オンライン広告の数理モデルと数学ソフトウェア MSFD#23

数学ソフトウェアとフリードキュメント #23

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1. Hiroki Mizukami ެ։༻ͷࢿྉʹ͖ͭɼߨԋʹ࢖༻͠ ͨ΋ͷͱҰ෦಺༰͕ҟͳΓ·͢ɽ Կଔ͝༰͍ࣻͩ͘͞ɽ ※มߋՕॴʹ͸྘ͷҹΛ͚͓ͭͯΓɼͦͷଞมߋ఺͸͋Γ·ͤΜɽ
2. ΦϯϥΠϯ޿ࠂͷ਺ཧϞσϧͱ ਺ֶιϑτ΢ΣΞ ਺ֶιϑτ΢ΣΞͱϑϦʔυΩϡϝϯτ#23 2016೥౓ ೔ຊ਺ֶձळق૯߹෼Պձ גࣜձࣾ αΠόʔΤʔδΣϯτ ΞυςΫຊ෦ ٕज़ઓུࣨ AI Lab ਫ্ ͻΖ͖ mizukami_hiroki@cyberagent.co.jp 2
3. ࢢ৔Λઃܭ͍ͨ͠ʂʂ 3 ༗རʹऔҾ͍ͨ͠ʂʂ ޮՌΛܭଌ͍ͨ͠ʂ ػցֶश Ϗοάσʔλॲཧ ౷ܭϞσϦϯά ਺ཧ࠷దԽ ήʔϜཧ࿦ ORTB ޿ࠂͷ༷ʑͳ՝୊Λ਺ཧతͳ໰୊ʹؼணͤ͞Δ࿩
4. Introduction! 4
5. ࣗݾ঺հ Έ͔ͣΈ ͻΖ͖ AI Lab. @ CyberAgent ιϑτ΢ΣΞΤϯδχΞʗσʔλαΠΤϯςΟετ म࢜ˏ਺ֶ ڠྗήʔϜ খചʗ෺ྲྀ ޿ࠂʗσʔλ෼ੳ ༧ଌͱܭଌ 5
6. σʔλαΠΤϯςΟετͱͯ͠ͷ࠷ۙͷ͠͝ͱͿΓ 6
7. σʔλαΠΤϯςΟετͱͯ͠ͷ࠷ۙͷ͠͝ͱͿΓ 7 ༧ࢉ഑෼࠷దԽͷͨΊͷɼ޿ࠂࢪࡦͷϞσϦϯά ϢʔβείΞϦϯάʗΫϥελϦϯά Ϧϫʔυ޿ࠂͷίϯςϯπਪનγεςϜͷ։ൃ ϢʔβͷΦϑϥΠϯߦಈ༧ଌ དྷ๚ܭଌͷͨΊͷ԰಺ܭଌٕज़ ʼʼ
8. σʔλαΠΤϯςΟετͬͯʁʁʁ 8 ਺ֶͱܭࢉػͱίω Λۦ࢖ͯ͠ ͍ΖΜͳ͜ͱΛԿͱ͔͢Δ ͦΜͳਓͨͪ ※ಠஅͱภݟʹΑΔఆٛͰ͢
9. CyberAgentͬͯʁʁʁ 9 ΠϯλʔωοτΛ࣠ʹ༷ʑͳαʔϏεΛల։͍ͯ͠·͢ɽ ͜ͷଞʹ΋ଟ਺ͷࣄۀʂ
10. CyberAgentͬͯʁʁʁ ձ໊ࣾΑΓ΋༗໊ͳαʔϏε͕݁ߏ͋Δɽ ͳ͔Ͱ΋޿ࠂ୅ཧళࣄۀ͸ओྗࣄۀɽ ຊ೔ͷ಺༰ͷΩʔϫʔυ Πϯλʔωοτ޿ࠂ ΞυςΫϊϩδʔ 10
11. ޿ࠂ୅ཧࣄۀͱΠϯλʔωοτ޿ࠂ 11 ޿ࠂओʢAdvertiserʣ ֤छϝσΟΞʢPublisher) ৽ฉ TV ަ௨޿ࠂ ɾɾɾɾ ޮ཰ѱ͍ʁʁ
12. ޿ࠂ୅ཧࣄۀͱΠϯλʔωοτ޿ࠂ 12 ޿ࠂओʢAdvertiserʣ ֤छϝσΟΞʢPublisher) ৽ฉ TV ަ௨޿ࠂ ɾɾɾɾ ޿ࠂ୅ཧళʢAgency) ֤ϝσΟΞͱͷௐ੔ ϝσΟΞԣஅͷ૯߹తͳϓϩϞʔγϣϯ
13. ޿ࠂ୅ཧࣄۀͱΠϯλʔωοτ޿ࠂ 13 ޿ࠂओʢAdvertiserʣ ֤छϝσΟΞ ʢPublisher) ޿ࠂ୅ཧళʢAgency) ΠϯλʔωοτϝσΟΞ ແ਺ʹ͋Δʂ
