhmVDuvRG7D5UJue5F7cLmQe17kAVwu5IEXeQiXC3mokIgdks7d+AZcLnzDy/kOXC7kHS/yLlwu5F0v8h5cLuQ9L/I7uFzI77zI63C5kNe9yJtwuZA3vcgmXC5k04s8gsuFPPIid+FyIXcVsnymDuHKiE7PMyuvQbnIAy1FCjXXvPJtkXV0YbcC5nS7BOuf1Tvw143dCdBpUoLdDRh3JyVY/8jbAxvpxvpt0Q1aTVzYG17sPowAN3bfi/1aPC3Bfh0w056VYP1z7QDaubF+6/sN3Lmx33ixt6DkxvrXqNtQ48beDlgxBiXYQy/2jnhegg2x+sMSrN/uN8CuuLH+daoJ7d3YEGs6KcH67ek98GDcWP9qdR9q3dj7XuwD8bIE+8CL/Rasuxv7bcAK+7oEq9fYFVpBuuSPJDBjq6jF+azE0gCoxR7+ab62pOQbt6Deh+nmmC5hTr2IvRyxF4g4yBEHwXKNcjs6In/Xz6WRIxqBiFa+NmFp7G3fydtjKQ1A7OSInQVElUeK71r3ZUreha7xIcf5yoWlkD5luf3GUqLGQ7Xl1YjbBQSP7Sc08q9QtIQRFGqqitqTfI1npKT7KsQLit50LzUPP26cWwUb9dKLajlQLS/qlQP1youaOFATL2rqQE29KDPzbVwUMAKM/vFdzOiORwD7yOWXBK/gGqw6N2COShg/h+AF3qWa2/C3QbG376qSDKN5XCcxy/GoYImHUJqJVag3UeEOxdcpzbAEJOOWt1WMj3eY25ipOcdWeJ6v5DLPmITT6ZE83ZwOeouS5lM9OjepZk7eHZfq4W/k816X6uF3SeNz8uK5VA8/VtKPzyB7U2GbZ8A2YDYNlPZNuS4Nzr8wDV1eoVUXLS6+1VM1ZpDey5r099Wb2T/De9mmEuvHlOvRGFn9GxX6V4eG0fPI0nM9Kug9sderS7J2T/oq7jXlujJktIr2lRzmru6bwTYd9WZ0uR6NQ/C4tinmnlnluqN3kPfGlOvRuCc47zknT16X69Ho0j3rw5Tr0cBsS6zifFOua9lRAxw7m3Jdq96nLDDmgHjMc43xiobkJ00UtR75B9XZGtvnX17HMGfzOI8RqikZ37acTitfy6ol0v5CAlZtXFMO9C8mlg9WpDETm974imUYF9b3ZTpmjUfNH4AWJcx+3gPw5cxTkFDnJNB6p0Bxwxt1FXumcZteHI6SkwVUpGrHXm/R8OWsUbHumGp9cZnprdFjRPZ6RGNvQD7hAWnWp4eD0jdcRtGnoYOChvz06ujutZqvRe2ve3GDBcQgH2lt2hHinbTqONWl9Yal44tql2cMF+/5mPGL2eYTZW0w5snIFqEsVTztdjqPZNfhunpFmBw3P5P0RtFeTclq9GhHauSNQnW2mL3xGd0b2ke0J4c8mEYb3qNUVAaCd80wi475dEkW1ba3Pt6oL52h4/KIrK62x9XoroXuOtD1Y5xtWDFuQakJMcMR3DUDopyVXFcZaXwoPs53RzN6g9URfVqwkJoG25ukYCGrouwnBSovAI2jgaP0cBqLdDQ+WqLkj/pd8pjYtWj5L9LOrd7fjmmMl4/m8kxMh7huEldJs4Z3dflukQNLMHM+2ST/tbqXyK8OR7ShPq6PLc6slz7t+CcUwQ7IM05ptvlmR7G1nZ9afKI5HQq9d4672RlZSEn2T8L6lNGYlPSxzw7oHXS2CCnZyBC708u9G5ev0/OOMePH9QSfajDjLSFbNiH+mq49u0Y0Fjli4HVgvjC2tU4OyBdMiOtQWXczt6tXH0SacxL2KGGKZqxcIv6X6bf+6HGyujQiUMP4BkbK1rneR0YxC+ooplW+2gbptraUH+YyPFZSm/XPyPRhQbIdirhQHlytO8C5TffMC0fJkOQeLbXhdbQqm4uUBwt6xN6eUBTPdr+rVmCU+wqtkqs05yIaJV0YBeM8itBtfVnkRb7VvIrUw2iP/i/Uja6LWkOKUpgMLmvIl99PKFqzpUxhVPP4fUazya314UKraj59Goun1lx+A7W/hN9abn0fRqdVsApbNAaYgrkzGuEaudQijNdWgZcemZqWuTf8zJjUreyas8TXbN1MjD2tTeWQRs1LlbXQ5bPQeGrReBqowybtNRot6nptiY69sUVT7VaG8qvDrVmD8sRL2e+RaVQvQEo7lgqj2vFS9cf4GvXaS2vdSyuG2WrvBthzPgTpnuuLs/tNvrpLcZ18mzZ5YBy/dGiW9sjn0rXVkRpTQM5XlX21Z39ENci9RRYUKfM5TpwxvOvUpmueS/prtbJlZOeNRdDnll6oNtrGRlT+ZAl5SnNiRPNSI65Si0TJb8shFyzSmuVzSMr8x+RTsd9RHTPbrc07kQV/wsSbPKsML44U+qR/X+Ztfyl63bfiV0kx4UR51y2gVf8NIwXG6EyC27Mc0RvCVY53EtijbZH9XLZTvIvXtyRaI6ln4vcBNoajXjPW7bGle6z79htoiVo3b93Vws8vDebo43eWHb2YVrVT5aPOFu7PRitWq1zxvkoPkwW+Rh8TamNHFibKK2Ii8WUwF5aoHhfGhHCp14s68teTvI7MvDsVSlm31pSLmQa2MU8oXvKdA0WEy7u75PTmLnv60Vqi1yKsTY1rfJQwG5ep/IBtaTErdX5pHeLa85WrUWqtRGUrhaZurxbGfrOFTMj6pcKXs+HWtuxRIUrxZ2GYQlvwid6y+NCm+SVc+FsKV3SoOYbkDhvg314T22L3LZyGeK7KnNGUVIO2oLMQe8eqn8UW1Tp6blG36YdwCOfRA137pO/RSlpXdqbsl9ymHk7/BVmBoUi80puW9ftgc/H3ZJlTnf70yLL5e9MT+rs4dfuiOYT0pMglnA/va/h6cSL0d5rq9UFT9/egyKEOD32OIeydm9b1edmcqvW1zCWUB68CesdF43DnrzxWMe1CLNTQeiNvnwNah5MK6nq1+F/7ofkYTvV5hXIb0XfNnga8dW6XqIws+sP154zhFjKayzmG88zy3hlvyc2P/T5Z601lVm/ePn30R80Y0LxmgvOgfukYb48iI28oFdwXcMmQiX+JP57zfxvheU6jTI46lPQ+RTk13cJPTX/j0tU7/SxEJkOnTKYiNRNHNOhE7LbYF9fhs517gHVPh/J3KfkvYt3fn+1A7QlZD51F58xBRHUJZT/MLlqH7s352TKJ8Swvn+1tQg3uhR9QLZ7zvUXt8axvs9C38m+Q8Fz/RmSiU4hIFnf3zLxqQQ+KO2+cA9Lf85V0lp6zWHzy7DRgb1Gfn1qUaEZP/CcLWqX4liVlm8bqQO3V484BnrCP8/yQFL+luljZeVxzfZwPSzkfLnAekXaKHF5az6rPZpVx2ba4dPLc2VS1yyjONvt51bnRnVIufAa9Gt+twHctKRuk/WcUCQ9FdTZvUkFzomSyd1j7QmciWQ8YZ8b5+66ObKcVvKYB/b9Zir5pSboHsrQo/y1ph21I9FKlm12Snk86VmdSb1RIq79H6f92Nn8jgjMT+r8NPKTMVIvswLq4Qp818Tm0nATNxamHJtK6oijPlWb9ZyP0Gcsqup/m0n4q5hYK6NN/eviCfiQXPruqCl9s5P/p4d7m2sbv1j65c3X1qy31Px/eF78QvxKXwN59Jr4CzR6KI+D/J/Gfc++ee2/rD1t/3frH1j+56TvnFObnovCz9e//AhQa+rk=</latexit> min v f(v) , min u 1 kA(u v) yk2 + kuk2 2 + kvk2 2 <latexit 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Proposition: f is smooth and <latexit sha1_base64="0J9DVzW8My87+/opFWIJ+xpB+3g=">AABB03ictVzddhu3EYbTv9j9s9vL3myruMfpcVxZ8Wma5vScyJIsK2Zs2aRkJ5Htw58VRXvJpbkkZZvRTU9v+wi9bR+jz9E3aK/6Cp0fYIElsTtY1TWOJCyIb2YwCwxmBqA742SQTdfX/3nhve9893vf/8H7Fy/98Ec//slPL1/52WGWzibd+KCbJunkSaedxclgFB9MB9MkfjKexO1hJ4kfd15u4eeP5/EkG6Sj1vTNOH46bPdHg+NBtz2FpueXr+yM5nGSjuNoehKnk3j4h+eX19ZvrNO/aLVyU1fWlP63n16JDtSR6qlUddVMDVWsRmoK9US1VQblG3VTrasxtD1VC2ibQG1An8fqTF0C7Ax6xdCjDa0v4Xcfnr7RrSN4RpoZobvAJYGfCSAjdRUwKfSbQB25RfT5jChjaxntBdFE2d7A346mNYTWqTqBVglneobicCxTdax+T2MYwJjG1IKj62oqM9IKSh45o5oChTG0Yb0Hn0+g3iWk0XNEmIzGjrpt0+f/op7Yis9d3Xem/k1SXoUSqaYefZpTaKs50Y/obc7gM5YnAc59oBDrMWLtlHQ9pNGPoP8C2u9DOaOa0UkHyoJazyqRW1B8yC0RuQvFh9wVkQ0oPmRDRO5D8SH3NRKxE9K5H9+E4sM3Rc4PofiQD0XkIyg+5CMReQjFhzwUkV9D8SG/FpF3oPiQd0TkPSg+5D0R2YLiQ7ZE5AEUH/JARO5A8SF3NLJ8pU6gpERnIKzKTagXeaClSKBlU5TvNllHH/Z2wJrulmDlVb0Nf/3Y7QCdxiXYnYB5d1yClWfeLthIP1a2RXdpN/Fh74rYPZgBfuyeiP1CvSjBfhGw0l6WYOW11oB+fqxsfb+EJz/2SxF7H2p+rLxHPYAWP/ZBwI4xLsHui9iH6lUJNsTqT0qwst1vgl3xY+V9qgX9/dgQazorwcr29BA8GD9W3q0eQ6sf+1jEPlGvS7BPROxXYN392K8Cdti3JVizx16iHaRP/kgMK7aKWjtflVgbA7W2wD/J95aEfOMOtEuYfo7pE2YoInZzxG4gopEjGsFyZbkdzcjflbk0c0QzENHJ9yasTcX+vbw/1pIAxHaO2F5CVHmk+K7NWObkXZgWCTnNdy6shYwpze031mI9H6otr0E8KCB4bp/QzL9O0RJGUKipKmon+R7PyIieqxCnFL2ZURoeMm6aWwUX9VpEdTyojoh640G9EVEzD2omouYe1FxE2ZXv4o4CZoDVP76LBT3xDGAfubxE4BVswq5zF9ZoBPNnH7zAR9TyAP42KfaWSpVkGM3jPolZjqcFSzyB2kKtQbuNCrcpvk5ohcUgGfd8oGN8fMLcxkKvObbCZ/lOHuUZk3A6A5Knn9NBbzGi9VSPzj1qOSPvjmv18HfzdW9q9fA7pPEz8uK5Vg8/1dJPzyF7S2Nb58A2YTWNtfZtvS4Nzr8wDVO/RLsuWlx8q0M9Z5De65r09/Sb2TvHe9miGuvH1uvRyJzxZYXx1aFh9Zw5eq5HBb0n9npNLao9kpGOe229rgwp7aIjLYd9qvtmsE9PvxlTr0djHzyuLYq5F0697uwd56Ox9Xo0DhXnPc/Ikzf1ejT69Mz6sPV6NDDb0tZxvq3XteyoAY6dbb2uVR9RFhhzQDznucV6RRPyk2aa2oD8g+psjevzr+5jmLN5lscI1ZSsb1tOp5PvZdUSGX8hBqs2rSkH+hczxwcr0lioDTG+Yhmmhf19lY7d41HzDdBiBKufzwCknHkCEpqcBFrvBCjeFKOu4sgMbkPE4Sw5XkId6dap6C1avpw1KrY9p1YpLrOjtXo8Inud0dwbk0/YIM1KemiUvuEyipKGGgUNyfTq6O6tXq9F7a+LuPESYpzPtC6dCPFJWnWc6tN609HxVX3KM4XCZz52/mK2+VhbG4x5UrJFKEsVT7efySO5bbivXlc2x82fRfRG0V7NyWoM6EQqE6NQky1mb3xBz5b2AZ3JIQ+m0YX3GGkqY8WnZphFx3x6RBbVtbcSb9SXydBxPSOra+xxNbrvoPsedP0YZwt2jPtQa0HMcABPrYAo51Kuq5Q0PlEf5aejKb3B6og+KVhIQ4PtTVywkFVR9kmByimgcTZwlB5OY5mOwR+tUJKjfp88NnYtWv6rdHJrzrfbNMfLZ3N5JqZHXDeIa0Srhk91+WmZA0uw8H6yQf5r9SiRXx2OaEMlrs8czqyXEZ34xxTBjskzTmi1Sauj2NvNTy1/YjjtK3N2jqfZKVnIiOxfBPtTSnMyoh/37oA5QWeLkJCNDLE7g9y78fk6A3GOWT9uoPhWg51vMdmyGfE3dN3VldFc5IiB94GzpbltdNIgXzAmrhNt3e3art59EGnvSbizhCnauXKN+H9Iv82PmSdrKzMCNYxvINO2zvc+UopZUEdt2uWrbZDp60r5QS7DMy213f+sTB8UJNumiAvlwd26B5y79My8cJZMSO5spQ/vo1XZXKQ8XtIjjvaYoni2+329A6Pc12mXXKM1d0SzpA+zYJpHEaavlEVe5lvNq0g9jHb2f6FudV3UGlKMlM3gsoak/H5M0ZorZQKzmufvS1pNfq1PlnpV8xnRXBw6a/lbaP0l/DZym+cwOp2CVbhNc4Ap2CerEW6JVnqE8bpd4GVmpqFlny0/OydNL7flPPE1WzcbY89rU9mnWfNaZy1M/Tw0Xjg0XgTqsEVnjVaLpt1YoudibNHSp5Wh/Opwa9WgPBMpyx6ZQQ0CpHRjqTCqPZGqHOMb1FuR1rpIqw2r1T0NcNd8CNK/1pdX97f57h6pO+TbdMkD4/ilR6t0QD6Xaa2O1JgCcr6l7au7+o+oBbl3yIIiZb7HiSuGT526VM5ySX+td7aU7Ly1CObe0qnuY2zsEdU/XkEOaU1ktC4N4hb1iLX8rhzRkkW64fgcEWX+2+RTsd9RHTO7ve07iQr+hI03eVVZXhwpjEj/UuZtbyV63XPi14hiwpn2rjtAq/4bRgqMMZkEv2eZ0RvCXY5PEtij7ZD9XLVTfIo3ciS6QVIv1B8DbAxHvXauu3PLjNiM7TfQE7Vu37qvh8wvCeYo8TvPiV6bdrWh9lEXS8/no9XWu1zxuUoPsyW+Vh8z6uNGFjbKK2KO1GfBXFiielwYE8Kl3ijqyF9P8joy8+lUKGXT21AuZhrYxpxQvCTdA0WEz7u75vXmPhTG0Vmh1yGsS41bJEqYjUt1fsC1tJiVuriyD3HrxcrdKHF2orKdwlB3dwtrv9lCxmT9EiXlbLi3K/tRIUqRszBMoav4Rm9ZfOjS/AwK/o6ULzo0HENyh03wbzfVltp5B7chXuk6ZzQjakFb0FuKvdt6nMUe1Tp65VB36YdwCOcxAF1L0g9oJ60rO1OWJXeph9M/JSswUbEove1ZfwwuF3kkq5zqjGdAlk0ezUCZ7+LUHYvhEDKSIpdwPnyuIY3iWJnvNNUbg6Euj6DIoQ4Pc48h7J3b3vV5uZyq9bXKJZQH7wLmxMXg8OSvPFax/UIs1MR5I++eA1qH4wrqZrf4X8dh+FhO9XmFcsvou2YvAt4694t1Rhb94fprxnILmc3lHMN5pvnorLfk58d+X1TrTaXOaN49ffRH7RwwvBaK86CydIx3Z5GVN5QKngv4ZEjVf9Q/LsjfRniV0yiTow4lc05RTs30kKmZb1z6Rmc+C5HJ0imTqUjNxhFNuhG7pfbUHfjZyj3AurdD+buU/Bex/u/P9qD1mKyHyaJz5uCI2mLKfthTtB492/uzZRLjXV6+29uCFjwLb1Ar3vO9T/3xrm+rMLbyb5DwWv9SpapXiEiWT/fsuurACIonb5wDMt/zjeguPWex+ObZMOBs0dyfWpZoQZ/INws6pfiOI2WX5upYn9XjyQHesG/n+aFI/Zba2trO454rcd4v5by/xDkj7RQ5vHY+q76bVcZly+HSy3Nnc90vpTjbnudV50a3S7nwHfRqfL8C33ekbJL2X1IkPFHV2bxZBc2Zlsk9YR0pk4lkPWCc2c7fd3VkO6/gNQ8Y/71S9D1H0l2QpUP574hO2CZEL9G62SHp+aZjdSb1boW0+nuU9L8bfEr/Iq58cktXPr2Z/+8Ghxs3bv7uxscPN9Y+v63/n4P31S/Ur9Q1WOOfqM+B2r46AA6n6q/qb+rvmwebi80/bf6Zu753QWN+rgr/Nv/yXyjDqBc=</latexit> Envelope theorem: <latexit sha1_base64="AnwYxDOZfN2O18xp53N3zZMHoBc=">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</latexit> u?(v) , argminu F(u, v) <latexit sha1_base64="3D9R8zXUx54CQI4IoCxqXDCym5s=">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</latexit> = v A>(Adiag(v2)A> + Idn) 1y <latexit sha1_base64="UIo+BlLZbS+w+U5uLc9U+0P0w58=">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</latexit> rf(v) = rvF(u?(v), v) <latexit 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= 1 u? A>(A(u? v) y) + v <latexit sha1_base64="S9P0xoBr58M73xUuxR7rEyLC4NQ=">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</latexit> Case = 0: <latexit sha1_base64="CmFdWA/kChJXRhugLa9ERmYdM6I=">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</latexit> rf(v) = v (1 (A>a)2) <latexit 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a def. = (A diag(v2)A>)+y
  24. Mild non-convexity Fact: Gradient descent always avo For our f

