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
, 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
, 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
, 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=">AABB93ictVzNcty4EYY3f2vnz5scc2EiO+VNeRVZ62SztZWqlSVZ1lq2x56R7N0d28WZoUa0qeGY5Ei2Z/UkOeSWyjVPkMo1eYK8QXLKK6R/AAKcAQlQcYSSBgTxdTeaQKO7wdFgmsR5sbb2zwvvfevb3/nu996/eOn7P/jhj358+YOfHOTpLBtG+8M0SbMngzCPkngS7RdxkURPplkUHg+S6PHg5Sbef3wSZXmcTnrFm2n09DgcT+LDeBgW0PT88m+u9LN4fFSEWZaeXgnGWTiKo0kRjKJ8iJ/hSRqP8iAvsnhYBHk4GiVRvvr88sra6hr9BMuVG7KyIuRPJ/0g2Bd9MRKpGIqZOBaRmIgC6okIRQ7la3FDrIkptD0Vc2jLoBbT/UiciUuAnUGvCHqE0PoS/o7h6mvZOoFrpJkTeghcEvjNABmIq4BJoV8GdeQW0P0ZUcbWOtpzoomyvYHPgaR1DK2FOIJWF0719MXhWApxKH5HY4hhTFNqwdENJZUZaQUlD4xRFUBhCm1YH8H9DOpDQio9B4TJaeyo25Du/4t6YiteD2Xfmfg3SXkVSiC6cvRpSSEUJ0Q/oKc5g3ssTwKcx0AhkmPE2inp+phGP4H+c2i/D+WMakonAyhzaj1rRG5CsSE3ncgdKDbkjhO5B8WG3HMiO1BsyI5EIjYjndvxXSg2fNfJ+SEUG/KhE/kIig35yIk8gGJDHjiRX0GxIb9yIm9DsSFvO5F3odiQd53IHhQbsudE7kOxIfedyG0oNuS2RNav1AxKSnRix6rcgHqVB1qKBFo2nPLdIutow97yWNPDGqx7VW/Bpx275aHTqAa77THvDmuw7pm3AzbSjnXboju0m9iwd5zYXZgBduyuE/uFeFGD/cJjpb2swbrX2h70s2Pd1vceXNmx95zY+1CzY9171ANosWMfeOwY0xpsx4l9KF7VYH2sflaDddv9LtgVO9a9T/Wgvx3rY01nNVi3PT0AD8aOde9Wj6HVjn3sxD4Rr2uwT5zYL8G627Ffeuywb2uwao+9RDvImPyRCFZsE7WwXJVYmwK10ME/KfeWhHzjAbS7MOMSMybMsROxUyJ2PBF7JWLPW668tKM5+btuLt0S0fVEDMq9CWuFs/+o7I+1xAOxVSK2FhBNHik+azWWE/IuVIsLWZQ7F9Z8xpSW9htrkZwPzZZXIR5UEDy3j2jmX6doCSMo1FQTtaNyj2dkQNdNiFOK3tQoFQ83riitgol67UQNLKiBE/XGgnrjRM0sqJkTdWJBnThReuWbuL7HDND6x2cxpyueAewj15cAvIIN2HXuwBoNYP50wAt8RC0P4LNLsberNEmG0Tzuk5jleFqxxBnU5mIF2nVUuEXxdUIrLALJuOcDGePjFeY25nLNsRU+K3fyoMyY+NOJSZ5xSQe9xYDWUzs6d6nljLw7rrXD3ynXvaq1w2+Txs/Ii+daO3whpS/OIXtPYnvnwHZhNU2l9nW9LQ3OvzANVb9Euy5aXHyqx3LOIL3XLenvyieze47nskk11o+ut6ORG+PLK+NrQ0PrOTf03I4Kek/s9apa0HokExn36npbGVLaRSdSDn3V9slgn5F8MqrejkYHPK5NirnnRr3t7J2Wo9H1djQOBOc9z8iTV/V2NMZ0zfrQ9XY0MNsSyjhf19tadtQAx8663taqTygLjDkgnvPcor2ijPykmaQWk3/QnK0xff7lfQxzNs/KGKGZkvZt6+kMyr2sWSLlL0Rg1YqWcqB/MTN8sCqNuVh3xlcsQ1HZ35fp6D0eNb8HWgxg9fMZgCtnnoCEKieB1jsBijecUVd1ZAq37sThLDlcQPVla+H0FjVfzhpV255Tqysu06PVeuyTvc5p7k3JJ9wjzbr0sFf7hOsoujS0V9GQm14b3b2V67Wq/TUnbrqAmJYzbUgnQnyS1hyn2rTeNXR8VZ7yFFD4zEfPX8w2H0prgzFPSrYIZWniafZTeSSzDffV60LnuPleQE8U7dUJWY2YTqRyZxSqssXsjc/pWtPepzM55ME0hvAcA0llKvjUDLPomE8PyKKa9tbFG/WlMnRcz8nqKnvcjB4b6LEF3T7G2YQd4z7UehAz7MNVzyPKuVTqKiWNZ+Kj8nQ0pSfYHNEnFQupaLC9iSoWsinKPqpQOQU0zgaO0v1pLNJR+P4SJXfUb5NHx65Vy3+VTm7V+XZIc7x+NtdnYkbEdZ24BrRq+FSXrxY5sARz65118l+bR4n82nBEG+ri+szgzHqZ0Il/RBHslDzjhFaba3VUe5v5qcU7ilNHqLNzPM1OyUIGZP8C2J9SmpMB/ZrvDqgTdLYICdlIH7sTl96NzdeJnXNM+3Gx4Lca9HyLyJbNiL+ia66unOYiRwy8D5wtzG2lkz3yBSPimknrrtd28+6DSP2ehDlLmKKeK9eI/4f0V/2qebKyNCNQw/gEcmnrbM8jpZgFdRTSLt9sg1RfU8orpQzPpNR6/9MyXalItkURF8qDu/UIOA/pmnnhLMlI7nypD++jTdlcpDxd0COO9pCieLb7Y7kDo9zXaZdcoTXXp1kyhllQlFGE6uvKIi/ybeZVpe5HO/+/UNe6rmoNKQZCZ3BZQ678fkTRmillArOa5+9LWk12rWcLvZr5TGguHhtr+Rto/Tn8VXKraz86g4pVuEVzgCnoK60RbgmWevjxulXhpWamoqWvNT89J1Uvs+U88TVbNx1jn7Sm0qFZ81pmLVT9PDReGDReeOqwR2eNWouqXVmi587YoidPK335teHWa0F55qTs9sgUKvaQ0oyl/KiOnFTdMb5CvXXSWnPSCmG1mqcB5pr3QdrX+uLq/qbc3QNxm3ybIXlgHL+MaJXG5HOp1uZIjSkg55vSvpqrv08tyH1AFhQp83ucuGL41GlI5ayU9JdyZ0vJzmuLoN5bOpV9lI3tU/3jJeQxrYmc1qVC3KQekZTflCNYsEirhs8RUOY/JJ+K/Y7mmNnsrZ9JUPEndLzJq0rz4khhQvp3Zd52l6LXXSN+DSgmnEnvegC02j9hpMAYlUmwe5Y5PSHc5fgkgT3aAdnPZTvFp3gTQ6JVknoufu9hYzjq1XPdnFtqxGpsv4KeqHX91G093PwSb44ufuc50QtpVzuWPup84fp8tEK5y1Wvm/QwW+Cr9TGjPmZkoaO8KqYvPvPmwhK148IYHy7tRtFG/naSt5GZT6d8KaveinI108A25ojiJdd7oIiweXfXrN7ch45xDJboDQhrUuMWFyXMxqUyP2BaWsxKXVzah7j1YuNulBg7Ud1Ooaibu4W232whI7J+iXDlbLi3KXu/EqW4szBMYSj4jd66+NCk+RkU/BsIW3SoOPrkDrvg326ITbH9Dt6GeCXrnNEMqAVtwWgh9g7lOKs9mnX0yqBu0vfh4M8jBl27pI9pJ20rO1N2S25S96d/SlYgE5FTet2z/RhMLu6RLHNqM56YLJt7NLFQ38VpOxbFwWckVS7+fPhcwzWKQ6G+09RuDIq6ewRVDm14qPcY/J657t2el8mpWV/LXHx58C6gTlwUDk/+6mMV3c/HQmXGE3n3HNA6HDZQV7vF/zoOxUdzas/Ll1tO3zV74fHUuV8kM7LoD7dfM5qbz2yu5+jPMy1Hp70lOz/2+4JWTyo1RvPu6aM/queA4jUXnAd1S8d4cxZpeX2p4LmATYZU/Ef89YL72wivShp1crShpM4p6qmpHm5q6huXttGpez4yaTp1MlWp6TiiS2/EbopdcRt+N0sPsO3bofxdSv5ErP37syNoPSTrobLonDnoU1tE2Q99ijaia/3+bJ3E+C4vv9vbgxY8C9+jVnzP9z71x3d9e5Wx1X+DhNf6PZGKUSUiWTzd0+tqACOonrxxDkh9zzegd+k5i8Vvnh17nC2q96cWJZrTHfebBYNa/MCQckhzdSrP6vHkAN+wD8v8UCB+TW2htPO457o4d2o5dxY456SdKofXxr3md7PquGwaXEZl7uxE9kspztbnec250a1aLvwOejN+3IAfG1J2SfsvKRLORHM2b9ZAcyZlMk9YJ0JlIlkPGGeG5fNujmxPGnideIz/bi36riHpDsgyoPx3QCdsGdFLpG62SXp+07E5k3qnQVr5PUr67waf0k/AlU9uysqnN8r/bnCwvnrjt6sfP1xf+fyW/D8H74ufiV+Ia7DGPxGfA7WO2AcOfxB/E38X/9h4s/HHjT9t/Jm7vndBYn4qKj8bf/kvJDK24Q==</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
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
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=">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</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
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=">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</latexit> (T, n, d) = (139, 15362, 27) <latexit sha1_base64="qocYY1OkY5j/EKAP9WXtxgBo+Y0=">AABB1nictVxbdxu3EYbTW+zenLZvfdlWcY/do7qS4tTxyck5kSVZVqzYsknJTkLbh5cVTXvJpbmkfGHUt56+9if0tf0T/R39B+1T/0LnAiywJHYHq7rGkYQF8c0MZoHBzAB0Z5wMsuna2j/Pvfed737v+z94//yFH/7oxz/56cUPfnaUpbNJNz7spkk6edRpZ3EyGMWH08E0iR+NJ3F72Enih50XW/j5w5N4kg3SUXP6Zhw/Hrb7o8HxoNueQtPTi7+43FwdrfaufHb52sbqx59c/3h1/caVpxdX1q6u0b9oubKuKytK/ztIP4gOVUv1VKq6aqaGKlYjNYV6otoqg/KNWldragxtj9Uc2iZQG9DnsTpVFwA7g14x9GhD6wv43Yenb3TrCJ6RZkboLnBJ4GcCyEhdAkwK/SZQR24RfT4jythaRntONFG2N/C3o2kNoXWqnkGrhDM9Q3E4lqk6Vp/QGAYwpjG14Oi6msqMtIKSR86opkBhDG1Y78HnE6h3CWn0HBEmo7Gjbtv0+b+oJ7bic1f3nal/k5SXoESqoUef5hTa6oToR/Q2Z/AZy5MA5z5QiPUYsfaKdD2k0Y+g/xza70I5pZrRSQfKnFpPK5FbUHzILRG5C8WH3BWR+1B8yH0ReQDFhzzQSMROSOd+fAOKD98QOd+H4kPeF5EPoPiQD0TkERQf8khEfg3Fh/xaRN6C4kPeEpF3oPiQd0RkE4oP2RSRh1B8yEMRuQPFh9zRyPKVOoGSEp2BsCo3oV7kgZYigZZNUb6bZB192JsBa7pbgpVX9Tb89WO3A3Qal2B3AubdcQlWnnm7YCP9WNkW3abdxIe9LWL3YAb4sXsi9gv1vAT7RcBKe1GCldfaPvTzY2Xr+yU8+bFfiti7UPNj5T3qHrT4sfcCdoxxCfZAxN5XL0uwIVZ/UoKV7X4D7IofK+9TTejvx4ZY01kJVranR+DB+LHybvUQWv3YhyL2kXpdgn0kYr8C6+7HfhWww74twZo99gLtIH3yR2JYsVXU2vmqxNoYqLUF/km+tyTkG3egXcL0c0yfMEMRsZsjdgMR+zliP1iuLLejGfm7MpdGjmgEIjr53oS1qdi/l/fHWhKA2M4R2wuIKo8U37UZywl5F6ZFQk7znQtrIWNKc/uNtVjPh2rLaxD3Cgie289o5q9StIQRFGqqitqzfI9nZETPVYhXFL2ZURoeMm6aWwUX9VpEdTyojoh640G9EVEzD2omok48qBMRZVe+i2sFzACrf3wXc3riGcA+cnmJwCvYhF3nNqzRCObPAXiBD6jlHvxtUOwtlSrJMJrHfRKzHI8LlngCtblagXYbFW5TfJ3QCotBMu55T8f4+IS5jblec2yFT/OdPMozJuF0BiRPP6eD3mJE66kenTvUckreHdfq4W/n697U6uF3SOOn5MVzrR5+qqWfnkH2psY2z4BtwGoaa+3bel0anH9hGqZ+gXZdtLj4Vod6ziC91zXp7+k3s3eG97JFNdaPrdejkTnjywrjq0PD6jlz9FyPCnpP7PWaWlR7JCMd99p6XRlS2kVHWg77VPfNYJ+efjOmXo/GAXhcWxRzz5163dk7zkdj6/VoHCnOe56SJ2/q9Wj06Zn1Yev1aGC2pa3jfFuva9lRAxw723pdqz6iLDDmgHjOc4v1iibkJ800tQH5B9XZGtfnX97HMGfzJI8RqilZ37acTiffy6olMv5CDFZtWlMO9C9mjg9WpDFXG2J8xTJMC/v7Mh27x6Pm90GLEax+PgOQcuYJSGhyEmi9E6C4LkZdxZEZ3IaIw1lyvIBq6dap6C1avpw1KrY9pVYpLrOjtXpskb3OaO6NySfcJ81KetgvfcNlFCUN7Rc0JNOro7u3er0Wtb8m4sYLiHE+07p0IsQnadVxqk/rDUfHl/QpzxQKn/nY+YvZ5mNtbTDmSckWoSxVPN1+Jo/ktuG+uqpsjps/i+iNor06IasxoBOpTIxCTbaYvfE5PVvah3QmhzyYRhfeY6SpjBWfmmEWHfPpEVlU195KvFFfJkPH9YysrrHH1ei+g+570PVjnC3YMe5CrQkxwyE8NQOinAu5rlLS+ET9Lj8dTekNVkf0ScFCGhpsb+KChayKsp8VqLwCNM4GjtLDaSzSMfjWEiU56vfJY2PXouW/RCe35ny7TXO8fDaXZ2J6xHWDuEa0avhUl58WObAEc+8nG+S/Vo8S+dXhiDZU4vrE4cx6GdGJf0wR7Jg844RWm7Q6ir3d/NTiJ4bTgTJn53ianZKFjMj+RbA/pTQnI/px7w6YE3S2CAnZyBC7M8i9G5+vMxDnmPXjBopvNdj5FpMtmxF/Q9ddXRnNRY4YeB84XZjbRif75AvGxHWirbtd29W7DyLtPQl3ljBFO1cuE/8r9Nv8mHmysjQjUMP4BjJt63zvI6WYBXXUpl2+2gaZvq6UH+YyPNFS2/3PyvRhQbJtirhQHtyte8C5S8/MC2fJhOTOlvrwPlqVzUXK4wU94miPKYpnu9/XOzDKvUq75AqtuRbNkj7MgmkeRZi+UhZ5kW81ryL1MNrZ/4W61XVRa0gxUjaDyxqS8vsxRWuulAnMap6/L2g1+bU+WehVzWdEc3HorOVvofVX8NvIbZ7D6HQKVuEmzQGmYJ+sRrglWuoRxutmgZeZmYaWfbb87Jw0vdyWs8TXbN1sjH1Sm8oBzZrXOmth6meh8dyh8TxQh006a7RaNO3GEj0VY4umPq0M5VeHW7MG5ZlIWfbIDGoQIKUbS4VR7YlU5RjfoN6KtNZEWm1Yre5pgLvmQ5D+tb64ur/Nd/dI3SLfpkseGMcvPVqlA/K5TGt1pMYUkPM1bV/d1d+iFuTeIQuKlPkeJ64YPnXqUjnNJf2N3tlSsvPWIph7S690H2NjW1T/aAk5pDWR0bo0iGvUI9byu3JECxbpquNzRJT5b5NPxX5Hdczs9rbvJCr4Ezbe5FVleXGkMCL9S5m3vaXodc+JXyOKCWfau+4ArfpvGCkwxmQS/J5lRm8Idzk+SWCPtkP2c9lO8SneyJHoKkk9V58F2BiOeu1cd+eWGbEZ22