14. ޿ࠂ୅ཧࣄۀͱΠϯλʔωοτ޿ࠂ 14 ޿ࠂओʢAdvertiserʣ ֤छϝσΟΞ ʢPublisher) ޿ࠂ୅ཧళʢAgency) ΠϯλʔωοτϝσΟΞ Media RepʗAdTechnology ޿ࠂऔҾͷΦʔτϝʔγϣϯ Real Time BiddingʢRTBʣ
15. ༷ʑͳΠϯλʔωοτ޿ࠂ 15
16. Real Time Bidding 16 ޿ࠂओʢAdvertiserʣ ޿ࠂ୅ཧళʢAgency) ωοτϝσΟΞʢPublisherʣ DSP = Demand Side Platform SSP = Supply Side Platform Bid Request ! Bid ! AdCall ೖࡳ؅ཧʗӡ༻ Impression
17. ༷ʑͳAdTechnology 17
18. औΓѻ͏σʔλͷن໛ 18 SSP = Supply Side Platform DSP = Demand Side Platform ໿ 70ԯ request / day
19. ༗ݶ࣍ݩͷ໰୊͸ऴΘ͍ͬͯΔʁʁʁ 19 SSP = Supply Side Platform DSP = Demand Side Platform 20 ϛϦඵ ҎԼͷϨεϙϯε औΓѻ͏σʔλͷن໛
20. ϝΧχζϜσβΠϯͱ OpenRTBʢORTBʣ 20
21. 21 ࠷ߴֹೖࡳऀ Second Price Auction ̎൪Ίͷೖࡳֹ ࢀՃඅແྉ ୭͕མࡳ͢Δʁ ͍͘ΒͰʁ མࡳग़དྷͳ͍ͱʁ ʹ ʹ ʹ ҰൠతͳΦϯϥΠϯ޿ࠂऔҾͰ͸མࡳֹʹ2nd Price͕࠾༻͞Ε͍ͯΔ
22. 22 ࠷ߴֹೖࡳऀ Second Price Auction ̎൪Ίͷೖࡳֹ ࢀՃඅແྉ ୭͕མࡳ͢Δʁ ͍͘ΒͰʁ མࡳग़དྷͳ͍ͱʁ ʹ ʹ ʹ Ͳ͏ͯ͠ ̎ҐՁ֨ͳͷ͔ʁʁ
23. ϝΧχζϜσβΠϯ 23 DSP = Demand Side Platform SSP = Supply Side Platform Bid Request ! Bid ! ചΓखͱങ͍ख૒ํͷརӹΛ ࠷େԽ͢Δ࢓૊ΈʢʹϝΧχζϜʣ͕ඞཁ
24. ඇՄ෼୯ҰࡒରশΦʔΫγϣϯ 24 ೖࡳ
25. ඇՄ෼୯ҰࡒΦʔΫγϣϯ 25 མࡳ — ඇՄ෼୯ҰࡒରশΦʔΫγϣϯ
26. ඇՄ෼୯ҰࡒΦʔΫγϣϯ 26 — ti 2 T = [0, 1] : T ! R+ λΠϓ஋ ೖࡳؔ਺ʢઓུʣ Ձ஋ؔ਺ʢޮ༻ʣ ࡒʹର͢ΔϓϨΠϠʔͷબ޷ ࡒʹΑͬͯಘΒΕΔޮ༻ ࡒʹର͢Δೖࡳֹ ඇՄ෼୯ҰࡒରশΦʔΫγϣϯ vi : T ! R+
27. v 27 ඇՄ෼୯ҰࡒରশΦʔΫγϣϯ ೖࡳ݁Ռ ϝΧχζϜ ίετ མࡳ b = 0 B B B B B B B B @ (t1) (t2) . . . (ti) . . . (tn) 1 C C C C C C C C A c(b) = 0 B B B B B B B B @ 10 10 . . . 20 . . . 0 1 C C C C C C C C A w(b) = 0 B B B B B B B B @ False True . . . False . . . False 1 C C C C C C C C A