    , all stationary points are strict saddle points (at least one n †Jason D Lee et al. “First-order methods almost always avoid (2017), Chi Jin et al. “How to escape saddle points e ciently” PMLR. 2017, pp. 1724–1732. Property 2: “mildly nonconvex” Definition: v is a stationary point if rf (v) = 0. It is saddle point if rf (v) = 0 but r2 f (v) ⌫ 0 does not h Fact: Gradient descent always avoid strict saddle poin For our f , all stationary points are either global minim strict saddle points (at least one negative eigenvalue). †Jason D Lee et al. “First-order methods almost always avoid saddle points”. In: arXiv preprint a (2017), Chi Jin et al. “How to escape saddle points e ciently”. In: International Conference on M PMLR. 2017, pp. 1724–1732. <latexit 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non-strict <latexit sha1_base64="Dbv6b8Un6bo2YTNsw6NlAwHxaN4=">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</latexit> ! gradient descent avoids strict saddles. <latexit sha1_base64="g4I80irPOcKLFKkO1gC+a5Foi9w=">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</latexit> Example: 0 is a strict saddle for Lasso VarPro. <latexit 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v strict saddle point: <latexit 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rf(v) = 0 and min(@2f(v) < 0
  25. Mild non-convexity Fact: Gradient descent always avo For our f

    , all stationary points are strict saddle points (at least one n †Jason D Lee et al. “First-order methods almost always avoid (2017), Chi Jin et al. “How to escape saddle points e ciently” PMLR. 2017, pp. 1724–1732. Property 2: “mildly nonconvex” Definition: v is a stationary point if rf (v) = 0. It is saddle point if rf (v) = 0 but r2 f (v) ⌫ 0 does not h Fact: Gradient descent always avoid strict saddle poin For our f , all stationary points are either global minim strict saddle points (at least one negative eigenvalue). †Jason D Lee et al. “First-order methods almost always avoid saddle points”. In: arXiv preprint a (2017), Chi Jin et al. “How to escape saddle points e ciently”. In: International Conference on M PMLR. 2017, pp. 1724–1732. <latexit 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non-strict <latexit sha1_base64="Dbv6b8Un6bo2YTNsw6NlAwHxaN4=">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</latexit> ! gradient descent avoids strict saddles. <latexit sha1_base64="g4I80irPOcKLFKkO1gC+a5Foi9w=">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</latexit> Example: 0 is a strict saddle for Lasso VarPro. <latexit 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v strict saddle point: <latexit 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rf(v) = 0 and min(@2f(v) < 0 <latexit 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Theorem: all stationary points are global minima or strict saddles. <latexit 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||@2f(v)|| 6 1 + 3||y||2||A||2/ <latexit sha1_base64="zQ6lGfcd08R+ugAIC85rpdztVig=">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</latexit> If rf(v) = 0, <latexit 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eig(@2f(v)) 2 [1 |⇠Ic |1, 4] <latexit 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I , supp(x) <latexit 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() <latexit 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x global minimum <latexit sha1_base64="QLvBWhF7FV9ZH5ZfNIOYs/4ofVU=">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</latexit> Primal variable: <latexit 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Dual certificate: <latexit 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x , u?(v) v <latexit 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⇠ , 1 A>(Ax y) <latexit 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⇠I = sign(xI) and ||⇠Ic ||1 6 1
  26. Mild non-convexity Fact: Gradient descent always avo For our f

    , all stationary points are strict saddle points (at least one n †Jason D Lee et al. “First-order methods almost always avoid (2017), Chi Jin et al. “How to escape saddle points e ciently” PMLR. 2017, pp. 1724–1732. Property 2: “mildly nonconvex” Definition: v is a stationary point if rf (v) = 0. It is saddle point if rf (v) = 0 but r2 f (v) ⌫ 0 does not h Fact: Gradient descent always avoid strict saddle poin For our f , all stationary points are either global minim strict saddle points (at least one negative eigenvalue). †Jason D Lee et al. “First-order methods almost always avoid saddle points”. In: arXiv preprint a (2017), Chi Jin et al. “How to escape saddle points e ciently”. In: International Conference on M PMLR. 2017, pp. 1724–1732. <latexit 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non-strict <latexit sha1_base64="Dbv6b8Un6bo2YTNsw6NlAwHxaN4=">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</latexit> ! gradient descent avoids strict saddles. <latexit sha1_base64="g4I80irPOcKLFKkO1gC+a5Foi9w=">AABB/HictVzNcxu3FYfTr9j9ctJjL9vK7jgdR5UVT9Mk05nIkiwrpm3apGQnoe1Zkit67SWX3iVl2Yz6t/TQW6fXXnvrtb32P2hP/Rf6PoAFlsQusKpjjCQsiN97D2+Bh/ceQPenSZzPNjb+de6d73z3e9//wbvnL/zwRz/+yU8vvvf+YZ7Os0F0MEiTNHvUD/MoiSfRwSyeJdGjaRaF434SPey/2MbPHx5HWR6nk+7s9TR6PA5Hk/goHoQzaHp68dPeLDoB3GL3JBxPk+jT0+DSxqUgzoMwyGdZPJgFeTgcJlFwlGZBK8zzNDgMs3aWrj+9uLaxvkH/gtXKNVlZE/JfO30vOBA9MRSpGIi5GItITMQM6okIRQ7la3FNbIgptD0WC2jLoBbT55E4FRcAO4deEfQIofUF/B7B09eydQLPSDMn9AC4JPCTATIQlwGTQr8M6sgtoM/nRBlbq2gviCbK9hr+9iWtMbTOxDNodeFUT18cjmUmjsTvaAwxjGlKLTi6gaQyJ62g5IExqhlQmEIb1ofweQb1ASGVngPC5DR21G1In/+bemIrPg9k37n4D0l5GUogOnL0aUEhFMdEP6C3OYfPWJ4EOI+AQiTHiLVXpOsxjX4C/RfQfhfKKdWUTvpQFtR6WovchmJDbjuRe1BsyD0nsgXFhmw5kW0oNmRbIhGbkc7t+A4UG77j5Hwfig1534l8AMWGfOBEHkKxIQ+dyK+g2JBfOZE3odiQN53I21BsyNtOZBeKDdl1Ig+g2JAHTuQuFBtyVyKrV2oGJSU6sWNVbkG9zAMtRQItW075bpB1tGFveKzpQQXWvap34K8du+Oh06gCu+sx744qsO6Ztwc20o5126JbtJvYsLec2H2YAXbsvhP7hXhegf3CY6W9qMC611oL+tmxbut7B57s2DtO7F2o2bHuPeoetNix9zx2jGkFtu3E3hcvK7A+Vj+rwLrtfgfsih3r3qe60N+O9bGm8wqs254eggdjx7p3q4fQasc+dGIfiZMK7CMn9kuw7nbslx477JsKrNpjL9AOMiJ/JIIVW0ctLFYl1qZALXTwT4q9JSHfuA/tLsyowIwIM3Yi9grEnieiVSBa3nLlhR3Nyd91c+kUiI4nol/sTVibOfsPi/5YSzwQOwViZwlR55Hiu1ZjOSbvQrW4kLNi58Kaz5jSwn5jLZLzod7yKsS9EoLn9jOa+VcpWsIICjVVR+1ZscczMqDnOsQrit7UKBUPN25WWAUTdeJE9S2ovhP12oJ67UTNLai5E3VsQR07UXrlm7iexwzQ+sd3saAnngHsI1eXALyCLdh1bsEaDWD+tMELfEAt9+Bvh2JvV6mTDKN53Ccxy/G4ZIkzqC3EGrTrqHCH4uuEVlgEknHPezLGxyfMbSzkmmMrfFrs5EGRMfGnE5M8o4IOeosBradmdG5Tyyl5d1xrhr9VrHtVa4bfJY2fkhfPtWb4mZR+dgbZuxLbPQO2A6tpKrWv601pcP6Faaj6Bdp10eLiWx3LOYP0ThrS35dvZv8M72WbaqwfXW9GIzfGl5fG14SG1nNu6LkZFfSe2OtVtaDxSCYy7tX1pjKktItOpBz6qembwT5D+WZUvRmNNnhc2xRzL4x609k7LUaj681oHArOe56SJ6/qzWiM6Jn1oevNaGC2JZRxvq43teyoAY6ddb2pVZ9QFhhzQDznuUV7RRn5SXNJLSb/oD5bY/r8q/sY5myeFDFCPSXt21bT6Rd7Wb1Eyl+IwKrNGsqB/sXc8MHKNBZi0xlfsQyz0v6+Skfv8aj5FmgxgNXPZwCunHkCEqqcBFrvBChec0Zd5ZEp3KYTh7PkaAnVk60zp7eo+XLWqNz2lFpdcZkerdZjj+x1TnNvSj5hizTr0kOr8g1XUXRpqFXSkJteE929keu1rP0NJ266hJgWM21AJ0J8klYfp9q03jF0fFme8syg8JmPnr+YbT6S1gZjnpRsEcpSx9Psp/JIZhvuq1eFznHzZwG9UbRXx2Q1YjqRyp1RqMoWsze+oGdN+4DO5JAH0xjAewwklangUzPMomM+PSCLatpbF2/Ul8rQcT0nq6vscT16ZKBHFnTzGGcbdoy7UOtCzHAAT12PKOdCoauUNJ6JD4vT0ZTeYH1En5QspKLB9iYqWci6KPtZicorQONs4Cjdn8YyHYXvrVByR/02eXTsWrb8l+nkVp1vhzTHq2dzdSZmSFw3iWtAq4ZPdflpmQNLsLB+skn+a/0okV8TjmhDXVyfGJxZLxM68Y8ogp2SZ5zQanOtjnJvMz+1/Ini1Bbq7BxPs1OykAHZvwD2p5TmZEA/5t0BdYLOFiEhG+ljd+LCu7H5OrFzjmk/LhZ8q0HPt4hs2Zz4K7rm6sppLnLEwPvA6dLcVjppkS8YEddMWne9tut3H0TqexLmLGGKeq5cIf4f0G/1o+bJ2sqMQA3jG8ilrbO9j5RiFtRRSLt8vQ1SfU0pLxUyPJFS6/1Py3SpJNkORVwoD+7WQ+A8oGfmhbMkI7nzlT68j9Zlc5HydEmPONojiuLZ7o/kDoxyX6Vdco3WXI9myQhmwayIIlRfVxZ5mW89rzJ1P9r5t0Jd67qsNaQYCJ3BZQ258vsRRWumlAnMap6/L2g12bWeLfWq5zOhuTg21vI30PoL+K3kVs9+dPolq3CD5gBT0E9aI9wSrPTw43WjxEvNTEVLP2t+ek6qXmbLWeJrtm46xj5uTKVNs+ZEZi1U/Sw0nhs0nnvqsEtnjVqLql1ZoqfO2KIrTyt9+TXh1m1Aee6k7PbIFCr2kNKMpfyoDp1U3TG+Qr1x0tpw0gphtZqnAeaa90Ha1/ry6v6m2N0DcZN8mwF5YBy/DGmVxuRzqdb6SI0pIOfr0r6aq79HLci9TxYUKfM9TlwxfOo0oHJaSPorubOlZOe1RVD3ll7JPsrG9qj+0QpyTGsip3WpENepRyTlN+UIlizSuuFzBJT5D8mnYr+jPmY2e+t3EpT8CR1v8qrSvDhSmJD+XZm3/ZXodd+IXwOKCefSu+4DreZvGCkwRmUS7J5lTm8Idzk+SWCPtk/2c9VO8SnexJBonaReiN972BiOevVcN+eWGrEa26+hJ2pdv3VbDze/xJuji99ZTvRC2tXG0kddLD2fjVYod7nyc50e5kt8tT7m1MeMLHSUV8b0xGfeXFiiZlwY48Ol2SiayN9M8iYy8+mUL2XVW1EuZxrYxjyjeMl1DxQRNu/uitWb+8Axjv4KvT5hTWrc4qKE2bhU5gdMS4tZqfMr+xC3nq/djRJjJ6raKRR1c7fQ9pstZETWLxGunA33NmXvlaIUdxaGKQwE3+itig9Nmp9Bwd+BsEWHiqNP7rAD/u2W2Ba7b+E2xEtZ54xmQC1oC4ZLsXcox1nuUa+jlwZ1k74PB38eMejaJX1MO2lT2ZmyW3KTuj/9V2QFMhE5pdc9m4/B5OIeySqnJuOJybK5RxML9V2cpmNRHHxGUubiz4fPNVyjOBLqO03NxqCou0dQ5tCEh7rH4PfOde/mvExO9fpa5eLLg3cBdeKicHjyVx2r6H4+Fioz3sjb54DW4aiGutot/t9xKD6aU3Nevtxy+q7Zc4+3zv0imZFFf7j5mtHcfGZzNUd/nmkxOu0t2fmx3xc0elOpMZq3Tx/9UT0HFK+F4DyoWzrGm7NIy+tLBc8FbDKk4r/ib+fc30Z4WdCokqMJJXVOUU1N9XBTU9+4tI1OfeYjk6ZTJVOZmo4jOnQjdlvsi5vws114gE1vh/J3KfkvYu3fnx1C6xFZD5VF58xBj9oiyn7oU7QhPev7s1US411evtvbhRY8C29RK97zvUv98a5vtzS26m+Q8Fq/I1IxLEUky6d7el31YQTlkzfOAanv+QZ0l56zWHzzbOxxtqjuTy1LtKBP3DcL+pX4viHlgObqVJ7V48kB3rAPi/xQIH5DbaG087jnuji3Kzm3lzjnpJ0yhxPjs/q7WVVctg0uwyJ3diz7pRRn6/O8+tzoTiUXvoNejx/V4EeGlB3S/guKhDNRn82b19CcS5nME9aJUJlI1gPGmWHxvusj2+MaXsce479dib5tSLoHsvQp/x3QCVtG9BKpm12Snm861mdSb9VIK79HSf+7wSf0L+DKx9dl5ZNrxf9ucLi5fu236x/d31z7/Ib8fw7eFT8XvxRXYI1/LD4Ham1xABz+KP4u/iH+ufWHrT9t/XnrL9z1nXMS8zNR+rf11/8BwcG3rQ==</latexit> Example: 0 is a strict saddle for Lasso VarPro. <latexit 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v strict saddle point: <latexit 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rf(v) = 0 and min(@2f(v) < 0 <latexit 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Theorem: all stationary points are global minima or strict saddles. <latexit 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||@2f(v)|| 6 1 + 3||y||2||A||2/ <latexit sha1_base64="zQ6lGfcd08R+ugAIC85rpdztVig=">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</latexit> If rf(v) = 0, <latexit 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eig(@2f(v)) 2 [1 |⇠Ic |1, 4] <latexit 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“non-degenerate” global minimum: <latexit 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=) <latexit 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eig(@2f(v)) > 0 <latexit 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⇠I = sign(x) and ||⇠Ic ||1 < 1 <latexit 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I , supp(x) <latexit 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() <latexit 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x global minimum <latexit sha1_base64="QLvBWhF7FV9ZH5ZfNIOYs/4ofVU=">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</latexit> Primal variable: <latexit 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Dual certificate: <latexit 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x , u?(v) v <latexit 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⇠ , 1 A>(Ax y) <latexit 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⇠I = sign(xI) and ||⇠Ic ||1 6 1
  27. General Quadratic Variational Formula <latexit sha1_base64="0ZcyfZpQlXIRnYF2W7OVgjdfKyU=">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</latexit> [Geman and Reynolds 1992]