+hJ2rdvnVfD5lfEsxR4neWE7027WpD7aPOF57PRqutd7nic5UeZgt8rT5m1MeNLGyUV8S01KfBXFiielwYE8Kl3ijqyF9P8joy8+lUKGXT21AuZhrYxjyjeEm6B4oIn3d32evNXRHG0Vmi1yGsS41bJEqYjUt1fsC1tJiVOr+0D3Hr+crdKHF2orKdwlB3dwtrv9lCxmT9EiXlbLi3K3urEKXIWRim0FV8o7csPnRpfgoFf0fKFx0ajiG5wwb4t5tqS+28g9sQL3WdM5oRtaAt6C3E3m09zmKPah29dKi79EM4hPMYgK4l6Qe0k9aVnSnLkrvUw+m/IiswUbEove1ZfwwuF3kky5zqjGdAlk0ezUCZ7+LUHYvhEDKSIpdwPnyuIY3iWJnvNNUbg6Euj6DIoQ4Pc48h7J3b3vV5uZyq9bXMJZQH7wLmxMXg8OSvPFax/UIs1MR5I++eA1qH4wrqZrf4X8dh+FhO9XmFcsvou2bPA94694t1Rhb94fprxnILmc3lHMN5pvnorLfk58d+X1TrTaXOaN49ffRH7RwwvOaK86CydIx3Z5GVN5QKngv4ZEjVf9Q/zsnfRniZ0yiTow4lc05RTs30kKmZb1z6Rmc+C5HJ0imTqUjNxhENuhG7pfbULfjZyj3AurdD+buU/Bex/u/P9qD1mKyHyaJz5qBFbTFlP+wpWo+e7f3ZMonxLi/f7W1CC56F71Mr3vO9S/3xrm+zMLbyb5DwWv9SpapXiEgWT/fsuurACIonb5wDMt/zjeguPWex+ObZMOBs0dyfWpRoTp/INws6pfiOI2WX5upYn9XjyQHesG/n+aFI/Z7a2trO454rcT4o5XywwDkj7RQ5vHY+q76bVcZly+HSy3NnJ7pfSnG2Pc+rzo1ul3LhO+jV+H4Fvu9I2SDtv6BIeKKqs3mzCpozLZN7wjpSJhPJesA4s52/7+rI9qSC10nA+O+Uou84ku6CLB3Kf0d0wjYheonWzQ5JzzcdqzOptyuk1d+jpP/d4Ab9i7hy/Zqu3FjP/3eDo42r63+4+tH9ayuf39T/z8H76pfq1+oyrPHr6nOgdqAOgcNb9Vf1N/X3zUebf9z80+afuet75zTm56rwb/Mv/wXOsqYJ</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
(x)] 1 rf t (x) <latexit 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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
(x)] 1 rf t (x) <latexit 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min x f(x) , 1 2 kAx yk2 + kxk1 <latexit sha1_base64="qGdzvB9Fb5Aqn/pljpCQmQOdgGU=">AABB03ictVzddhu3EYbTv9j9s9vL3myruMfpcVzZ8Wma5vScyJIsK1Zs2qRkJ6Htw58VRXvJpbmkJJvRTU9v+wi9bR+jz9E3aK/6Cp0fYIElsTtY1TWOJCyIb2YwCwxmBqC7k2SYzdbX/3nhve9893vf/8H7Fy/98Ec//slPL1/52UGWzqe9eL+XJun0abeTxclwHO/PhrMkfjqZxp1RN4mfdF9t4udPjuNpNkzHrdmbSfxs1BmMh4fDXmcGTS8uX2nP4lPALVpHcTqNR384e3F5bf3GOv2LVis3dWVN6X+N9Eq0r9qqr1LVU3M1UrEaqxnUE9VRGZRv1E21ribQ9kwtoG0KtSF9HqszdQmwc+gVQ48OtL6C3wN4+ka3juEZaWaE7gGXBH6mgIzUVcCk0G8KdeQW0edzooytZbQXRBNlewN/u5rWCFpn6ghaJZzpGYrDsczUofo9jWEIY5pQC46up6nMSSsoeeSMagYUJtCG9T58PoV6j5BGzxFhMho76rZDn/+LemIrPvd037n6N0l5FUqkmnr0aU6ho46JfkRvcw6fsTwJcB4AhViPEWsnpOsRjX4M/RfQ/gDKGdWMTrpQFtR6VonchOJDborIHSg+5I6I3IPiQ+6JyAYUH7KhkYidks79+CYUH74pcn4ExYd8JCIfQ/EhH4vIAyg+5IGI/BqKD/m1iLwLxYe8KyLvQ/Eh74vIFhQfsiUi96H4kPsichuKD7mtkeUrdQolJTpDYVVuQL3IAy1FAi0bonx3yDr6sHcC1nSvBCuv6i3468duBeg0LsFuB8y7wxKsPPN2wEb6sbItuke7iQ97T8TuwgzwY3dF7BfqZQn2i4CV9qoEK6+1Pejnx8rW90t48mO/FLEPoObHynvUQ2jxYx8G7BiTEmxDxD5Sr0uwIVZ/WoKV7X4T7IofK+9TLejvx4ZY03kJVranB+DB+LHybvUEWv3YJyL2qTotwT4VsV+BdfdjvwrYYd+WYM0ee4l2kAH5IzGs2CpqnXxVYm0C1DoC/yTfWxLyjbvQLmEGOWZAmJGI2MkRO4GIvRyxFyxXltvRjPxdmUszRzQDEd18b8LaTOzfz/tjLQlAbOWIrSVElUeK79qM5Zi8C9MiIWf5zoW1kDGluf3GWqznQ7XlNYiHBQTP7SOa+dcpWsIICjVVRe0o3+MZGdFzFeKEojczSsNDxs1yq+CiTkVU14Pqiqg3HtQbETX3oOYi6tiDOhZRduW7uHbADLD6x3exoCeeAewjl5cIvIIN2HXuwRqNYP40wAt8TC0P4W+TYm+pVEmG0Tzuk5jleFawxFOoLdQatNuocIvi64RWWAyScc+HOsbHJ8xtLPSaYyt8lu/kUZ4xCaczJHkGOR30FiNaT/Xo3KeWM/LuuFYPfy9f96ZWD79NGj8jL55r9fAzLf3sHLK3NLZ1DmwTVtNEa9/W69Lg/AvTMPVLtOuixcW3OtJzBumd1qS/q9/M7jneyybVWD+2Xo9G5owvK4yvDg2r58zRcz0q6D2x12tqUe2RjHXca+t1ZUhpFx1rOexT3TeDffr6zZh6PRoN8Lg2KeZeOPW6s3eSj8bW69E4UJz3PCNP3tTr0RjQM+vD1uvRwGxLR8f5tl7XsqMGOHa29bpWfUxZYMwB8ZznFusVTclPmmtqQ/IPqrM1rs+/uo9hzuZ5HiNUU7K+bTmdbr6XVUtk/IUYrNqsphzoX8wdH6xIY6FuifEVyzAr7O+rdOwej5rfAy1GsPr5DEDKmScgoclJoPVOgOJNMeoqjszgbok4nCWHS6i2bp2J3qLly1mjYtsLapXiMjtaq8c22euM5t6EfMI90qykh73SN1xGUdLQXkFDMr06unur12tR++sibrKEmOQzrUcnQnySVh2n+rTedHR8VZ/yzKDwmY+dv5htPtTWBmOelGwRylLF0+1n8khuG+6r15XNcfNnEb1RtFfHZDWGdCKViVGoyRazN76gZ0t7n87kkAfT6MF7jDSVieJTM8yiYz49Iovq2luJN+rLZOi4npHVNfa4Gj1w0AMPun6Mswk7xgOotSBm2IenVkCUcynXVUoan6qP8tPRlN5gdUSfFCykocH2Ji5YyKoo+6hA5QTQOBs4Sg+nsUzH4NsrlOSo3yePjV2Llv8qndya8+0OzfHy2VyeiekT11vENaJVw6e6/LTMgSVYeD+5Rf5r9SiRXx2OaEMlrs8dzqyXMZ34xxTBTsgzTmi1Sauj2NvNTy1/Yjg1lDk7x9PslCxkRPYvgv0ppTkZ0Y97d8CcoLNFSMhGhtidYe7d+HydoTjHrB83VHyrwc63mGzZnPgbuu7qymgucsTA+8DZ0tw2OtkjXzAmrlNt3e3art59EGnvSbizhCnauXKN+H9Iv82PmSdrKzMCNYxvINO2zvc+UopZUEcd2uWrbZDp60r5QS7Dcy213f+sTB8UJNuiiAvlwd26D5x79My8cJZMSe5spQ/vo1XZXKQ8WdIjjvaQoni2+wO9A6Pc12mXXKM116ZZMoBZMMujCNNXyiIv863mVaQeRjv7v1C3ui5qDSlGymZwWUNSfj+maM2VMoFZzfP3Fa0mv9anS72q+YxpLo6ctfwttP4Sfhu5zXMYnW7BKtyhOcAU7JPVCLdEKz3CeN0p8DIz09Cyz5afnZOml9tynviarZuNsY9rU2nQrDnVWQtTPw+Nlw6Nl4E6bNFZo9WiaTeW6IUYW7T0aWUovzrcWjUoz0XKskdmUMMAKd1YKoxqX6Qqx/gG9VaktS7S6sBqdU8D3DUfgvSv9eXV/W2+u0fqLvk2PfLAOH7p0yodks9lWqsjNaaAnG9r++qu/ja1IPcuWVCkzPc4ccXwqVOPylku6a/1zpaSnbcWwdxbOtF9jI1tU/3jFeSI1kRG69IgblOPWMvvyhEtWaQbjs8RUea/Qz4V+x3VMbPb276TqOBP2HiTV5XlxZHCmPQvZd52V6LXXSd+jSgmnGvvugu06r9hpMAYk0nwe5YZvSHc5fgkgT3aLtnPVTvFp3hjR6IbJPVC/THAxnDUa+e6O7fMiM3YfgM9Uev2rft6yPySYI4Sv/Oc6HVoVxtpH3Wx9Hw+Wh29yxWfq/QwX+Jr9TGnPm5kYaO8IqatPgvmwhLV48KYEC71RlFH/nqS15GZT6dCKZvehnIx08A25ojiJekeKCJ83t01rzf3oTCO7gq9LmFdatwiUcJsXKrzA66lxazUxZV9iFsvVu5GibMTle0Uhrq7W1j7zRYyJuuXKClnw71d2duFKEXOwjCFnuIbvWXxoUvzMyj4O1K+6NBwDMkdNsG/3VCbavsd3IZ4reuc0YyoBW1Bfyn27uhxFntU6+i1Q92lH8IhnMcQdC1JP6SdtK7sTFmW3KUeTv+ErMBUxaL0tmf9Mbhc5JGscqozniFZNnk0Q2W+i1N3LIZDyEiKXML58LmGNIpDZb7TVG8Mhro8giKHOjzMPYawd2571+flcqrW1yqXUB68C5gTF4PDk7/yWMX2C7FQU+eNvHsOaB0OK6ib3eJ/HYfhYznV5xXKLaPvmr0MeOvcL9YZWfSH668Zyy1kNpdzDOeZ5qOz3pKfH/t9Ua03lTqjeff00R+1c8DwWijOg8rSMd6dRVbeUCp4LuCTIVX/Uf+4IH8b4XVOo0yOOpTMOUU5NdNDpma+cekbnfksRCZLp0ymIjUbRzTpRuym2lV34Wcz9wDr3g7l71LyX8T6vz/bh9ZDsh4mi86Zgza1xZT9sKdofXq292fLJMa7vHy3twUteBa+R614z/cB9ce7vq3C2Mq/QcJr/UuVqn4hIlk+3bPrqgsjKJ68cQ7IfM83orv0nMXim2ejgLNFc39qWaIFfSLfLOiW4ruOlD2aqxN9Vo8nB3jDvpPnhyL1W2rraDuPe67EuVHKubHEOSPtFDmcOp9V380q47LpcOnnubNj3S+lONue51XnRrdKufAd9Gr8oAI/cKRskvZfUSQ8VdXZvHkFzbmWyT1hHSuTiWQ9YJzZyd93dWR7XMHrOGD890vR9x1Jd0CWLuW/IzphmxK9ROtmm6Tnm47VmdR7FdLq71HS/27wKf2LuPLJbV359Gb+vxsc3Lpx83c3Pn50e+3zO/r/OXhf/UL9Sl2DNf6J+hyoNdQ+cDhRf1V/U3/f2N9YbPxp48/c9b0LGvNzVfi38Zf/AtLKqJE=</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
/ non-convexity Simple algorithm Efficient sparse linear system ? Including pruning ? Practice ? ? <latexit sha1_base64="zf1DmE1bh8/d3yg+4mBebKWRF9I=">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</latexit>
/ 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>