28. v 28 ඇՄ෼୯ҰࡒରশΦʔΫγϣϯ pi = wi(b)v(ti) ci(b) ϓϨΠϠʔiͷརಘ n X i=0 pi + n X i=0 ci ചΓख΋ؚΊͨࣾձత༨৒ ങ͍खʼ ʻചΓख ചΓखʹͱͬͯͷࡒͷՁ஋ΛԾఆ͢Δ৔߹΋͋Δ ʢFloor Priceʣ
29. v 29 ඇՄ෼୯ҰࡒରশΦʔΫγϣϯ pi = wi(b)v(ti) ci(b) ϓϨΠϠʔiͷརಘ n X i=0 pi + n X i=0 ci ചΓख΋ؚΊͨࣾձత༨৒ ങ͍खʼ ʻചΓख ചΓखʹͱͬͯͷࡒͷՁ஋ΛԾఆ͢Δ৔߹΋͋Δ ʢFloor Priceʣ keyword: ऩӹಉ஋ੑఆཧ ϝΧχζϜ ʹ ୭͕͍͘Β෷͏͔ ʴ ୭͕མࡳ͢Δͷ͔
30. ྫʣద౰ʹઃܭͨ͠ྼѱΦʔΫγϣϯ མࡳऀ͸࠷௿ֹೖࡳऀͱ͢Δ མࡳֹۚ͸࠷ߴೖࡳֹ ߟ͑Δ·Ͱ΋ͳ͘୭΋ࢀՃ͠ͳ͍ 30
31. First Price AuctionͱSecond Price Auction ϓϨΠϠʔͷࢹ఺͔ΒΦʔΫγϣϯͷྑ͞Λൺֱ མࡳऀͷܾఆϧʔϧ͸ಉҰ ࠷ߴֹೖࡳऀ ͦͷࡍͷίετ͕ҟͳΔ ࠷ߴೖࡳֹ vs ̎Ґೖࡳֹ ̎ҐՁ֨ΦʔΫγϣϯͷݩͰ͸ҙࢥܾఆ͕༰қ 31
32. First Price Auction ϓϨΠϠʔiΛࣗ෼ͩͱࢥ͏ ࣗ਎ͷλΠϓ͸ఆ਺ ଞͷϓϨΠϠʔͷλΠϓ͸෼͔Βͳ͍ i.i.d ΛԾఆͨ֬͠཰ม਺ͱ͢Δ ͜͜Ͱ ͸ ֬཰ม਺ ͷ෼෍ؔ਺ 32 ti = t 2 [0, 1] F : R ! [0, 1] T1, T2, · · · , Ti 1, Ti+1, · · · , Tn ⇠ F T ࠓҪ ੖༤ ,Ԭా ষ. ήʔϜཧ࿦ͷԠ༻, Ⴛ૲ॻ๪ [2005]
33. First Price Auction 33 pi = wi(b)v(ti) ci(b) ϓϨΠϠʔiͷརಘ ϓϨΠϠʔiͷظ଴རಘ উͭ֬཰ ʢॱং౷ܭྔͷ෼෍ʣ উͬͨ࣌ͷརಘ ↑̍ҐՁ֨ E[pi] = (v(ti) (ti)) · F(ti)n 1
34. First Price Auction 34 ϓϨΠϠʔiͷظ଴རಘ উͭ֬཰ ʢॱং౷ܭྔͷ෼෍ʣ উͬͨ࣌ͷརಘ ↑̍ҐՁ֨ E[pi] = (v(ti) (ti)) · F(ti)n 1 = (v(ti) bi) · F( 1(bi))n 1 ͜ͷ஋Λ࠷େԽ͢Δೖࡳؔ਺͸ղੳతʹಋग़Մೳ͕ͩɽɽɽ λΠϓͷ෼෍ΛϞσϦϯά͢Δඞཁ͕ग़ͯ͘Δ ؆୯͡Όͳ͍
35. Second Price Auction 35 Ձ஋ vi ೖࡳֹ ࣗ෼Λআ͘࠷ߴೖࡳֹ bM = max i6=j bj bi ͜ͷݩͰ৔߹෼͚Λͯ͠ߟ͑Δ 1) 2) 3) bi < vi bi = vi bi > vi উͬͨ࣌ͷརಘ pi = vi bM ෛ͚ͨ࣌ͷརಘ pi = 0 ࠓҪ ੖༤ ,Ԭా ষ. ήʔϜཧ࿦ͷԠ༻, Ⴛ૲ॻ๪ [2005]