    <latexit sha1_base64="Pu6LJwnLe+hZqQx2FUq3AzXOEmk=">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</latexit> [Black and Rangarajan 1992] <latexit sha1_base64="ataKamassm3Laqh/AfGdiT8hbMY=">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</latexit> = 2↵ ↵ + 2 <latexit 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↵ <latexit 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(smooth VarPro) <latexit 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8 > > > > > > < > > > > > > : <latexit 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8 < : <latexit sha1_base64="yavsPsf7g3vXOvf7mEKVUrHTLos=">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</latexit> convex regul. <latexit sha1_base64="YVop+r+9BBCwQwQLmi0q/6k/cLM=">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</latexit> Non-convex regularization: <latexit sha1_base64="eHUX4dwmSP7kGZJcPNU1wzh2iXU=">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</latexit> |x| / min x=uv u2 + v↵
  28. General Quadratic Variational Formula <latexit sha1_base64="0ZcyfZpQlXIRnYF2W7OVgjdfKyU=">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</latexit> [Geman and Reynolds 1992]

    <latexit sha1_base64="Pu6LJwnLe+hZqQx2FUq3AzXOEmk=">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</latexit> [Black and Rangarajan 1992] <latexit sha1_base64="ataKamassm3Laqh/AfGdiT8hbMY=">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</latexit> = 2↵ ↵ + 2 <latexit 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↵ <latexit 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(smooth VarPro) <latexit 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8 > > > > > > < > > > > > > : <latexit 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8 < : <latexit sha1_base64="yavsPsf7g3vXOvf7mEKVUrHTLos=">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</latexit> convex regul. <latexit sha1_base64="YVop+r+9BBCwQwQLmi0q/6k/cLM=">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</latexit> Non-convex regularization: <latexit 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|x| / min x=uv u2 + v↵ <latexit 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Group Lasso: <latexit 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||x||1,2 , X g ||xg || <latexit sha1_base64="b0kY131rmD1NEMD0IQ0axodowxM=">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</latexit> Disjoint: {1, . . . , n} = S g g <latexit sha1_base64="grsa22GhNADhBltXcp+NUoJcBLg=">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</latexit> = min ugvg=xg X g ||ug ||2 2 + v2 g 2 <latexit sha1_base64="pe63Kmcbx97Hn/YmiBJPHpl91Fk=">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</latexit> ug 2 R|g|, vg 2 R
  29. General Quadratic Variational Formula <latexit sha1_base64="0ZcyfZpQlXIRnYF2W7OVgjdfKyU=">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</latexit> [Geman and Reynolds 1992]

    <latexit sha1_base64="Pu6LJwnLe+hZqQx2FUq3AzXOEmk=">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</latexit> [Black and Rangarajan 1992] <latexit sha1_base64="ataKamassm3Laqh/AfGdiT8hbMY=">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</latexit> = 2↵ ↵ + 2 <latexit 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↵ <latexit 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(smooth VarPro) <latexit 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8 > > > > > > < > > > > > > : <latexit 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8 < : <latexit sha1_base64="yavsPsf7g3vXOvf7mEKVUrHTLos=">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</latexit> convex regul. <latexit sha1_base64="YVop+r+9BBCwQwQLmi0q/6k/cLM=">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</latexit> Non-convex regularization: <latexit 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|x| / min x=uv u2 + v↵ <latexit 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Group Lasso: <latexit 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||x||1,2 , X g ||xg || <latexit sha1_base64="b0kY131rmD1NEMD0IQ0axodowxM=">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</latexit> Disjoint: {1, . . . , n} = S g g <latexit 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= min ugvg=xg X g ||ug ||2 2 + v2 g 2 <latexit 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ug 2 R|g|, vg 2 R <latexit 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Trace norm: <latexit 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X 2 Rr⇥s <latexit 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||X||⇤ , P k k(X) <latexit sha1_base64="3ONCWHVZszM7TbB1BJHp6JsNE0U=">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</latexit> ||X||⇤ = min X=UV ||U||2 F + ||V ||2 F 2 <latexit sha1_base64="nf2tsuOVslg4w+bGyPe5oUAx/xM=">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</latexit> U 2 Rr⇥min(r,s), V 2 Rmin(r,s)⇥s
  30. General Quadratic Variational Formula <latexit sha1_base64="0ZcyfZpQlXIRnYF2W7OVgjdfKyU=">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</latexit> [Geman and Reynolds 1992]

    <latexit sha1_base64="Pu6LJwnLe+hZqQx2FUq3AzXOEmk=">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</latexit> [Black and Rangarajan 1992] <latexit sha1_base64="ataKamassm3Laqh/AfGdiT8hbMY=">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</latexit> = 2↵ ↵ + 2 <latexit 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↵ <latexit 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(smooth VarPro) <latexit 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8 > > > > > > < > > > > > > : <latexit 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8 < : <latexit sha1_base64="yavsPsf7g3vXOvf7mEKVUrHTLos=">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</latexit> convex regul. <latexit sha1_base64="YVop+r+9BBCwQwQLmi0q/6k/cLM=">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</latexit> Non-convex regularization: <latexit 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|x| / min x=uv u2 + v↵ <latexit 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Group Lasso: <latexit 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||x||1,2 , X g ||xg || <latexit sha1_base64="b0kY131rmD1NEMD0IQ0axodowxM=">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</latexit> Disjoint: {1, . . . , n} = S g g <latexit 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= min ugvg=xg X g ||ug ||2 2 + v2 g 2 <latexit 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ug 2 R|g|, vg 2 R <latexit 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Trace norm: <latexit 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X 2 Rr⇥s <latexit 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||X||⇤ , P k k(X) <latexit sha1_base64="3ONCWHVZszM7TbB1BJHp6JsNE0U=">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</latexit> ||X||⇤ = min X=UV ||U||2 F + ||V ||2 F 2 <latexit 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U 2 Rr⇥min(r,s), V 2 Rmin(r,s)⇥s <latexit sha1_base64="rD2uViTq2LCt//2OHuuLL1eGPaA=">AABB03ictVzddhu3EYbTn8Tun51e9mZbxT1Oj+PKik/TNKfnRJZkWbFsyyYlOwltH/6sKNpLLs0lJdmMbnp620fobfsYfY6+QXvVV+j8AAssid3Bqq5xJGFBfDODWWAwMwDdGSeDbLq6+s8L733v+z/44fsfXLz0ox//5Kc/u3zlw4MsnU268X43TdLJ0047i5PBKN6fDqZJ/HQ8idvDThI/6bzawM+fHMeTbJCOmtM34/jZsN0fDQ4H3fYUml5cvtKaxqeAmzeP4nQSD/9w9uLyyuqNVfoXLVdu6sqK0v/20ivRvmqpnkpVV83UUMVqpKZQT1RbZVC+VTfVqhpD2zM1h7YJ1Ab0eazO1CXAzqBXDD3a0PoKfvfh6VvdOoJnpJkRugtcEviZADJSVwGTQr8J1JFbRJ/PiDK2ltGeE02U7Q387WhaQ2idqiNolXCmZygOxzJVh+r3NIYBjGlMLTi6rqYyI62g5JEzqilQGEMb1nvw+QTqXUIaPUeEyWjsqNs2ff4v6omt+NzVfWfq3yTlVSiRaujRpzmFtjom+hG9zRl8xvIkwLkPFGI9RqydkK6HNPoR9J9D+wMoZ1QzOulAmVPrWSVyA4oPuSEit6H4kNsicheKD7krIveg+JB7GonYCencj29A8eEbIudHUHzIRyLyMRQf8rGIPIDiQx6IyG+g+JDfiMg7UHzIOyLyHhQf8p6IbELxIZsich+KD7kvIreg+JBbGlm+UidQUqIzEFblOtSLPNBSJNCyLsp3m6yjD3s7YE13S7Dyqt6Ev37sZoBO4xLsVsC8OyzByjNvG2ykHyvboru0m/iwd0XsDswAP3ZHxH6lXpZgvwpYaa9KsPJa24V+fqxsfe/Dkx97X8Q+gJofK+9RD6HFj30YsGOMS7B7IvaRel2CDbH6kxKsbPcbYFf8WHmfakJ/PzbEms5KsLI9PQAPxo+Vd6sn0OrHPhGxT9VpCfapiP0arLsf+3XADvu2BGv22Eu0g/TJH4lhxVZRa+erEmtjoNYW+Cf53pKQb9yBdgnTzzF9wgxFxHaO2A5E7OaI3WC5styOZuTvylwaOaIRiOjkexPWpmL/Xt4fa0kAYjNHbC4gqjxSfNdmLMfkXZgWCTnNdy6shYwpze031mI9H6otr0E8LCB4bh/RzL9O0RJGUKipKmpH+R7PyIieqxAnFL2ZURoeMm6aWwUXdSqiOh5UR0S98aDeiKiZBzUTUcce1LGIsivfxbUCZoDVP76LOT3xDGAfubxE4BWsw65zF9ZoBPNnD7zAx9TyEP42KPaWSpVkGM3jPolZjmcFSzyB2lytQLuNCjcpvk5ohcUgGfd8qGN8fMLcxlyvObbCZ/lOHuUZk3A6A5Knn9NBbzGi9VSPzj1qOSPvjmv18HfzdW9q9fBbpPEz8uK5Vg8/1dJPzyF7U2Ob58A2YDWNtfZtvS4Nzr8wDVO/RLsuWlx8q0M9Z5DeaU36O/rN7JzjvWxQjfVj6/VoZM74ssL46tCwes4cPdejgt4Te72mFtUeyUjHvbZeV4aUdtGRlsM+1X0z2Ken34yp16OxBx7XBsXcc6ded/aO89HYej0aB4rznmfkyZt6PRp9emZ92Ho9Gphtaes439brWnbUAMfOtl7Xqo8oC4w5IJ7z3GK9ogn5STNNbUD+QXW2xvX5l/cxzNk8z2OEakrWty2n08n3smqJjL8Qg1Wb1pQD/YuZ44MVaczVmhhfsQzTwv6+TMfu8aj5XdBiBKufzwCknHkCEpqcBFrvBCjeFKOu4sgMbk3E4Sw5XEC1dOtU9BYtX84aFdteUKsUl9nRWj22yF5nNPfG5BPukmYlPeyWvuEyipKGdgsakunV0d1bvV6L2l8VceMFxDifaV06EeKTtOo41af1hqPjq/qUZwqFz3zs/MVs86G2NhjzpGSLUJYqnm4/k0dy23Bfva5sjps/i+iNor06JqsxoBOpTIxCTbaYvfE5PVva+3QmhzyYRhfeY6SpjBWfmmEWHfPpEVlU195KvFFfJkPH9YysrrHH1ei+g+570PVjnA3YMR5ArQkxwz48NQOinEu5rlLS+ER9kp+OpvQGqyP6pGAhDQ22N3HBQlZF2UcFKieAxtnAUXo4jUU6Bt9aoiRH/T55bOxatPxX6eTWnG+3aY6Xz+byTEyPuK4R14hWDZ/q8tMiB5Zg7v1kjfzX6lEivzoc0YZKXJ87nFkvIzrxjymCHZNnnNBqk1ZHsbebn1r8xHDaU+bsHE+zU7KQEdm/CPanlOZkRD/u3QFzgs4WISEbGWJ3Brl34/N1BuIcs37cQPGtBjvfYrJlM+Jv6LqrK6O5yBED7wNnC3Pb6GSXfMGYuE60dbdru3r3QaS9J+HOEqZo58o14v8x/TY/Zp6sLM0I1DC+gUzbOt/7SClmQR21aZevtkGmryvlR7kMz7XUdv+zMn1UkGyTIi6UB3frHnDu0jPzwlkyIbmzpT68j1Zlc5HyeEGPONpDiuLZ7vf1DoxyX6ddcoXWXItmSR9mwTSPIkxfKYu8yLeaV5F6GO3s/0Ld6rqoNaQYKZvBZQ1J+f2YojVXygRmNc/fV7Sa/FqfLPSq5jOiuTh01vJ30PpL+G3kNs9hdDoFq3Cb5gBTsE9WI9wSLfUI43W7wMvMTEPLPlt+dk6aXm7LeeJrtm42xj6uTWWPZs2pzlqY+nlovHRovAzUYZPOGq0WTbuxRC/E2KKpTytD+dXh1qxBeSZSlj0ygxoESOnGUmFUeyJVOcY3qLcirVWRVhtWq3sa4K75EKR/rS+u7u/y3T1Sd8i36ZIHxvFLj1bpgHwu01odqTEF5HxL21d39beoBbl3yIIiZb7HiSuGT526VM5ySX+td7aU7Ly1CObe0onuY2xsi+qfLiGHtCYyWpcGcYt6xFp+V45owSLdcHyOiDL/bfKp2O+ojpnd3vadRAV/wsabvKosL44URqR/KfO2sxS97jjxa0Qx4Ux71x2gVf8NIwXGmEyC37PM6A3hLscnCezRdsh+LtspPsUbORLdIKnn6o8BNoajXjvX3bllRmzG9hvoiVq3b93XQ+aXBHOU+J3nRK9Nu9pQ+6jzhefz0WrrXa74XKWH2QJfq48Z9XEjCxvlFTEt9UUwF5aoHhfGhHCpN4o68teTvI7MfDoVStn0NpSLmQa2MUcUL0n3QBHh8+6ueb25j4VxdJbodQjrUuMWiRJm41KdH3AtLWalLi7tQ9x6sXI3SpydqGynMNTd3cLab7aQMVm/REk5G+7tyt4qRClyFoYpdBXf6C2LD12aX0DB35HyRYeGY0jusAH+7braUFvv4DbEa13njGZELWgLeguxd1uPs9ijWkevHeou/RAO4TwGoGtJ+gHtpHVlZ8qy5C71cPonZAUmKhaltz3rj8HlIo9kmVOd8QzIssmjGSjzXZy6YzEcQkZS5BLOh881pFEcKvOdpnpjMNTlERQ51OFh7jGEvXPbuz4vl1O1vpa5hPLgXcCcuBgcnvyVxyq2X4iFmjhv5N1zQOtwWEHd7Bb/6zgMH8upPq9Qbhl91+xlwFvnfrHOyKI/XH/NWG4hs7mcYzjPNB+d9Zb8/Njvi2q9qdQZzbunj/6onQOG11xxHlSWjvHuLLLyhlLBcwGfDKn6j/rHBfnbCK9zGmVy1KFkzinKqZkeMjXzjUvf6MxnITJZOmUyFanZOKJBN2I31I66Az8buQdY93Yof5eS/yLW//3ZHrQekvUwWXTOHLSoLabshz1F69GzvT9bJjHe5eW7vU1owbPwXWrFe74PqD/e9W0Wxlb+DRJe6/dVqnqFiGTxdM+uqw6MoHjyxjkg8z3fiO7ScxaLb54NA84Wzf2pRYnm9Il8s6BTiu84UnZpro71WT2eHOAN+3aeH4rUb6mtre087rkS571SznsLnDPSTpHDqfNZ9d2sMi4bDpdenjs71v1SirPteV51bnSzlAvfQa/G9yvwfUfKBmn/FUXCE1WdzZtV0JxpmdwT1pEymUjWA8aZ7fx9V0e2xxW8jgPGf68Ufc+RdBtk6VD+O6ITtgnRS7Rutkh6vulYnUm9WyGt/h4l/e8Gn9O/iCuf3dKVz2/m/7vBwdqNm7+78emjtZUvb+v/5+AD9Qv1K3UN1vhn6kugtqf2gcOJ+qv6m/r7+v76fP1P63/mru9d0Jifq8K/9b/8F9IqqI8=</latexit> Theorem: <latexit sha1_base64="fR2GMiIKm8A1qgvRTIr6/95h2m4=">AABB6HictVzdchu3FYbTn8Tun9Ne9mZbyRm74zqy4mmayWQmsiTLimmbNinZSWh7luSKWnvJpbkkJZvRG/Sid53e9hF62870OfoG7VVfoecHWGBJ7AKrusZIwoL4zjk4CxyccwC6O07ibLqx8c8L733v+z/44fsfXLz0ox//5Kc/u/zhzw+zdDbpRQe9NEknT7thFiXxKDqYxtMkejqeROGwm0RPuq+28fMn82iSxemoPX0zjp4Nw8EoPop74RSaXlz+aP3x1dNrwRdBZ3wcXz19vnltPTiJp8fBOjasB7101Avn0YvLaxs3NuhfsFq5KStrQv5rph8GB6Ij+iIVPTETQxGJkZhCPRGhyKB8K26KDTGGtmdiAW0TqMX0eSTOxCXAzqBXBD1CaH0Fvwfw9K1sHcEz0swI3QMuCfxMABmIK4BJod8E6sgtoM9nRBlby2gviCbK9gb+diWtIbROxTG0unCqpy8OxzIVR+L3NIYYxjSmFhxdT1KZkVZQ8sAY1RQojKEN6334fAL1HiGVngPCZDR21G1In/+LemIrPvdk35n4N0l5BUogWnL0aU4hFHOiH9DbnMFnLE8CnAdAIZJjxNoJ6XpIox9B/wW0P4ByRjWlky6UBbWeVSK3odiQ207kHhQbcs+JbECxIRtOZBOKDdmUSMROSOd2fAuKDd9ycn4ExYZ85EQ+hmJDPnYiD6HYkIdO5DdQbMhvnMg7UGzIO07kPSg25D0nsg3Fhmw7kQdQbMgDJ3IXig25K5HlK3UCJSU6sWNVbkG9yAMtRQItW075bpN1tGFve6zpXgnWvap34K8du+Oh06gEu+sx745KsO6Ztwc20o5126K7tJvYsHed2H2YAXbsvhP7lXhZgv3KY6W9KsG611oD+tmxbut7H57s2PtO7AOo2bHuPeohtNixDz12jHEJtunEPhKvS7A+Vn9SgnXb/RbYFTvWvU+1ob8d62NNZyVYtz09BA/GjnXvVk+g1Y594sQ+Facl2KdO7Ndg3e3Yrz122LclWLXHXqIdZED+SAQrtopamK9KrI2BWujgn+R7S0K+cRfaXZhBjhkQZuhE7OWIPU9EI0c0vOXKcjuakb/r5tLKES1PRDffm7A2dfbv5/2xlnggdnLEzhKiyiPFd63GMifvQrW4kNN858Kaz5jS3H5jLZLzodryKsTDAoLn9jHN/OsULWEEhZqqonac7/GMDOi5CnFC0ZsapeLhxk1zq2CiTp2orgXVdaLeWFBvnKiZBTVzouYW1NyJ0ivfxHU8ZoDWP76LBT3xDGAfubwE4BVswa5zF9ZoAPOnCV7gY2p5CH9bFHu7SpVkGM3jPolZjmcFSzyB2kKsQbuOCncovk5ohUUgGfd8KGN8fMLcxkKuObbCZ/lOHuQZE386MckzyOmgtxjQeqpH5x61nJF3x7V6+Lv5ule1evhd0vgZefFcq4efSumn55C9LbHtc2BbsJrGUvu6XpcG51+Yhqpfol0XLS6+1aGcM0jvtCb9fflm9s/xXrapxvrR9Xo0MmN8WWF8dWhoPWeGnutRQe+JvV5VC2qPZCTjXl2vK0NKu+hIyqGf6r4Z7NOXb0bV69Fogse1TTH3wqjXnb3jfDS6Xo/GoeC85xl58qpej8aAnlkful6PBmZbQhnn63pdy44a4NhZ1+ta9RFlgTEHxHOeW7RXNCE/aSapxeQfVGdrTJ9/dR/DnM3zPEaopqR923I63Xwvq5ZI+QsRWLVpTTnQv5gZPliRxkJsOuMrlmFa2N9X6eg9HjXfAC0GsPr5DMCVM09AQpWTQOudAMWbzqirODKF23TicJYcLaE6snXq9BY1X84aFdteUKsrLtOj1XrskL3OaO6NySdskGZdemiUvuEyii4NNQoactOro7u3cr0Wtb/hxI2XEON8pvXoRIhP0qrjVJvWW4aOr8hTnikUPvPR8xezzUfS2mDMk5ItQlmqeJr9VB7JbMN99brQOW7+LKA3ivZqTlYjphOpzBmFqmwxe+MLeta0D+hMDnkwjR68x0BSGQs+NcMsOubTA7Kopr118UZ9qQwd1zOyusoeV6MHBnpgQdePcbZhx3gAtTbEDAfw1PaIci7lukpJ4xPx2/x0NKU3WB3RJwULqWiwvYkKFrIqyj4uUDkBNM4GjtL9aSzTUfjOCiV31G+TR8euRct/hU5u1fl2SHO8fDaXZ2L6xHWTuAa0avhUl5+WObAEC+snm+S/Vo8S+dXhiDbUxfW5wZn1MqIT/4gi2DF5xgmtNtfqKPY281PLnyhOTaHOzvE0OyULGZD9C2B/SmlOBvRj3h1QJ+hsERKykT52J869G5uvEzvnmPbjYsG3GvR8i8iWzYi/omuurozmIkcMvA+cLc1tpZMG+YIRcZ1I667XdvXug0h9T8KcJUxRz5WrxP8a/VY/ap6srcwI1DC+gUzaOtv7SClmQR2FtMtX2yDV15RyPZfhuZRa739apvWCZDsUcaE8uFv3gXOPnpkXzpIJyZ2t9OF9tCqbi5THS3rE0R5RFM92fyB3YJT7Ou2Sa7TmOjRLBjALpnkUofq6ssjLfKt5Fan70c7+L9S1rotaQ4qB0Blc1pArvx9RtGZKmcCs5vn7ilaTXeuTpV7VfEY0F4fGWv4OWn8Fv5Xc6tmPTrdgFW7THGAK+klrhFuClR5+vG4XeKmZqWjpZ81Pz0nVy2w5T3zN1k3H2PPaVJo0a05l1kLVz0PjpUHjpacO23TWqLWo2pUleuGMLdrytNKXXx1u7RqUZ07Kbo9MoWIPKc1Yyo9q30nVHeMr1FsnrQ0nrRBWq3kaYK55H6R9rS+v7u/y3T0Qd8i36ZEHxvFLn1ZpTD6Xaq2O1JgCcr4l7au5+jvUgty7ZEGRMt/jxBXDp049Kme5pB/JnS0lO68tgrq3dCL7KBvbofonK8ghrYmM1qVC3KIekZTflCNYskg3DJ8joMx/SD4V+x3VMbPZW7+ToOBP6HiTV5XmxZHCiPTvyrztr0Sv+0b8GlBMOJPedRdo1X/DSIExKpNg9ywzekO4y/FJAnu0XbKfq3aKT/FGhkQ3SOqF+MLDxnDUq+e6ObfUiNXYfgM9Uev6rdt6uPkl3hxd/M5zohfSrjaUPupi6fl8tEK5yxWfq/QwW+Kr9TGjPmZkoaO8IqYjPvfmwhLV48IYHy71RlFH/nqS15GZT6d8KaveinIx08A25pjiJdc9UETYvLurVm/ummMc3RV6XcKa1LjFRQmzcanMD5iWFrNSF1f2IW69WLkbJcZOVLZTKOrmbqHtN1vIiKxfIlw5G+5tyt4pRCnuLAxT6Am+0VsWH5o0P4eCvwNhiw4VR5/cYQv82y2xLXbfwW2I17LOGc2AWtAW9Jdi71COs9ijWkevDeomfR8O/jxi0LVL+ph20rqyM2W35CZ1f/onZAUmInJKr3vWH4PJxT2SVU51xhOTZXOPJhbquzh1x6I4+IykyMWfD59ruEZxJNR3muqNQVF3j6DIoQ4PdY/B753r3vV5mZyq9bXKxZcH7wLqxEXh8OSvPFbR/Xws1MR4I++eA1qHowrqarf4X8eh+GhO9Xn5csvou2YvPd4694tkRhb94fprRnPzmc3lHP15pvnotLdk58d+X1DrTaXGaN49ffRH9RxQvBaC86Bu6RhvziItry8VPBewyZCK/4h/XHB/G+F1TqNMjjqU1DlFOTXVw01NfePSNjr1mY9Mmk6ZTEVqOo5o0Y3YbbEv7sDPdu4B1r0dyt+l5L+ItX9/tg+tR2Q9VBadMwcdaoso+6FP0fr0rO/PlkmMd3n5bm8bWvAsvEGteM/3AfXHu77twtjKv0HCa/2+SEW/EJEsn+7pddWFERRP3jgHpL7nG9Bdes5i8c2zocfZoro/tSzRgj5x3yzoluK7hpQ9mqtjeVaPJwd4wz7M80OB+JjaQmnncc91cW6Wcm4ucc5IO0UOp8Zn1XezyrhsG1z6ee5sLvulFGfr87zq3OhOKRe+g16NH1TgB4aULdL+K4qEJ6I6mzeroDmTMpknrCOhMpGsB4wzw/x9V0e28wpec4/x3ytF3zMk3QNZupT/DuiEbUL0EqmbXZKebzpWZ1LvVkgrv0dJ/7vBZ/Qv4Mqnt2Tls5v5/25wuHnj5u9ufPJoc+3L2/L/OfhA/FL8WlyFNf6p+BKoNcUBcPiD+Kv4m/j71sutP279aevP3PW9CxLzC1H4t/WX/wKjr64T</latexit> R(x) = '(x2) with ' concave <latexit 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() <latexit 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h(⌘) , 2( ')⇤(1/⌘) <latexit 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R(x) = min x=u v ||u||2 + h(v2) 2
  31. Numerics for Lasso Leukemia (38, 7129) ⇤ 1 2 max