36. Second Price Auction 36 vi bM bM bM vi = bi bi bi མࡳ མࡳ མࡳ pi = 0 pi = 0 pi > 0 pi > 0 pi > 0 pi = 0 pi = 0 pi > 0 pi = 0 pi < 0 vi
37. Second Price Auction 37 vi bM bM bM vi = bi bi bi མࡳ མࡳ མࡳ pi = 0 pi = 0 pi > 0 pi > 0 pi > 0 pi = 0 pi = 0 pi > 0 pi = 0 pi < 0 = = = = = = > < vi
38. Second Price Auction 38 vi vi bM bM bM vi = bi bi bi མࡳ མࡳ མࡳ pi = 0 pi = 0 pi > 0 pi > 0 pi > 0 pi = 0 pi = 0 pi > 0 pi = 0 pi < 0 = = = = = = > < ࠷దઓུ͸ ࣗ෼ʹͱͬͯͷՁ஋Λ ਃࠂ͢Δࣄ
39. Second Price Auction 39 vi vi bM bM bM vi = bi bi bi མࡳ མࡳ མࡳ pi = 0 pi = 0 pi > 0 pi > 0 pi > 0 pi = 0 pi = 0 pi > 0 pi = 0 pi < 0 = = = = = = > < ࣗ෼ʹͱͬͯͷ Ձ஋ʁʁ
40. ػցֶशʹΑΔ ೖࡳઓུͷܾఆ 40
41. Real Time Bidding ʢ࠶ܝʣ 41 ޿ࠂओʢAdvertiserʣ ޿ࠂ୅ཧళʢAgency) ωοτϝσΟΞʢPublisherʣ DSP = Demand Side Platform SSP = Supply Side Platform Bid Request ! Bid ! AdCall ೖࡳ؅ཧʗӡ༻ Impression
42. Real Time Bidding ʢ࠶ܝʣ 42 ޿ࠂओʢAdvertiserʣ ޿ࠂ୅ཧళʢAgency) ωοτϝσΟΞʢPublisherʣ DSP = Demand Side Platform SSP = Supply Side Platform Bid Request ! Bid ! AdCall ೖࡳ؅ཧʗӡ༻ Impression DSP ͸ Impression ʹରͯ͠ ೖࡳ͢Δʢങ͍͍ͨʣ
43. Demand Side ࢹ఺ͰݟΔΫϦοΫ՝ۚϞσϧ ͇͇ϒϩά xxxxxxxxx xxxxxxxxx xxxxxxxxx xxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxx ܹ҆ʂ Impression ͇͇ϒϩά xxxxxxxxx xxxxxxxxx xxxxxxxxx xxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxx ܹ҆ʂ Click ͓΍ʁ PublisherʗSell Sideʹ ର͢Δࢧ෷͍ൃੜ ̎Ґೖࡳֹ Advertiser͔Βͷใु͕ൃੜ ݻఆֹʢCPC=cost/clickʣ
44. Demand Side ࢹ఺ͰݟΔΫϦοΫ՝ۚϞσϧ Impression ͷՁ஋ ΫϦοΫ୯Ձ ʹ ͇ p(Click|Imp) CPC CTR ʹ ͇ Cost Per Click Click Through Rate ※̏จࣈΞϧϑΝϕοτଟͯ͘͢Έ·ͤΜ
45. Demand Side ࢹ఺ͰݟΔΫϦοΫ՝ۚϞσϧ Impression ͷՁ஋ ΫϦοΫ୯Ձ ʹ ͇ p(Click|Imp) CPC CTR ʹ ͇ Cost Per Click Click Through Rate ※̏จࣈΞϧϑΝϕοτଟͯ͘͢Έ·ͤΜ Second Price Auction ͷ΋ͱͰ ࠷దೖࡳઓུ
46. ݻఆ Demand Side ࢹ఺ͰݟΔΫϦοΫ՝ۚϞσϧ Impression ͷՁ஋ ΫϦοΫ୯Ձ ʹ ͇ p(Click|Imp) CPC CTR ʹ ͇ Cost Per Click Click Through Rate ※̏จࣈΞϧϑΝϕοτଟͯ͘͢Έ·ͤΜ Second Price Auction ͷ΋ͱͰ ࠷దೖࡳઓུ
47. ༧ଌ͍ͨ͠ʂʂʂ ݻఆ Demand Side ࢹ఺ͰݟΔΫϦοΫ՝ۚϞσϧ Impression ͷՁ஋ ΫϦοΫ୯Ձ ʹ ͇ p(Click|Imp) CPC CTR ʹ ͇ Cost Per Click Click Through Rate ※̏จࣈΞϧϑΝϕοτଟͯ͘͢Έ·ͤΜ Second Price Auction ͷ΋ͱͰ ࠷దೖࡳઓུ
48. ΫϦοΫ༧ଌͷ໰୊ઃఆ 48 ϝσΟΞ ޿ࠂ ͦͷଞಛ௃ ΫϦοΫͨ͠ʁ ඒ༰ Խহ ɽɽɽ 1 ඒ༰ ΰϧϑ ɽɽɽ 0 ཱྀߦ ΰϧϑ ɽɽɽ 0.9ʁ ৯඼ ݈߁ ɽɽɽ 0.8ʁ ܇࿅σʔλ ༧ଌσʔλ ͜ͷΫϦοΫ֬཰Λ༧ଌ͍ͨ͠
49. ࣄ৅ɿClick ࣄ৅ɿImpͷΈ ͜ͷͱ͖฼ฏۉ ͸ CTR Click or Not ΛϕϧψʔΠ෼෍Ͱଊ͑Δ ΞΫηεϩά ɿ i.i.d Y1, Y2, · · · , Yn ⇠ Be(p) Yi = 1 Yi = 0 p
50. Click or Not ΛϕϧψʔΠ෼෍Ͱଊ͑Δ ΞΫηεϩά ɿ i.i.d ฼ฏۉ ͷ࠷໬ਪఆྔ͸ ͜ͷ࠷໬ਪఆྔͷ؍ଌ஋Λ༧ଌCTRʢeCTR)ͱͯ͠࠾༻͢Δʁ ࣮͸͜ΕͰ͸ෆे෼ʢͰ΋ͳ͔ͳ͔͍͍ʣ ͳͥʁʁʁʁʁʁ p ¯ p = 1 n n X i=1 Yi Y1, Y2, · · · , Yn ⇠ Be(p)
51. Click or Not ΛϕϧψʔΠ෼෍Ͱଊ͑Δ ঁੑ޲͚ϝσΟΞ ए೥૚޲͚Խহ඼ͷAd ঁੑ޲͚ϝσΟΞ ΰϧϑ৔༧໿αʔϏεͷAd ͇ ͇ ͲͪΒͷ΄͏͕CTR͕ߴ͍͔ ౰વલऀɼϝσΟΞͱ޿ࠂओͷ਌࿨ੑ͕ߴ͍͔Β ͜ͷ͜ͱΛϞσϦϯά͢Δ VS