    1 10 max 1 50 max 36 / 49 thmover distance on graphs Quadratic Results
  32. From Gradient to Quasi-Newton <latexit sha1_base64="vroLI/5T1AopQPnYeJhwA76BFSg=">AABB0XictVzbchvHER05N0u5WE4e87IJrZSckhVKVsVxuVJliqQoWpBECSAl25BUuCwgiAsshAWoC8yqVF7zCXlNviPfkT9InvIL6cvMziwwuz3LKJwiODs7p7und6anu2fB7jQZZfPNzX+ee+973//BD3/0/vkLP/7JT3/2wcUPf36UpYtZLz7spUk6e9ztZHEymsSH89E8iR9PZ3Fn3E3iR93jbbz/6CSeZaN00pq/mcZPxp3hZDQY9TpzaHp28YPB5ZNnxx9Hn0Tt8WgSDZ5d3Ni8ukk/0Xrlmq5sKP1zkH4YHaq26qtU9dRCjVWsJmoO9UR1VAblW3VNbaoptD1RS2ibQW1E92N1qi4AdgG9YujRgdZj+BzC1be6dQLXSDMjdA+4JPA7A2SkLgEmhX4zqCO3iO4viDK2ltFeEk2U7Q387WpaY2idq+fQKuFMz1AcjmWuBuoPNIYRjGlKLTi6nqayIK2g5JEzqjlQmEIb1vtwfwb1HiGNniPCZDR21G2H7v+LemIrXvd034X6N0l5CUqkmnr0aU6ho06IfkRPcwH3WJ4EOA+BQqzHiLVXpOsxjX4C/ZfQfg/KKdWMTrpQltR6WonchuJDbovIPSg+5J6IbEDxIRsi8gCKD3mgkYidkc79+CYUH74pcn4AxYd8ICIfQvEhH4rIIyg+5JGI/AaKD/mNiLwFxYe8JSLvQPEh74jIFhQfsiUiD6H4kIcicheKD7mrkeUrdQYlJTojYVVuQb3IAy1FAi1bonw3yTr6sDcD1nSvBCuv6h3468fuBOg0LsHuBsy7QQlWnnl7YCP9WNkW3abdxIe9LWL3YQb4sfsi9iv1ogT7VcBKOy7BymutAf38WNn63oUrP/auiL0HNT9W3qPuQ4sfez9gx5iWYA9E7AP1sgQbYvVnJVjZ7jfBrvix8j7Vgv5+bIg1XZRgZXt6BB6MHyvvVo+g1Y99JGIfq9cl2Mci9muw7n7s1wE77NsSrNljL9AOMiR/JIYVW0Wtk69KrE2BWkfgn+R7S0K+cRfaJcwwxwwJMxYRezliLxDRyBGNYLmy3I5m5O/KXJo5ohmI6OZ7E9bmYv9+3h9rSQBiJ0fsrCCqPFJ81mYsJ+RdmBYJOc93LqyFjCnN7TfWYj0fqi2vQdwvIHhuP6eZf4WiJYygUFNV1J7nezwjI7quQryi6M2M0vCQcfPcKrio1yKq60F1RdQbD+qNiFp4UAsRdeJBnYgou/JdXDtgBlj947NY0hXPAPaRy0sEXsEW7Dq3YY1GMH8OwAt8SC334W+TYm+pVEmG0Tzuk5jleFKwxDOoLdUGtNuocIfi64RWWAyScc/7OsbHK8xtLPWaYyt8mu/kUZ4xCaczInmGOR30FiNaT/Xo3KGWU/LuuFYPfztf96ZWD79LGj8lL55r9fBzLf38DLK3NLZ1BmwTVtNUa9/W69Lg/AvTMPULtOuixcWnOtZzBum9rkl/Xz+Z/TM8l22qsX5svR6NzBlfVhhfHRpWz5mj53pU0Htir9fUotojmei419brypDSLjrRctiruk8G+/T1kzH1ejQOwOPapph76dTrzt5pPhpbr0fjSHHe85Q8eVOvR2NI16wPW69HA7MtHR3n23pdy44a4NjZ1uta9QllgTEHxHOeW6xXNCM/aaGpjcg/qM7WuD7/+j6GOZuneYxQTcn6tuV0uvleVi2R8RdisGrzmnKgf7FwfLAijaW6LsZXLMO8sL+v07F7PGq+AVqMYPXzGYCUM09AQpOTQOudAMVrYtRVHJnBXRdxOEsGK6i2bp2L3qLly1mjYtszapXiMjtaq8c22euM5t6UfMIGaVbSQ6P0CZdRlDTUKGhIpldHd2/1ei1qf1PETVcQ03ym9ehEiE/SquNUn9abjo4v6VOeORQ+87HzF7PNA21tMOZJyRahLFU83X4mj+S24b56RdkcN9+L6ImivTohqzGiE6lMjEJNtpi98SVdW9qHdCaHPJhGD55jpKlMFZ+aYRYd8+kRWVTX3kq8UV8mQ8f1jKyuscfV6KGDHnrQ9WOcbdgx7kGtBTHDIVy1AqKcC7muUtL4TH2Sn46m9ASrI/qkYCENDbY3ccFCVkXZzwtUXgEaZwNH6eE0VukYfHuNkhz1++SxsWvR8l+ik1tzvt2hOV4+m8szMX3iep24RrRq+FSXr1Y5sARL753r5L9WjxL51eGINlTi+tThzHqZ0Il/TBHslDzjhFabtDqKvd381Oodw+lAmbNzPM1OyUJGZP8i2J9SmpMR/brvDpgTdLYICdnIELszyr0bn68zEueY9eNGit9qsPMtJlu2IP6Grru6MpqLHDHwPnC6MreNThrkC8bEdaatu13b1bsPIu17Eu4sYYp2rlwm/h/Tp/k182RjbUaghvEJZNrW+Z5HSjEL6qhDu3y1DTJ9XSk/ymV4qqW2+5+V6aOCZDsUcaE8uFv3gXOPrpkXzpIZyZ2t9eF9tCqbi5SnK3rE0Q4oime7P9Q7MMp9hXbJDVpzbZolQ5gF8zyKMH2lLPIq32peRephtLP/C3Wr66LWkGKkbAaXNSTl92OK1lwpE5jVPH+PaTX5tT5b6VXNZ0Jzceys5e+g9VfwaeQ212F0ugWrcJPmAFOwV1Yj3BKt9QjjdbPAy8xMQ8teW352TppebstZ4mu2bjbGPqlN5YBmzWudtTD1s9B44dB4EajDFp01Wi2admOJnomxRUufVobyq8OtVYPyQqQse2QGNQqQ0o2lwqj2RapyjG9Qb0VamyKtDqxW9zTAXfMhSP9aX13d3+W7e6RukW/TIw+M45c+rdIR+VymtTpSYwrI+Ya2r+7qb1MLcu+SBUXK/B4nrhg+depROc0l/Y3e2VKy89YimPeWXuk+xsa2qf7pGnJMayKjdWkQN6hHrOV35YhWLNJVx+eIKPPfIZ+K/Y7qmNntbZ9JVPAnbLzJq8ry4khhQvqXMm/7a9HrvhO/RhQTLrR33QVa9Z8wUmCMyST4PcuMnhDucnySwB5tl+znup3iU7yJI9FVknqp/hhgYzjqtXPdnVtmxGZsv4WeqHX71H09ZH5JMEeJ31lO9Dq0q421j7pcuT4brY7e5YrXVXpYrPC1+lhQHzeysFFeEdNWXwRzYYnqcWFMCJd6o6gjfz3J68jMp1OhlE1vQ7mYaWAb85ziJek9UET4vLvLXm/uY2Ec3TV6XcK61LhFooTZuFTnB1xLi1mp82v7ELeer9yNEmcnKtspDHV3t7D2my1kTNYvUVLOhnu7srcLUYqchWEKPcVv9JbFhy7NL6DgZ6R80aHhGJI7bIJ/u6W21e47eBvipa5zRjOiFrQF/ZXYu6PHWexRraOXDnWXfgiHcB4j0LUk/Yh20rqyM2VZcpd6OP1XZAVmKhaltz3rj8HlIo9knVOd8YzIssmjGSnzXZy6YzEcQkZS5BLOh881pFEMlPlOU70xGOryCIoc6vAw7zGEPXPbuz4vl1O1vta5hPLgXcCcuBgcnvyVxyq2X4iFmjlP5N1zQOswqKBudov/dRyGj+VUn1cot4y+a/Yi4Klzv1hnZNEfrr9mLLeQ2VzOMZxnmo/Oekt+fuz3RbWeVOqM5t3TR3/UzgHDa6k4DypLx3h3Fll5Q6nguYBPhlT9R/3jnPxthJc5jTI56lAy5xTl1EwPmZr5xqVvdOZeiEyWTplMRWo2jmjSG7Hbal/dgt/t3AOs+3Yof5eS/yLW//3ZPrQOyHqYLDpnDtrUFlP2w56i9enavj9bJjG+y8vv9ragBc/CG9SK7/neo/74rm+rMLbyb5DwWr+rUtUvRCSrp3t2XXVhBMWTN84Bme/5RvQuPWex+M2zccDZonl/alWiJd2R3yzoluK7jpQ9mqtTfVaPJwf4hn0nzw9F6nfU1tF2HvdcifNBKeeDFc4ZaafI4bVzr/rdrDIu2w6Xfp47O9H9Uoqz7XledW50p5QLv4NejR9W4IeOlE3S/jFFwjNVnc1bVNBcaJncE9aJMplI1gPGmZ38eVdHticVvE4Cxn+nFH3HkXQPZOlS/juiE7YZ0Uu0bnZJen7TsTqTertCWv09SvrvBp/TT8SVz27oyufX8v9ucHT96rXfX/30wY2NL2/q/3Pwvvql+rW6DGv8M/UlUDtQhwr/38Ff1d/U37eaW2+2/rT1Z+763jmN+YUq/Gz95b8FjqYD</latexit> f(vk) min f n

    = 1000 n = 2000 n = 1000 n = 2000 <latexit sha1_base64="QOIy9kekBqEQ6UQzCbvGdsez0Ko=">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</latexit> n = 100 <latexit sha1_base64="3cpXHthmw5OuOiQU5oNx1CAjNBE=">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</latexit> n = 2000 <latexit sha1_base64="jI0JEeGu+2uDma7ex8sFzukkciU=">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</latexit> f(v) = minv F(u, v) <latexit 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F(u, v) <latexit sha1_base64="5kUsxZ4P8zM9/xGkJ/2V2C/LKo0=">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</latexit> F(u, v) <latexit sha1_base64="jI0JEeGu+2uDma7ex8sFzukkciU=">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</latexit> f(v) = minv F(u, v) <latexit sha1_base64="CYy96L3hGh6w9Y39WO9D0ZB+7YM=">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</latexit> Gradient descent: <latexit sha1_base64="Au88g4t7OzUyeWnS+eqSvKCH11A=">AABC2HictVxLcxvHER45L0t52ckxl01opeSUwlC0HNtxpcriQxQtWKIEkJIlSio8lhCkBRbCAtADZlVuqVxzyjX5I/kdyS9ITvkL6cfMziwwuz3LKNwCOTs7X3dP70xPd8+AnXEyyKYbG/849863vv2d737v3fMXvv+DH/7ox++9/5OjLJ1NuvFhN03Syf1OO4uTwSg+nA6mSXx/PInbw04S3+s838bn9+bxJBuko9b09Th+NGz3R4OTQbc9harHO3E3Hc3TZIZ3v3vy3trG+gb9RKuFK7qwpvTPQfp+9E91rHoqVV01U0MVq5GaQjlRbZXB9VBdURtqDHWP1ALqJlAa0PNYnaoLgJ1BqxhatKH2Ofzuw91DXTuCe6SZEboLXBL4TAAZqYuASaHdBMrILaLnM6KMtWW0F0QTZXsNfzua1hBqp+op1Eo40zIUh32ZqhP1KfVhAH0aUw32rqupzEgrKHnk9GoKFMZQh+UePJ9AuUtIo+eIMBn1HXXbpuf/opZYi/dd3Xam/k1SXoQrUk3d+zSn0FZzoh/R25zBM5YnAc59oBDrPmLpJel6SL0fQfsF1N+C65RKRicduBZUe1qJ3IbLh9wWkXtw+ZB7IrIBlw/ZEJEHcPmQBxqJ2Anp3I9vwuXDN0XOd+DyIe+IyLtw+ZB3ReQRXD7kkYh8AJcP+UBEXofLh7wuIm/C5UPeFJEtuHzIlog8hMuHPBSRu3D5kLsaWT5TJ3ClRGcgzMprUC7yQEuRQM01Ub4tso4+7FbAnO6WYOVZvQN//didAJ3GJdjdgHF3UoKVR94e2Eg/VrZFN2g18WFviNh9GAF+7L6I/VI9K8F+GTDTnpdg5bnWgHZ+rGx9v4I7P/YrEXsLSn6svEbdhho/9nbAijEuwR6I2DvqRQk2xOpPSrCy3W+CXfFj5XWqBe392BBrOivByvb0CDwYP1Zere5BrR97T8TeV69KsPdF7Ndg3f3YrwNW2DclWLPGXqAVpE/+SAwztopaO5+VWBoDtbbAP8nXloR84w7US5h+jukTZigi9nLEXiCikSMawXJluR3NyN+VuTRzRDMQ0cnXJixNxfa9vD2WkgDETo7YWUJUeaT4rk1f5uRdmBoJOc1XLiyF9CnN7TeWYj0eqi2vQdwuIHhsP6WRf5miJYygUFNV1J7mazwjI7qvQryk6M300vCQcdPcKrioVyKq40F1RNRrD+q1iJp5UDMRNfeg5iLKznwXdxwwAqz+8V0s6I5HAPvI5VcEXsE1WHVuwByNYPwcgBd4l2puw98mxd7SVSUZRvO4TmKW41HBEk+gtFBrUG+jwh2KrxOaYTFIxi1v6xgf7zC3sdBzjq3wab6SR3nGJJzOgOTp53TQW4xoPtWjc5NqTsm741I9/I183ptSPfwuafyUvHgu1cNPtfTTM8je0tjWGbBNmE1jrX1brkuD8y9Mw5Qv0KqLFhff6lCPGaT3qib9ff1m9s/wXrapxPqx5Xo0Mqd/WaF/dWhYPWeOnutRQe+JvV5Timr3ZKTjXluuK0NKq+hIy2Hv6r4ZbNPTb8aU69E4AI9rm2LuhVOuO3rHeW9suR6NI8V5z1Py5E25Ho0+3bM+bLkeDcy2tHWcb8t1LTtqgGNnW65r1UeUBcYcEI95rrFe0YT8pJmmNiD/oDpb4/r8q+sY5mwe5zFCNSXr25bT6eRrWbVExl+IwapNa8qB/sXM8cGKNBZqU4yvWIZpYX1fpWPXeNR8A7QYweznPQApZ56AhCYngdY7AYpXxKir2DOD2xRxOEpOllDHunYqeouWL2eNinVPqFaKy2xvrR6PyV5nNPbG5BM2SLOSHhqlb7iMoqShRkFDMr06unuj52tR+xsibryEGOcjrUs7QryTVh2n+rTedHR8Ue/yTOHiPR87fjHbfKKtDcY8KdkilKWKp9vO5JHcOlxXLyub4+ZnEb1RtFdzshoD2pHKxCjUZIvZG1/QvaV9SHtyyINpdOE9RprKWPGuGWbRMZ8ekUV17a3EG/VlMnRczsjqGntcje476L4HXT/G2YYV4xaUWhAzHMJdKyDKuZDrKiWNT9Sv893RlN5gdUSfFCykocH2Ji5YyKoo+2mByktA42jgKD2cxjIdgz9eoSRH/T55bOxatPwXaefW7G+3aYyXj+byTEyPuG4S14hmDe/q8t0yB5Zg4X2ySf5rdS+RXx2OaEMlro8dzqyXEe34xxTBjskzTmi2SbOj2NrNTy0/MZwOlNk7x93slCxkRPYvgvUppTEZ0cc9O2B20NkiJGQjQ+zOIPdufL7OQBxj1o8bKD7VYMdbTLZsRvwNXXd2ZTQWOWLgdeB0aWwbnTTIF4yJ60Rbdzu3q1cfRNpzEu4oYYp2rFwi/h/Sb/Mx42RtZUSghvENZNrW+d5HSjEL6qhNq3y1DTJtXSk/yGV4rKW265+V6YOCZDsUcaE8uFr3gHOX7pkXjpIJyZ2ttOF1tCqbi5THS3rE3p5QFM92v69XYJT7Mq2SazTnjmmU9GEUTPMowrSVssjLfKt5FamH0c7+L9StrotaQ4qRshlc1pCU348pWnOlTGBU8/h9TrPJr/XJUqtqPiMai0NnLn8DtT+H30Zucx9Gp1OwCls0BpiCvbMa4ZpopUUYr60CLzMyDS17b/nZMWlauTVnia/ZutkYe16bygGNmlc6a2HKZ6HxzKHxLFCHLdprtFo09cYSPRFji5berQzlV4dbqwblmUhZ9sgMahAgpRtLhVHtiVTlGN+g3oi0NkRabZit7m6AO+dDkP65vjy7v8lX90hdJ9+mSx4Yxy89mqUD8rlMbXWkxhSQ81VtX93Zf0w1yL1DFhQp8zlOnDG869Sl6zSX9Jd6ZUvJzluLYM4tvdRtjI09pvJHK8ghzYmM5qVBXKUWsZbflSNaskjrjs8RUea/TT4V+x3VMbPb2r6TqOBP2HiTZ5XlxZHCiPQvZd72V6LXfSd+jSgmnGnvugO06r9hpMAYk0nwe5YZvSFc5XgngT3aDtnPVTvFu3gjR6J1knqhfh9gYzjqtWPdHVumx6Zvv4KWqHX71n0tZH5JMEeJ31l29Nq0qg21j7pYuj8brbZe5Yr3VXqYLfG1+phRGzeysFFeEXOsPg/mwhLV48KYEC71elFH/nqS15GZd6dCKZvWhnIx08A25inFS9I5UET4vLtLXm/uQ6EfnRV6HcK61LhGooTZuFTnB1xLi1mp8yvrENeer1yNEmclKlspDHV3tbD2my1kTNYvUVLOhlu7sh8XohQ5C8MUuopP9JbFhy7Nz+HC35HyRYeGY0jusAn+7TW1rXbfwmmIF7rMGc2IatAW9JZi77buZ7FFtY5eONRd+iEcwnkMQNeS9ANaSevKzpRlyV3q4fRfkhWYqFiU3ras3weXi9yTVU51+jMgyyb3ZqDMd3Hq9sVwCOlJkUs4H97XkHpxosx3mur1wVCXe1DkUIeHOccQ9s5t6/q8XE7V+lrlEsqDVwGz42JwuPNXHqvYdiEWauK8kbfPAa3DSQV1s1r8r/0wfCyn+rxCuWX0XbNnAW+d28U6I4v+cP05Y7mFjOZyjuE807x31lvy82O/L6r1plKnN2+fPvqjdgwYXgvFeVBZOsa7o8jKG0oF9wV8MqTqP+rv5+RvI7zIaZTJUYeS2acop2ZayNTMNy59vTPPQmSydMpkKlKzcUSTTsRuq311HT7buQdY93Qof5eS/yLW//3ZHtSekPUwWXTOHBxTXUzZD7uL1qN7e362TGI8y8tne1tQg3vhDarFc763qD2e9W0V+lb+DRKe61+pVPUKEcny7p6dVx3oQXHnjXNA5nu+EZ2l5ywWnzwbBuwtmvNTyxIt6Il8sqBTiu84UnZprI71Xj3uHOAJ+3aeH4rUb6iure08rrkS54NSzgdLnDPSTpHDK+dZ9dmsMi7bDpdenjub63Ypxdl2P686N7pTyoXPoFfj+xX4viNlk7T/nCLhiarO5s0qaM60TO4O60iZTCTrAePMdv6+qyPbeQWveUD/b5aibzqS7oEsHcp/R7TDNiF6idbNLknPJx2rM6k3KqQ136OUv53N34jgzIT5bwMPKTPVITuwoS7TZ119Ci1nQXNxLtBEWpc15VOt2eqciT1hWUX141zWjxXmkAwKqNP/efiMfiIufHJVFz67kv+fh6PN9Su/Xf/ozubaF1v6Pz68q36mfqEugbX7RH0Bej1Qh7RP+xf1V/W3rQdbf9j649afuOk75zTmp6rws/Xn/wK359mb</latexit> Deconvolution:
  33. From Gradient to Quasi-Newton <latexit sha1_base64="vroLI/5T1AopQPnYeJhwA76BFSg=">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</latexit> f(vk) min f n

    = 1000 n = 2000 n = 1000 n = 2000 <latexit sha1_base64="QOIy9kekBqEQ6UQzCbvGdsez0Ko=">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</latexit> n = 100 <latexit sha1_base64="3cpXHthmw5OuOiQU5oNx1CAjNBE=">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</latexit> n = 2000 <latexit sha1_base64="jI0JEeGu+2uDma7ex8sFzukkciU=">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</latexit> f(v) = minv F(u, v) <latexit 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F(u, v) <latexit sha1_base64="5kUsxZ4P8zM9/xGkJ/2V2C/LKo0=">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</latexit> F(u, v) <latexit sha1_base64="jI0JEeGu+2uDma7ex8sFzukkciU=">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</latexit> f(v) = minv F(u, v) <latexit 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Gradient descent: <latexit 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f is smooth ! use quasi-Newton <latexit sha1_base64="RMkXZkwvehZD3q+xy6xqk11m5Ek=">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</latexit> vk+1 = vk ⌧kBk rf(vk) <latexit sha1_base64="QyIaoHK+hiZ/4Y8cMaEmN1MqY8w=">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</latexit> Near non-degenerate solution: linear convergence. <latexit sha1_base64="EHakCRPUEZpBoZKDstsegQO1Lb4=">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</latexit> Bk ⇡ [@2f(vk)] 1 <latexit sha1_base64="HTLKOuJkxWeE1rsasMwj47zrYLg=">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</latexit> Bk+1(rf(vk+1) rf(vk)) = vk+1 vk <latexit 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Secant condition: <latexit sha1_base64="gipnqoPLTsCk44yFLciKrxeTv0M=">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</latexit> B0 = Id <latexit 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Bk+1 = Bk + hh> <latexit 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Rank-1 update: <latexit sha1_base64="7buY6ZIT4AOYrvUqW5N6ae4pBQI=">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</latexit> rf(vk+1) rf(vk) = ⌧@2f(vk)(vk+1 vk) + o(||vk+1 vk ||) <latexit 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Deconvolution:
  34. Lasso a8a (22696, 122) ⇤ 1 2 max 1 10

    max 1 50 max 35 / 4 <latexit sha1_base64="PqFYzLxTYQ8pS/3B9SQCpxNKEDY=">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</latexit> a8a, (n, d) = (22696, 122) <latexit sha1_base64="8zhSvP8gFRtnm+2PthhVHxufP7E=">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</latexit> (UCI/Adult, income prediction)
  35. Lasso Leukemia (38, 7129) ⇤ 1 2 max 1 10

    max 1 50 max <latexit 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Leukemia (n, d) = (38, 7129) <latexit 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[Golub et al. 1999] <latexit 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Molecular classification of cancer
  36. Group Lasso - MEG+EEG umerics: Group Lasso = 1 2

    max = 1 10 max = 1 100 max Numerics: Group Lasso Multitask Lasso: given X 2 Rm⇥n, Y 2 Rm⇥q min W 2Rn⇥q kXW Y k 2 F + X i kWi k2 where Wi is ith row of W . MEG/EEG brain imaging example⇤: • X forward operator with n = 22494 source locations, and 301 MEG sensors and 59 EEG sensors. So m = 360. • Y time-series measurements. Each sensor measures q = 181 timepoints. • Goal is to recover W which locates the source locations. ⇤Eugene Ndiaye et al. “Gap safe screening rules for sparse multi-task and multi-class models”. In: arXiv preprint arXiv:1506.03736 (2015). <latexit sha1_base64="aXFgc7mGYZ+Od6wQulGb68VM4YU=">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</latexit> Group in time, |g| = 181. <latexit 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d = 2294 ⇥ 181 <latexit sha1_base64="NttSvvqx/DB7uFarYEvxd0lppOI=">AABB1HictVxbcxPJFW42t4Xc2M1jXibxkmJThNhA7aW2tmqNbYwXLRgkG3ZXQOkyFoKRRmgkYxB+SuU1PyGvyb/I78g/SJ7yF3Iu3dM9Us+cHofQZbun1d85p890nz7ndIvuJBlms/X1f5577wc//NGPf/L++Qs//dnPf/HLix98eJil82kvPuilSTp91O1kcTIcxwez4SyJH02mcWfUTeKH3Rdb+PnD43iaDdNxa/Z6Ej8edQbj4dGw15lB09OLH46jL6Prn6xH7dlwFGfRxmcbTy+urV9dp3/RamVDV9aU/reffhAdqLbqq1T11FyNVKzGagb1RHVUBuV7taHW1QTaHqsFtE2hNqTPY3WqLgB2Dr1i6NGB1hfwewBP3+vWMTwjzYzQPeCSwM8UkJG6BJgU+k2hjtwi+nxOlLG1jPaCaKJsr+FvV9MaQetMPYNWCWd6huJwLDN1pD6jMQxhTBNqwdH1NJU5aQUlj5xRzYDCBNqw3ofPp1DvEdLoOSJMRmNH3Xbo839RT2zF557uO1f/JikvQYlUU48+zSl01DHRj+htzuEzlicBzgOgEOsxYu0V6XpEox9D/wW034VySjWjky6UBbWeViK3oPiQWyJyF4oPuSsiG1B8yIaI3IfiQ+5rJGKnpHM/vgnFh2+KnO9D8SHvi8gHUHzIByLyEIoPeSgiv4PiQ34nIm9B8SFvicg7UHzIOyKyBcWHbInIAyg+5IGI3IHiQ+5oZPlKnUJJic5QWJWbUC/yQEuRQMumKN9Nso4+7M2ANd0rwcqrehv++rHbATqNS7A7AfPuqAQrz7xdsJF+rGyLbtNu4sPeFrF7MAP82D0R+7V6XoL9OmClvSjBymutAf38WNn6fgNPfuw3IvYu1PxYeY+6By1+7L2AHWNSgt0XsffVyxJsiNWflmBlu98Eu+LHyvtUC/r7sSHWdF6Cle3pIXgwfqy8Wz2EVj/2oYh9pE5KsI9E7Ldg3f3YbwN22DclWLPHXqAdZED+SAwrtopaJ1+VWJsAtY7AP8n3loR84y60S5hBjhkQZiQidnPEbiCikSMawXJluR3NyN+VuTRzRDMQ0c33JqzNxP79vD/WkgDEdo7YXkJUeaT4rs1Yjsm7MC0ScpbvXFgLGVOa22+sxXo+VFteg7hXQPDcfkYz/wpFSxhBoaaqqD3L93hGRvRchXhF0ZsZpeEh42a5VXBRJyKq60F1RdRrD+q1iJp7UHMRdexBHYsou/JdXDtgBlj947tY0BPPAPaRy0sEXsEm7Dq3YY1GMH/2wQt8QC334G+TYm+pVEmG0Tzuk5jleFywxFOoLdQatNuocJvi64RWWAyScc97OsbHJ8xtLPSaYyt8mu/kUZ4xCaczJHkGOR30FiNaT/Xo3KGWU/LuuFYPfztf96ZWD79DGj8lL55r9fAzLf3sDLK3NLZ1BmwTVtNEa9/W69Lg/AvTMPULtOuixcW3OtJzBumd1KS/p9/M3hneyxbVWD+2Xo9G5owvK4yvDg2r58zRcz0q6D2x12tqUe2RjHXca+t1ZUhpFx1rOexT3TeDffr6zZh6PRr74HFtUcy9cOp1Z+8kH42t16NxqDjveUqevKnXozGgZ9aHrdejgdmWjo7zbb2uZUcNcOxs63Wt+piywJgD4jnPLdYrmpKfNNfUhuQfVGdrXJ9/dR/DnM2TPEaopmR923I63Xwvq5bI+AsxWLVZTTnQv5g7PliRxkJdE+MrlmFW2N9X6dg9HjXfAC1GsPr5DEDKmScgoclJoPVOgOKGGHUVR2Zw10QczpKjJVRbt85Eb9Hy5axRse0ptUpxmR2t1WOb7HVGc29CPmGDNCvpoVH6hssoShpqFDQk06ujuzd6vRa1vy7iJkuIST7TenQixCdp1XGqT+tNR8eX9CnPDAqf+dj5i9nmI21tMOZJyRahLFU83X4mj+S24b56RdkcN38W0RtFe3VMVmNIJ1KZGIWabDF74wt6trQP6EwOeTCNHrzHSFOZKD41wyw65tMjsqiuvZV4o75Mho7rGVldY4+r0QMHPfCg68c4W7Bj3IVaC2KGA3hqBUQ5F3JdpaTxqfpDfjqa0husjuiTgoU0NNjexAULWRVlPytQeQVonA0cpYfTWKZj8O0VSnLU75PHxq5Fy3+JTm7N+XaH5nj5bC7PxPSJ6zXiGtGq4VNdflrmwBIsvJ9cI/+1epTIrw5HtKES1ycOZ9bLmE78Y4pgJ+QZJ7TapNVR7O3mp5Y/MZz2lTk7x9PslCxkRPYvgv0ppTkZ0Y97d8CcoLNFSMhGhtidYe7d+HydoTjHrB83VHyrwc63mGzZnPgbuu7qymgucsTA+8Dp0tw2OmmQLxgT16m27nZtV+8+iLT3JNxZwhTtXLlM/D+m3+bHzJO1lRmBGsY3kGlb53sfKcUsqKMO7fLVNsj0daX8KJfhiZba7n9Wpo8Kkm1TxIXy4G7dB849emZeOEumJHe20of30apsLlKeLOkRR3tEUTzb/YHegVHuK7RLrtGaa9MsGcAsmOVRhOkrZZGX+VbzKlIPo539X6hbXRe1hhQjZTO4rCEpvx9TtOZKmcCs5vn7glaTX+vTpV7VfMY0F0fOWn4Lrb+B30Zu8xxGp1uwCjdpDjAF+2Q1wi3RSo8wXjcLvMzMNLTss+Vn56Tp5bacJb5m62Zj7OPaVPZp1pzorIWpn4XGc4fG80Adtuis0WrRtBtL9FSMLVr6tDKUXx1urRqU5yJl2SMzqGGAlG4sFUa1L1KVY3yDeiPSWhdpdWC1uqcB7poPQfrX+vLqfpvv7pG6Rb5Njzwwjl/6tEqH5HOZ1upIjSkg5xvavrqrv00tyL1LFhQp8z1OXDF86tSjcppL+ju9s6Vk561FMPeWXuk+xsa2qX59BTmiNZHRujSIG9Qj1vK7ckRLFumq43NElPnvkE/Ffkd1zOz2tu8kKvgTNt7kVWV5caQwJv1Lmbe9leh1z4lfI4oJ59q77gKt+m8YKTDGZBL8nmVGbwh3OT5JYI+2S/Zz1U7xKd7YkegqSb1QXwbYGI567Vx355YZsRnb76Enat2+dV8PmV8SzFHid5YTvQ7taiPtoy6Wns9Gq6N3ueJzlR7mS3ytPubUx40sbJRXxLTVF8FcWKJ6XBgTwqXeKOrIX0/yOjLz6VQoZdPbUC5mGtjGPKN4SboHigifd3fZ6819LIyju0KvS1iXGrdIlDAbl+r8gGtpMSt1fmUf4tbzlbtR4uxEZTuFoe7uFtZ+s4WMyfolSsrZcG9X9nYhSpGzMEyhp/hGb1l86NL8Agr+jpQvOjQcQ3KHTfBvN9WW2nkHtyFe6jpnNCNqQVvQX4q9O3qcxR7VOnrpUHfph3AI5zEEXUvSD2knrSs7U5Yld6mH039FVmCqYlF627P+GFwu8khWOdUZz5AsmzyaoTLfxak7FsMhZCRFLuF8+FxDGsWRMt9pqjcGQ10eQZFDHR7mHkPYO7e96/NyOVXra5VLKA/eBcyJi8HhyV95rGL7hVioqfNG3j0HtA5HFdTNbvG/jsPwsZzq8wrlltF3zZ4HvHXuF+uMLPrD9deM5RYym8s5hvNM89FZb8nPj/2+qNabSp3RvHv66I/aOWB4LRTnQWXpGO/OIitvKBU8F/DJkKr/qH+ck7+N8DKnUSZHHUrmnKKcmukhUzPfuPSNznwWIpOlUyZTkZqNI5p0I3ZL7alb8LOVe4B1b4fydyn5L2L935/tQ+sRWQ+TRefMQZvaYsp+2FO0Pj3b+7NlEuNdXr7b24IWPAtvUCve871L/fGub6swtvJvkPBa/0alql+ISJZP9+y66sIIiidvnAMy3/ON6C49Z7H45tko4GzR3J9almhBn8g3C7ql+K4jZY/m6kSf1ePJAd6w7+T5oUj9kdo62s7jnitx3i/lvL/EOSPtFDmcOJ9V380q47LlcOnnubNj3S+lONue51XnRrdLufAd9Gr8oAI/cKRskvZfUCQ8VdXZvHkFzbmWyT1hHSuTiWQ9YJzZyd93dWR7XMHrOGD8d0rRdxxJd0GWLuW/IzphmxK9ROtmh6Tnm47VmdTbFdLq71HS/27wOf2LuPLpDV35fCP/3w0Or13d+OTq9fs31r66qf+fg/fVr9Vv1WVY45+qr4DavjoADifqr+pv6u+bh5tvN/+0+Wfu+t45jfmVKvzb/Mt/AS4epnM=</latexit> n = 360 ⇥ 181 <latexit 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⇢ <latexit 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MEG <latexit 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EEG <latexit 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2294 sources locations <latexit 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301 MEG + 59 EEG sensors <latexit 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A
  37. Multi-task Learning <latexit sha1_base64="DhLkAtbU0kY3ysITcMgItDnmzxk=">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</latexit> min X=(xt)T t=1 1 2 T

    X t=1 ||Atxt yt ||2 + ||X||⇤ merical experiments on 3 datasets Schools Parkinsons SARCOS T = 139 T = 42 T = 7 m = 15, 362 m = 5875 m = 48, 933 merical experiments on 3 datasets Schools Parkinsons SARCOS T = 139 T = 42 T = 7 m = 15, 362 m = 5875 m = 48, 933 merical experiments on 3 datasets Schools Parkinsons SARCOS T = 139 T = 42 T = 7 m = 15, 362 m = 5875 m = 48, 933 Numerical experiments on 3 datasets Schools Parkinsons T = 139 T = 42 m = 15, 362 m = 5875 n = 27 n = 19 Convergence plots for multi-task feature learnin IRLS-d corresponds to IRLS with " = 10 d . <latexit 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Schools <latexit 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SARCOS <latexit sha1_base64="8Dv15pnDEWBKz4H8pD812NlbJ1A=">AABB2HictVxbcxS5FRab20JubFKVl7x04iUFWw6xDVlCbW3VGtsYLwYGZmxY1kDNpT0MtKeH6RlzGVyVt1Re8xPymvyH/I78g+QpfyHnIrXUM+o+aoegsq3W6Dvn6LR0dM6Rhs4oGWSTlZV/nvnoO9/93vd/8PHZcz/80Y9/8tPzn/xsP0un4268102TdPyo087iZDCM9yaDSRI/Go3j9lEniR92Xm7g5w+P43E2SIetydtR/OSo3R8ODgfd9gSanp3/xcXW8nC5d+nLi6tXri+v/v7K52vLa9cuPTu/tHJ5hf5Fi5VVXVlS+l8j/STaUweqp1LVVVN1pGI1VBOoJ6qtMijfqlW1okbQ9kTNoG0MtQF9HqsTdQ6wU+gVQ482tL6E3314+la3DuEZaWaE7gKXBH7GgIzUBcCk0G8MdeQW0edTooytZbRnRBNlewt/O5rWEbRO1HNolXCmZygOxzJRh+oPNIYBjGlELTi6rqYyJa2g5JEzqglQGEEb1nvw+RjqXUIaPUeEyWjsqNs2ff4v6omt+NzVfafq3yTlBSiRaurRpzmFtjom+hG9zSl8xvIkwLkPFGI9Rqy9Jl0f0eiH0H8G7XehnFDN6KQDZUatJ5XIDSg+5IaI3IbiQ26LyF0oPuSuiGxA8SEbGonYMencj29C8eGbIuf7UHzI+yLyARQf8oGI3IfiQ+6LyMdQfMjHIvImFB/ypoi8DcWHvC0iW1B8yJaI3IPiQ+6JyC0oPuSWRpav1DGUlOgMhFW5DvUiD7QUCbSsi/LdIOvow94IWNPdEqy8qjfhrx+7GaDTuAS7FTDvDkuw8szbBhvpx8q26BbtJj7sLRG7AzPAj90RsV+rFyXYrwNW2ssSrLzWdqGfHytb3zvw5MfeEbF3oebHynvUPWjxY+8F7BijEmxDxN5Xr0qwIVZ/XIKV7X4T7IofK+9TLejvx4ZY02kJVran++DB+LHybvUQWv3YhyL2kXpTgn0kYr8B6+7HfhOww74rwZo99hztIH3yR2JYsVXU2vmqxNoIqLUF/km+tyTkG3egXcL0c0yfMEciYjtHbAcidnPEbrBcWW5HM/J3ZS7NHNEMRHTyvQlrE7F/L++PtSQAsZkjNucQVR4pvmszlmPyLkyLhJzkOxfWQsaU5vYba7GeD9WW1yDuFRA8t5/TzF+maAkjKNRUFbXn+R7PyIieqxCvKXozozQ8ZNwktwou6o2I6nhQHRH11oN6K6KmHtRURB17UMciyq58F3cQMAOs/vFdzOiJZwD7yOUlAq9gHXadW7BGI5g/DfACH1DLPfjbpNhbKlWSYTSP+yRmOZ4ULPEYajO1BO02Ktyk+DqhFRaDZNzzno7x8QlzGzO95tgKn+Q7eZRnTMLpDEiefk4HvcWI1lM9Orep5YS8O67Vw9/K172p1cNvkcZPyIvnWj38REs/OYXsLY1tnQLbhNU00tq39bo0OP/CNEz9HO26aHHxrR7pOYP03tSkv6PfzM4p3ssG1Vg/tl6PRuaMLyuMrw4Nq+fM0XM9Kug9sddralHtkQx13GvrdWVIaRcdajnsU903g316+s2Yej0aDfC4Nijmnjn1urN3lI/G1uvR2Fec9zwhT97U69Ho0zPrw9br0cBsS1vH+bZe17KjBjh2tvW6Vn1IWWDMAfGc5xbrFY3JT5pqagPyD6qzNa7Pv7iPYc7maR4jVFOyvm05nU6+l1VLZPyFGKzapKYc6F9MHR+sSGOm1sT4imWYFPb3RTp2j0fN74IWI1j9fAYg5cwTkNDkJNB6J0BxVYy6iiMzuDURh7PkcA51oFsnordo+XLWqNj2jFqluMyO1urxgOx1RnNvRD7hLmlW0sNu6RsuoyhpaLegIZleHd290+u1qP0VETeaQ4zymdalEyE+SauOU31abzo6vqBPeSZQ+MzHzl/MNh9qa4MxT0q2CGWp4un2M3kktw331WVlc9z8WURvFO3VMVmNAZ1IZWIUarLF7I3P6NnS3qMzOeTBNLrwHiNNZaT41Ayz6JhPj8iiuvZW4o36Mhk6rmdkdY09rkb3HXTfg64f42zAjnEXai2IGfbgqRUQ5ZzLdZWSxsfqt/npaEpvsDqiTwoW0tBgexMXLGRVlP28QOU1oHE2cJQeTmOejsEfLFCSo36fPDZ2LVr+C3Rya8632zTHy2dzeSamR1zXiGtEq4ZPdflpngNLMPN+skb+a/UokV8djmhDJa5PHc6slyGd+McUwY7IM05otUmro9jbzU/Nf2I4NZQ5O8fT7JQsZET2L4L9KaU5GdGPe3fAnKCzRUjIRobYnUHu3fh8nYE4x6wfN1B8q8HOt5hs2ZT4G7ru6spoLnLEwPvAydzcNjrZJV8wJq5jbd3t2q7efRBp70m4s4Qp2rlykfhfot/mx8yTpYUZgRrGN5BpW+d7HynFLKijNu3y1TbI9HWl/DSX4amW2u5/VqZPC5JtUsSF8uBu3QPOXXpmXjhLxiR3ttCH99GqbC5SHs3pEUd7SFE82/2+3oFR7mXaJZdozR3QLOnDLJjkUYTpK2WR5/lW8ypSD6Od/V+oW10XtYYUI2UzuKwhKb8fU7TmSpnArOb5+5JWk1/r47le1XyGNBePnLX8Hlp/Bb+N3OY5jE6nYBVu0BxgCvbJaoRbooUeYbxuFHiZmWlo2WfLz85J08ttOU18zdbNxtjHtak0aNa80VkLUz8NjRcOjReBOmzRWaPVomk3luiZGFu09GllKL863Fo1KE9FyrJHZlCDACndWCqMak+kKsf4BvVOpLUi0mrDanVPA9w1H4L0r/X51f0+390jdZN8my55YBy/9GiVDsjnMq3VkRpTQM5XtX11V/8BtSD3DllQpMz3OHHF8KlTl8pJLulv9M6Wkp23FsHcW3qt+xgbe0D1KwvII1oTGa1Lg7hKPWItvytHNGeRLjs+R0SZ/zb5VOx3VMfMbm/7TqKCP2HjTV5VlhdHCkPSv5R521mIXnec+DWimHCqvesO0Kr/hpECY0wmwe9ZZvSGcJfjkwT2aDtkPxftFJ/iDR2JLpPUM/VlgI3hqNfOdXdumRGbsX0GPVHr9q37esj8kmCOEr/TnOi1aVc70j7qbO75dLTaepcrPlfpYTrH1+pjSn3cyMJGeUXMgfoimAtLVI8LY0K41BtFHfnrSV5HZj6dCqVsehvKxUwD25jnFC9J90AR4fPuLnq9uUvCODoL9DqEdalxi0QJs3Gpzg+4lhazUmcX9iFuPVu5GyXOTlS2Uxjq7m5h7TdbyJisX6KknA33dmU/KEQpchaGKXQV3+gtiw9dml9Awd+R8kWHhmNI7rAJ/u262lBbH+A2xCtd54xmRC1oC3pzsXdbj7PYo1pHrxzqLv0QDuE8BqBrSfoB7aR1ZWfKsuQu9XD6r8kKjFUsSm971h+Dy0UeySKnOuMZkGWTRzNQ5rs4dcdiOISMpMglnA+fa0ijOFTmO031xmCoyyMocqjDw9xjCHvntnd9Xi6nan0tcgnlwbuAOXExODz5K49VbL8QCzV23siH54DW4bCCutkt/tdxGD6WU31eodwy+q7Zi4C3zv1inZFFf7j+mrHcQmZzOcdwnmk+Oust+fmx3xfVelOpM5oPTx/9UTsHDK+Z4jyoLB3j3Vlk5Q2lgucCPhlS9R/1jzPytxFe5TTK5KhDyZxTlFMzPWRq5huXvtGZz0JksnTKZCpSs3FEk27EbqgddRN+NnIPsO7tUP4uJf9FrP/7sz1oPSTrYbLonDk4oLaYsh/2FK1Hz/b+bJnEeJeX7/a2oAXPwnepFe/53qX+eNe3VRhb+TdIeK3fUanqFSKS+dM9u646MILiyRvngMz3fCO6S89ZLL55dhRwtmjuT81LNKNP5JsFnVJ8x5GyS3N1pM/q8eQAb9i38/xQpH5HbW1t53HPlTg3Sjk35jhnpJ0ihzfOZ9V3s8q4bDhcennu7Fj3SynOtud51bnRzVIufAe9Gt+vwPcdKZuk/ZcUCY9VdTZvWkFzqmVyT1iHymQiWQ8YZ7bz910d2R5X8DoOGP/tUvRtR9JtkKVD+e+ITtjGRC/Rutki6fmmY3Um9VaFtPp7lPS/G1ynfxFXrl3Vleur+f9usL92efXzy1fuX1366ob+fw4+Vr9Uv1YXYY1fU18BtYbaAw7v1V/V39Tf1x+v/3H9T+t/5q4fndGYn6vCv/W//BejL6Z7</latexit> (T, n, d) = (139, 15362, 27) <latexit sha1_base64="qocYY1OkY5j/EKAP9WXtxgBo+Y0=">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</latexit> (T, n, d) = (42, 5875, 19) <latexit sha1_base64="tBtEbGBCy+yU3HVleG2SawatY8Y=">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</latexit> (T, n, d) = (7, 48933, 21) <latexit 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Parkinson <latexit 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n students <latexit 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T robot harms <latexit 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d joints positions <latexit 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T patients <latexit 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d bio-medical features <latexit 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y=symptoms <latexit 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y=exam scores <latexit 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y=motor
  38. Earthmover distance on graphs (200, 588), (428, 1266) (7 W1

    Optimal Transport <latexit sha1_base64="xj77qPmiy85Yk1seYF68A/Z/TsY=">AABB7HictVzNchvHER45f5byJyfHXDahlJJdikLSqjgul6tMkRRFi5IoAaRkG5IKCywhSEsshAWoH5jvkENuqVzzCLk6r5E3SE55hfTPzM4sMLs9yyiaIjk7mK+7p3emp7tnoHicDvPp6uo/z733ve//4Ic/ev/8hR//5Kc/+/nFD35xmGezSS856GVpNnkUd/MkHY6Sg+lwmiaPxpOkexynycP4xSZ+/vAkmeTDbNSevhknj4+7g9HwaNjrTqHp6cWPHl56unalQ4Tmk6R/GnW66dVIN8TpLDntxMmH0eeXoqcXV1avrdK/aLmypisrSv/bzz6IDlRH9VWmemqmjlWiRmoK9VR1VQ7lG7WmVtUY2h6rObRNoDakzxN1qi4Adga9EujRhdYX8HsAT9/o1hE8I82c0D3gksLPBJCRugyYDPpNoI7cIvp8RpSxtYr2nGiibG/gb6xpHUPrVD2DVglneobicCxTdaT+SGMYwpjG1IKj62kqM9IKSh45o5oChTG0Yb0Pn0+g3iOk0XNEmJzGjrrt0uf/op7Yis893Xem/k1SXoYSqZYefVZQ6KoToh/R25zBZyxPCpwHQCHRY8TaK9L1MY1+BP3n0H4XyinVjE5iKHNqPa1FbkLxITdF5A4UH3JHRO5B8SH3ROQ+FB9yXyMROyGd+/EtKD58S+R8H4oPeV9EPoDiQz4QkYdQfMhDEfk1FB/yaxF5E4oPeVNE3obiQ94WkW0oPmRbRB5A8SEPROQ2FB9yWyOrV+oESkZ0hsKq3IB6mQdaihRaNkT5bpB19GFvBKzpXgVWXtVb8NeP3QrQaVKB3Q6Yd0cVWHnm7YCN9GNlW3SLdhMf9paI3YUZ4Mfuitgv1fMK7JcBK+1FBVZea3vQz4+Vre8dePJj74jYu1DzY+U96h60+LH3AnaMcQV2X8TeVy8rsCFWf1KBle1+C+yKHyvvU23o78eGWNNZBVa2p4fgwfix8m71EFr92Ici9pF6XYF9JGK/Auvux34VsMO+rcCaPfYC7SAD8kcSWLF11LrFqsTaGKh1Bf5psbek5BvH0C5hBgVmQJhjEbFTIHYCEXsFYi9Yrrywozn5uzKXVoFoBSLiYm/C2lTs3y/6Yy0NQGwViK0FRJ1Hiu/ajOWEvAvTIiGnxc6FtZAxZYX9xlqi50O95TWIeyUEz+1nNPOvUrSEERRqqo7as2KPZ2REz3WIVxS9mVEaHjJuWlgFF/VaRMUeVCyi3nhQb0TUzIOaiagTD+pERNmV7+I6ATPA6h/fxZyeeAawj1xdIvAKNmDXuQVrNIL5sw9e4ANquQd/WxR7S6VOMozmcZ/ELMfjkiWeQG2uVqDdRoVbFF+ntMISkIx73tMxPj5hbmOu1xxb4dNiJ4+KjEk4nSHJMyjooLcY0XpqRuc2tZySd8e1Zvhbxbo3tWb4bdL4KXnxXGuGn2rpp2eQva2x7TNgW7Caxlr7tt6UBudfmIapX6BdFy0uvtVjPWeQ3uuG9Hf1m9k9w3vZpBrrx9ab0cid8eWl8TWhYfWcO3puRgW9J/Z6TS1qPJKRjnttvakMGe2iIy2HfWr6ZrBPX78ZU29GYx88rk2KuedOvensHRejsfVmNA4V5z1PyZM39WY0BvTM+rD1ZjQw29LVcb6tN7XsqAGOnW29qVUfURYYc0A857nFekUT8pNmmtqQ/IP6bI3r8y/vY5izeVLECPWUrG9bTScu9rJ6iYy/kIBVmzaUA/2LmeODlWnM1boYX7EM09L+vkzH7vGo+T3QYgSrn88ApJx5ChKanARa7xQorolRV3lkBrcu4nCWHC2gOrp1KnqLli9njcptT6lVisvsaK0eO2Svc5p7Y/IJ90izkh72Kt9wFUVJQ3slDcn0mujurV6vZe2virjxAmJczLQenQjxSVp9nOrTesvR8WV9yjOFwmc+dv5itvlIWxuMeTKyRShLHU+3n8kjuW24r15VNsfNn0X0RtFenZDVGNKJVC5GoSZbzN74nJ4t7QM6k0MeTKMH7zHSVMaKT80wi4759IgsqmtvJd6oL5Oh43pOVtfY43r0wEEPPOjmMc4m7Bh3odaGmOEAntoBUc6FQlcZaXyiflecjmb0Busj+rRkIQ0NtjdJyULWRdnPSlReARpnA0fp4TQW6Rh8Z4mSHPX75LGxa9nyX6aTW3O+3aU5Xj2bqzMxfeK6TlwjWjV8qstPixxYgrn3k3XyX+tHifyacEQbKnF94nBmvYzoxD+hCHZMnnFKq01aHeXebn5q8RPDaV+Zs3M8zc7IQkZk/yLYnzKakxH9uHcHzAk6W4SUbGSI3RkW3o3P1xmKc8z6cUPFtxrsfEvIls2Iv6Hrrq6c5iJHDLwPnC7MbaOTPfIFE+I60dbdru363QeR9p6EO0uYop0rV4j/h/Tb/Jh5srI0I1DD+AZybet87yOjmAV11KVdvt4Gmb6ulJcKGZ5oqe3+Z2W6VJJsiyIulAd36z5w7tEz88JZMiG586U+vI/WZXOR8nhBjzjaI4ri2e4P9A6Mcl+lXXKF1lyHZskAZsG0iCJMXymLvMi3nleZehjt/P9C3eq6rDWkGCmbwWUNSfn9hKI1V8oUZjXP3xe0mvxanyz0quczorl47Kzlb6H11/DbyG2ew+jEJatwg+YAU7BPViPcEi31CON1o8TLzExDyz5bfnZOml5uy1nia7ZuNsY+aUxln2bNa521MPWz0Hju0HgeqMM2nTVaLZp2Y4meirFFW59WhvJrwq3dgPJMpCx7ZAY1DJDSjaXCqPZFqnKMb1BvRVqrIq0urFb3NMBd8yFI/1pfXN3fFrt7pG6Sb9MjD4zjlz6t0iH5XKa1PlJjCsj5urav7urvUAtyj8mCImW+x4krhk+delROC0l/q3e2jOy8tQjm3tIr3cfY2A7VP15CHtOayGldGsR16pFo+V05ogWLdM3xOSLK/HfJp2K/oz5mdnvbdxKV/Akbb/Kqsrw4UhiR/qXM2+5S9LrrxK8RxYQz7V3HQKv5G0YKjDGZBL9nmdMbwl2OTxLYo43Jfi7bKT7FGzkSXSOp5+rzABvDUa+d6+7cMiM2Y/sIeqLW7Vv39ZD5pcEcJX5nOdHr0q52rH3U+cLz2Wh19S5Xfq7Tw2yBr9XHjPq4kYWN8sqYjvosmAtL1IwLY0K4NBtFE/mbSd5EZj6dCqVsehvK5UwD25hnFC9J90AR4fPurni9uQ+FccRL9GLCutS4RaKE2bhM5wdcS4tZqfNL+xC3nq/djVJnJ6raKQx1d7ew9pstZELWL1VSzoZ7u7J3SlGKnIVhCj3FN3qr4kOX5mdQ8HekfNGh4RiSO2yBf7uhNtX2O7gN8VLXOaMZUQvagv5C7N3V4yz3qNfRS4e6Sz+EQziPIehakn5IO2lT2ZmyLLlLPZz+K7ICE5WI0tuezcfgcpFHssypyXiGZNnk0QyV+S5O07EYDiEjKXMJ58PnGtIojpT5TlOzMRjq8gjKHJrwMPcYwt657d2cl8upXl/LXEJ58C5gTlwMDk/+qmMV2y/EQk2cN/LuOaB1OKqhbnaL/3Ucho/l1JxXKLecvmv2POCtc79EZ2TRH26+Ziy3kNlczTGcZ1aMznpLfn7s90WN3lTmjObd00d/1M4Bw2uuOA8qS8d4dxZZeUOp4LmAT4ZM/Ud9d07+NsLLgkaVHE0omXOKamqmh0zNfOPSNzrzWYhMlk6VTGVqNo5o0Y3YTbWrbsLPZuEBNr0dyt+l5L+I9X9/tg+tR2Q9TBadMwcdakso+2FP0fr0bO/PVkmMd3n5bm8bWvAsfI9a8Z7vXeqPd33bpbFVf4OE1/odlal+KSJZPN2z6yqGEZRP3jgHZL7nG9Fdes5i8c2z44CzRXN/alGiOX0i3yyIK/GxI2WP5upYn9XjyQHesO8W+aFI/Z7autrO454rcd6v5Ly/wDkn7ZQ5vHY+q7+bVcVl0+HSL3JnJ7pfRnG2Pc+rz41uVXLhO+j1+EENfuBI2SLtv6BIeKLqs3mzGpozLZN7wjpSJhPJesA4s1u87/rI9qSG10nA+G9Xom87ku6ALDHlvyM6YZsQvVTrZpuk55uO9ZnUWzXS6u9R0v9u8Cn9i7jyyXVd+XSt+N8NDtevrf3h2sf311e+uKH/n4P31a/Ub9QVWOOfqC+A2r46AA5/Un9X36l/bIw2/rzxl42/ctf3zmnML1Xp38bf/gt2q7ED</latexit> W1(↵, ) = <latexit 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Discretization rthmover distance on graphs Earthmover distance on graphs Earthmover distance on graphs (200, 588), (428, 1266) (726, 2172) <latexit 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A = div 2 Rn⇥d <latexit 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n = |vertex| <latexit 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d = |edges| <latexit sha1_base64="HiL3BeimvdANV1gusHXMpcw5RBM=">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</latexit> min ! w ⇢Z ||! w (x)|| ; div(! w ) = ↵ <latexit sha1_base64="mq+1sgaZ7ooXQESpf7MruK2wlH0=">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</latexit> finite elements: <latexit 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group Lasso ( = 0) <latexit 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graph: <latexit sha1_base64="zKq4tceIr2KyTvuP+29dxMyf07s=">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</latexit> Lasso ( = 0)
  39. Non-convex Regularization q Evolution of vk : q = 0.7

    q = 0.8 q = 1 Phase transition: q Evolution of vk : q = 0.7 q = 0.8 q = 1 Phase transition: q volution of vk : q = 0.7 q = 0.8 q = 1 Phase transition: ution of vk : q = 0.7 q = 0.8 q = 1 Phase transition: <latexit 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min Ax=y X i |xi | <latexit 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VarPro is smooth for > 2/3 <latexit 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Ai,j ⇠ N(0, 1) <latexit 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Compressed sensing <latexit sha1_base64="xOSIp6kGSCxGBvqRYj7M5CqeDNE=">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</latexit> y = Ax0 <latexit sha1_base64="UQhH38BCa7eXuxNMM8HkXT33Edo=">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</latexit> = 0.7 <latexit sha1_base64="8r5zFaiOjvtxh4K3peVZ9jXmEaI=">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</latexit> = 0.8 <latexit 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= 1 <latexit 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iteration of GD <latexit sha1_base64="itMu3Y4AfMgSObWXPhb6OyevH+I=">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</latexit> % of x? = x0 <latexit sha1_base64="6eMZZu9+5F3SaIZY5W6axEAqYHs=">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</latexit> ||x0 ||0 = 25 <latexit 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n
  40. Mirror Flows and Over-Parameterization <latexit 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Mirror descent: <latexit sha1_base64="XidA7g6PctGiqben4x4CW55K5m4=">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</latexit>

    Hessian manifold flow: <latexit sha1_base64="7mRkNdciANctCkmIefcyX2BGhAY=">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</latexit> Entropy function: ' smooth and strongly convex. <latexit sha1_base64="Z2CcuDKGnuWvaBZC2uMkeyVziKs=">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</latexit> ˙ x(t) = ['00(x(t))] 1f0(x(t)) <latexit 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xk+1 , ('0) 1 ⇥ '0(xk) ⌧kf0(xk) ⇤ <latexit 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⌧ ! 0 <latexit 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t = k⌧
  41. Mirror Flows and Over-Parameterization <latexit 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Mirror descent: <latexit sha1_base64="XidA7g6PctGiqben4x4CW55K5m4=">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</latexit>

    Hessian manifold flow: <latexit sha1_base64="7mRkNdciANctCkmIefcyX2BGhAY=">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</latexit> Entropy function: ' smooth and strongly convex. <latexit sha1_base64="Z2CcuDKGnuWvaBZC2uMkeyVziKs=">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</latexit> ˙ x(t) = ['00(x(t))] 1f0(x(t)) <latexit 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xk+1 , ('0) 1 ⇥ '0(xk) ⌧kf0(xk) ⇤ <latexit 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⌧ ! 0 <latexit 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t = k⌧ 2: Divergence-generating functions (plain) and their second-order derivatives (dashed). ⌘ (resp. D¯ ⌘) be the Bregman divergence associated to ⌘ (resp. ¯ ⌘), given for f, g 2 L1(⌧) ⌘(a, b) := ⌘(a) ⌘(b) ⌘0(b) a b and D¯ ⌘(f, g) := Z D⌘(f(✓), g(✓))d⌧(✓). <latexit 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x = uv <latexit 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' (x) , x ArcSinh(x ) <latexit 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p x2 + 2 + <latexit 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, |u(0)2 v(0)2|/2 <latexit 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Hyperbolic flow on R: <latexit sha1_base64="Gir747q3Zb0IOKjikXZJm6joJRw=">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</latexit> ˙ x = ['00(x)] 1f0(x) <latexit 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F(u, v) , f(uv) <latexit sha1_base64="0FZPnSMjNNIKRhkF3GAf9dq9AmU=">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</latexit> (˙ u, ˙ v) = F0(u, v)
  42. Mirror Flows and Over-Parameterization <latexit 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Mirror descent: <latexit sha1_base64="XidA7g6PctGiqben4x4CW55K5m4=">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</latexit>

    Hessian manifold flow: <latexit sha1_base64="7mRkNdciANctCkmIefcyX2BGhAY=">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</latexit> Entropy function: ' smooth and strongly convex. <latexit sha1_base64="Z2CcuDKGnuWvaBZC2uMkeyVziKs=">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</latexit> ˙ x(t) = ['00(x(t))] 1f0(x(t)) <latexit 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xk+1 , ('0) 1 ⇥ '0(xk) ⌧kf0(xk) ⇤ <latexit 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⌧ ! 0 <latexit 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t = k⌧ 2: Divergence-generating functions (plain) and their second-order derivatives (dashed). ⌘ (resp. D¯ ⌘) be the Bregman divergence associated to ⌘ (resp. ¯ ⌘), given for f, g 2 L1(⌧) ⌘(a, b) := ⌘(a) ⌘(b) ⌘0(b) a b and D¯ ⌘(f, g) := Z D⌘(f(✓), g(✓))d⌧(✓). <latexit 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x = uv <latexit 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' (x) , x ArcSinh(x ) <latexit 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p x2 + 2 + <latexit 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, |u(0)2 v(0)2|/2 <latexit 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Hyperbolic flow on R: <latexit sha1_base64="Gir747q3Zb0IOKjikXZJm6joJRw=">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</latexit> ˙ x = ['00(x)] 1f0(x) <latexit 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F(u, v) , f(uv) <latexit sha1_base64="0FZPnSMjNNIKRhkF3GAf9dq9AmU=">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</latexit> (˙ u, ˙ v) = F0(u, v) <latexit 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'+(x) , x log(x) x + 1 <latexit sha1_base64="zI1a/0Fr/18S6umph2/BZAKYmwE=">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</latexit> Fisher-Rao flow on R+: <latexit 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'00 + <latexit 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˙ x = ['00 + (x)] 1f0(x) <latexit 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F(u) , f(u2) <latexit sha1_base64="OVgaky0ip8/QeiAastCDa6M7E2Q=">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</latexit> ˙ u = F0(u) <latexit sha1_base64="TTQOlQDLU2GuRbbWFWAdV+ggyoQ=">AABDcnictVzddhu3EYbTv9j9SdLetTfrKu5xclRVVpwmOTk5JxYly4oVWzYp2Ylp+/BnRdNecWkuKctm9BK9bd+lz9E3aK960wfo/AALLIndwaqu9kjCgvhmBrPAYGaAZXecDLPp+vo/Lrzzox//5Kc/e/fipZ//4pe/eu/9D359mKWzSS8+6KVJOnnY7WRxMhzFB9PhNIkfjidx57ibxA+6Lxr4+YOTeJIN01Fr+nocPz7uDEbDo2GvM4Wqh6fRV1F79mTj6fsr62vr9BMtF67pworSP/vpB5c/Vm3VV6nqqZk6VrEaqSmUE9VRGVyP1DW1rsZQ91jNoW4CpSF9HqszdQmwM2gVQ4sO1L6AvwO4e6RrR3CPNDNC94BLAr8TQEbqCmBSaDeBMnKL6PMZUcbaMtpzoomyvYb/XU3rGGqn6hnUSjjTMhSHfZmqI/U59WEIfRpTDfaup6nMSCsoeeT0agoUxlCH5T58PoFyj5BGzxFhMuo76rZDn/+TWmIt3vd025n6F0l5Ba5INXXv05xCR50Q/Yie5gw+Y3kS4DwACrHuI5Zeka6PqfcjaD+H+jtwnVHJ6KQL15xqzyqRDbh8yIaI3IHLh9wRkXtw+ZB7InIfLh9yXyMROyGd+/FNuHz4psj5Hlw+5D0ReR8uH/K+iDyEy4c8FJHfw+VDfi8ib8LlQ94Ukbfh8iFvi8gWXD5kS0QewOVDHojIbbh8yG2NLJ+pE7hSojMUZuUNKBd5oKVIoOaGKN8mWUcfdjNgTvdKsPKs3oL/fuxWgE7jEux2wLg7KsHKI28HbKQfK9uiW7Sa+LC3ROwujAA/dlfEfqOel2C/CZhpL0qw8lzbg3Z+rGx9v4U7P/ZbEXsHSn6svEbdhRo/9m7AijEuwe6L2HvqZQk2xOpPSrCy3W+CXfFj5XWqBe392BBrOivByvb0EDwYP1ZerR5ArR/7QMQ+VKcl2Ici9juw7n7sdwEr7JsSrFljL9EKMiB/JIYZW0Wtk89KLI2BWkfgn+RrS0K+cRfqJcwgxwwIcywidnLETiBiL0fsBcuV5XY0I39X5tLMEc1ARDdfm7A0Fdv38/ZYSgIQWzliawFR5ZHiszZ9OSHvwtRIyGm+cmEppE9pbr+xFOvxUG15DeJuAcFj+xmN/FWKljCCQk1VUXuWr/GMjOi+CvGKojfTS8NDxk1zq+CiTkVU14PqiqjXHtRrETXzoGYi6sSDOhFRdua7uHbACLD6x2cxpzseAewjl18ReAU3YNW5BXM0gvGzD17gfaq5C/+bFHtLV5VkGM3jOolZjscFSzyB0lytQL2NCrcovk5ohsUgGbe8q2N8vMPcxlzPObbCZ/lKHuUZk3A6Q5JnkNNBbzGi+VSPzm2qOSPvjkv18LfyeW9K9fDbpPEz8uK5VA8/1dJPzyF7S2Nb58A2YTaNtfZtuS4Nzr8wDVO+RKsuWlx8qsd6zCC905r0d/WT2T3Hc2lQifVjy/VoZE7/skL/6tCwes4cPdejgt4Te72mFNXuyUjHvbZcV4aUVtGRlsPe1X0y2Kavn4wp16OxDx5Xg2LuuVOuO3rHeW9suR6NQ8V5zzPy5E25Ho0B3bM+bLkeDcy2dHScb8t1LTtqgGNnW65r1UeUBcYcEI95rrFe0YT8pJmmNiT/oDpb4/r8y+sY5mye5DFCNSXr25bT6eZrWbVExl+IwapNa8qB/sXM8cGKNOZqQ4yvWIZpYX1fpmPXeNT8HmgxgtnPewBSzjwBCU1OAq13AhSviVFXsWcGtyHicJQcLaDaunYqeouWL2eNinVPqVaKy2xvrR7bZK8zGntj8gn3SLOSHvZKn3AZRUlDewUNyfTq6O6Nnq9F7a+LuPECYpyPtB7tCPFOWnWc6tN609HxFb3LM4WL93zs+MVs85G2NhjzpGSLUJYqnm47k0dy63BdXVU2x82fRfRE0V6dkNUY0o5UJkahJlvM3vic7i3tA9qTQx5MowfPMdJUxop3zTCLjvn0iCyqa28l3qgvk6HjckZW19jjavTAQQ886PoxTgNWjDtQakHMcAB3rYAo51Kuq5Q0PlF/zHdHU3qC1RF9UrCQhgbbm7hgIaui7GcFKq8AjaOBo/RwGot0DL69REmO+n3y2Ni1aPmv0M6t2d/u0BgvH83lmZg+cd0grhHNGt7V5btFDizB3PvJBvmv1b1EfnU4og2VuD5xOLNeRrTjH1MEOybPOKHZJs2OYms3P7X4ieG0r8zeOe5mp2QhI7J/EaxPKY3JiH7dswNmB50tQkI2MsTuDHPvxufrDMUxZv24oeJTDXa8xWTLZsTf0HVnV0ZjkSMGXgfOFsa20cke+YIxcZ1o627ndvXqg0h7TsIdJUzRjpWrxP8j+mt+zThZWRoRqGF8Apm2db7nkVLMgjrq0CpfbYNMW1fKD3MZnmip7fpnZfqwINkWRVwoD67WfeDco3vmhaNkQnJnS214Ha3K5iLl8YIesbdHFMWz3R/oFRjlXqVVcoXmXJtGyQBGwTSPIkxbKYu8yLeaV5F6GO3s/0Ld6rqoNaQYKZvBZQ1J+f2YojVXygRGNY/fFzSb/FqfLLSq5jOisXjszOUfoPYy/DVym/swOt2CVdikMcAU7J3VCNdESy3CeG0WeJmRaWjZe8vPjknTyq05T3zN1s3G2Ce1qezTqDnVWQtTPg+N5w6N54E6bNFeo9WiqTeW6KkYW7T0bmUovzrcWjUoz0TKskdmUMMAKd1YKoxqX6Qqx/gG9UaktS7S6sBsdXcD3DkfgvTP9cXZ/UO+ukfqJvk2PfLAOH7p0ywdks9laqsjNaaAnK9r++rO/jbVIPcuWVCkzOc4ccbwrlOPrrNc0j/olS0lO28tgjm39Eq3MTa2TeVPlpDHNCcympcGcZ1axFp+V45owSKtOT5HRJn/DvlU7HdUx8xua/tMooI/YeNNnlWWF0cKI9K/lHnbXYped534NaKYcKa96y7Qqv+EkQJjTCbB71lm9IRwleOdBPZou2Q/l+0U7+KNHInWSOq5+irAxnDUa8e6O7ZMj03fPoaWqHX71H0tZH5JMEeJ33l29Dq0qh1rH3W+cH8+Wh29yhXvq/QwW+Br9TGjNm5kYaO8IqatvgzmwhLV48KYEC71elFH/nqS15GZd6dCKZvWhnIx08A25hnFS9I5UET4vLurXm/uI6Ef3SV6XcK61LhGooTZuFTnB1xLi1mpi0vrENderFyNEmclKlspDHV3tbD2my1kTNYvUVLOhlu7srcLUYqchWEKPcUnesviQ5fml3Dh30j5okPDMSR32AT/9oZqqO23cBripS5zRjOiGrQF/YXYu6P7WWxRraOXDnWXfgiHcB5D0LUk/ZBW0rqyM2VZcpd6OP1XZAUmKhalty3r98HlIvdkmVOd/gzJssm9GSrzLk7dvhgOIT0pcgnnw/saUi+OlHmnqV4fDHW5B0UOdXiYcwxhz9y2rs/L5VStr2UuoTx4FTA7LgaHO3/lsYptF2KhJs4Tefsc0DocVVA3q8X/2g/Dx3KqzyuUW0bvmj0PeOrcLtYZWfSH688Zyy1kNJdzDOeZ5r2z3pKfH/t9Ua0nlTq9efv00R+1Y8DwmivOg8rSMd4dRVbeUCq4L+CTIVX/Vn+/IL+N8DKnUSZHHUpmn6KcmmkhUzNvXPp6Zz4LkcnSKZOpSM3GEU06EdtQu+om/DZyD7Du6VB+l5L/I9b//mwfao/IepgsOmcO2lQXU/bD7qL16d6eny2TGM/y8tneFtTgXvge1eI53zvUHs/6tgp9K3+DhOf6typV/UJEsri7Z+dVF3pQ3HnjHJB5zzeis/ScxeKTZ8cBe4vm/NSiRHP6RD5Z0C3Fdx0pezRWx3qvHncO8IR9J88PRepPVNfRdh7XXInzfinn/QXOGWmnyOHU+az6bFYZl4bDpZ/nzk50u5TibLufV50b3SrlwmfQq/GDCvzAkbJJ2n9BkfBEVWfzZhU0Z1omd4d1pEwmkvWAcWYnf97Vke1JBa+TgP7fLkXfdiTdAVm6lP+OaIdtQvQSrZttkp5POlZnUm9VSGveo5TfzuY3IjgzYb5t4BFlprpkB9bVKv2uqc+h5SxoLp4INJHWqqZ8pjVb1dODWjKGvDdXRz75XbqesidAq6h+msv5qcIcl0EBdfoeii/oJ+LCZ9d14Ytr+fdQHG6sXfvz2if3rq98vam/keJd9Tv1e3UVrPFn6mt47vvQf1zF/qL+qv62+Z/GbxuXG/rrK965oDG/UYWfxup/AfDY8o0=</latexit> x = u2
  43. Quadratic Formulation Flows <latexit sha1_base64="mXniv8LkBBcNjJ6ZqCDXasUgXr0=">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</latexit> ˙ x = ['00 t

    (x)] 1 rf t (x) <latexit sha1_base64="Qu6klfvGGUADbnSPMICdPRxJB1Q=">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</latexit> min x f(x) , 1 2 kAx yk2 + kxk1 <latexit sha1_base64="qGdzvB9Fb5Aqn/pljpCQmQOdgGU=">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</latexit> Theorem: <latexit sha1_base64="u1q4ild5Z+ezbZlfoGncooWzndk=">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</latexit> min x f (x) , 1 2 kAx yk2 + X i q 2 + x2 i Figure 2: Divergence-generating functions (plain) and their second-order derivatives (da Let D⌘ (resp. D¯ ⌘) be the Bregman divergence associated to ⌘ (resp. ¯ ⌘), given for f, g 2 by D⌘(a, b) := ⌘(a) ⌘(b) ⌘0(b) a b and D¯ ⌘(f, g) := Z ⇥ D⌘(f(✓), g(✓))d⌧(✓ We consider the following assumptions on the divergence-generating function ⌘: <latexit 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' (x) , x ArcSinh(x ) <latexit 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p x2 + 2 + <latexit sha1_base64="H8cl+LGpZIT9PEA8SRgKo3xMvNY=">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</latexit> min u,v F(u, v) , 1 kA(u v) yk2 + kuk2 2 + kvk2 2 <latexit sha1_base64="YHhV1AfFkpHyXevHzkVbxvUsX4E=">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</latexit> t , |u(0)2 v(0)2|e 2 t <latexit sha1_base64="o8LP1/CSXMjH76VT/mKe16KokpM=">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</latexit> (˙ u, ˙ v) = rF(u, v) <latexit sha1_base64="RqW5xN+y7Wg7uKfjtPOkj4k6fOg=">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</latexit> x = u v <latexit sha1_base64="RqW5xN+y7Wg7uKfjtPOkj4k6fOg=">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</latexit> x = u v
  44. Quadratic Formulation Flows <latexit sha1_base64="mXniv8LkBBcNjJ6ZqCDXasUgXr0=">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</latexit> ˙ x = ['00 t

    (x)] 1 rf t (x) <latexit sha1_base64="Qu6klfvGGUADbnSPMICdPRxJB1Q=">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</latexit> min x f(x) , 1 2 kAx yk2 + kxk1 <latexit sha1_base64="qGdzvB9Fb5Aqn/pljpCQmQOdgGU=">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</latexit> Theorem: <latexit sha1_base64="u1q4ild5Z+ezbZlfoGncooWzndk=">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</latexit> min x f (x) , 1 2 kAx yk2 + X i q 2 + x2 i Figure 2: Divergence-generating functions (plain) and their second-order derivatives (da Let D⌘ (resp. D¯ ⌘) be the Bregman divergence associated to ⌘ (resp. ¯ ⌘), given for f, g 2 by D⌘(a, b) := ⌘(a) ⌘(b) ⌘0(b) a b and D¯ ⌘(f, g) := Z ⇥ D⌘(f(✓), g(✓))d⌧(✓ We consider the following assumptions on the divergence-generating function ⌘: <latexit 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' (x) , x ArcSinh(x ) <latexit 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p x2 + 2 + <latexit sha1_base64="H8cl+LGpZIT9PEA8SRgKo3xMvNY=">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</latexit> min u,v F(u, v) , 1 kA(u v) yk2 + kuk2 2 + kvk2 2 <latexit sha1_base64="YHhV1AfFkpHyXevHzkVbxvUsX4E=">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</latexit> t , |u(0)2 v(0)2|e 2 t <latexit sha1_base64="o8LP1/CSXMjH76VT/mKe16KokpM=">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</latexit> (˙ u, ˙ v) = rF(u, v) <latexit sha1_base64="RqW5xN+y7Wg7uKfjtPOkj4k6fOg=">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</latexit> x = u v <latexit 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Open problem: mirror-like interpretation for VarPro? <latexit 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˙ x = [· · · ](x) <latexit 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min v g(v) , min u 1 kA(u v) yk2 + kuk2 2 + kvk2 2 <latexit 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˙ v = rg(v) <latexit 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u?(v) , v A>(Adiag(v2)A> + Idn) 1y <latexit 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x = u?(v) v <latexit sha1_base64="RqW5xN+y7Wg7uKfjtPOkj4k6fOg=">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</latexit> x = u v
  45. Conclusion Handles small and even 0 value of Trade smoothness

    / non-convexity Simple algorithm Efficient sparse linear system ? Including pruning ? Practice ? ? <latexit sha1_base64="zf1DmE1bh8/d3yg+4mBebKWRF9I=">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</latexit>
  46. Conclusion Handles small and even 0 value of Trade smoothness

    / non-convexity Simple algorithm Efficient sparse linear system ? Including pruning ? Practice ? ? Fine-grid analysis? Hyperbolic geometry is better than Euclidean Operates a reconditioning Theory Mild non-convexity Mirror-flow analysis? ? ? <latexit sha1_base64="zf1DmE1bh8/d3yg+4mBebKWRF9I=">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</latexit>