52. Click or Not ΛϕϧψʔΠ෼෍Ͱଊ͑Δ ΞΫηεϩά ɿ ( , , ) ޿ࠂओͷಛ௃ ϝσΟΞͷಛ௃ Yi ⇠ Be(pi) ͨͩ͠ ͜ͷ Λ࠷໬ਪఆ͢Ε͹ྑ͍ ͜ͷϞσϧΛLogistic Regressionͱ͍͏ pi = f ✓ ( x ) = 1 1 + e x = ( X j ✓jXij + ✓0) ✓0, ✓1, · · · , ✓f minimize L ( ✓ ) = log p ( Y |X, ✓ ) = n X i=0 log p ( Yi |Xi, ✓ )
53. γάϞΠυʹ͍ͭͯ ࣦഊʹର͢Δ੒ޭͷׂ߹ˠΦοζ ͦͷର਺ˠϩδοτؔ਺ ͦͷٯؔ਺ˠγάϞΠυʢϩδεςΟοΫʣؔ਺ p 1 p logit( p ) = log p 1 p logit 1 (x) = (x) = 1 1 + e x wikipedia : γάϞΠυؔ਺ ΑΓ
54. ػցֶशʹΑΔ༧ଌ͕͏·͍͔͘ͳ͍৔߹ͷݪҼ σʔλʹରͯ͠Ϟσϧͷදݱྗ͕௿͗͢Δ ܇࿅σʔλ಺Ͱ΋ਫ਼౓͕ѱ͍ σʔλʹରͯ͠Ϟσϧͷදݱྗ͕ߴ͗͢Δ ܇࿅σʔλҎ֎ͷσʔλ΁ͷਫ਼౓ʢ൚Խੑೳʣ͕௿͍ 54 pi = ( X j ✓jXij + ✓0) ʦࢀߟʧަޓ࡞༻߲ΛೖΕΕ͹ϩδεςΟοΫճؼͰ΋ඇઢܗ෼཭ՄೳʹͳΔ͜ͱ΋͋Δ http://tjo.hatenablog.com/entry/2015/03/26/190000 wikimedia Commons File:Overfitting.svg pi = ( X j ✓jXij + X j X k j+1 wjkXjXk + ✓0)
55. ʦରࡦ̍ʧදݱྗͷ௿͍ϞσϧΛେྔʹ࡞ͬͯฏۉΛऔΔ ֓ཁ Ξϯαϯϒϧֶशͱݺ͹Ε͍ͯΔ ҎԼͷखॱͰಘΒΕֶͨशثΛऑֶशثͱݺͿ આ໌ม਺΍ֶशσʔλΛϥϯμϜʹ࡟ͬͨσʔληοτ࡞੒ ͦͷσʔληοτΛֶश ऑֶशثΛେྔʹੜ੒ ͦΕͧΕͷऑֶशثͷ݁ՌΛूܭͯ͠ɼ݁Ռͱͯ͠࠾༻ɽ Random Forest, Gradient Boosting Decision Tree ͳͲ
56. ʦରࡦ̎ʧදݱྗͷߴ͍Ϟσϧ࡞ͬͯม਺ΛറΔ -ਖ਼ଇԽ- ਖ਼ଇԽ߲ɿม਺͕େ͖͍͜ͱʹର͍͍ͯ͠۩߹ͷേଇΛ༩͑Δ ࠷໬ਪఆͰ͸ͳ͘ͳΔ ༗ҙͰͳ͍ม਺ͷޮՌΛམͱ͢ɽ ͸ม਺ΛറΔڧ͞Λௐઅ͢ΔϋΠύʔύϥϝλʢަࠩݕূͰ୳ࡧʣ minimize log p ( Y |X, ✓ ) log p ( Y |X, ✓ ) + f X i=0 ✓2 i log p ( Y |X, ✓ ) + f X i=0 |✓i | minimize minimize േଇ߲
57. ʦରࡦ̏ʧFactorization Machineͷࣗ༝౓࡟ݮͷΞΠσΟΞ pi = ( X j ✓jXij + X j X k j+1 wjkXjXk + ✓0) pi = ( X j ✓jXij + X j X k j+1 hvj, vk iXjXk + ✓0) ( ( ' ( ( ( ( W V f f f k <͘͢͝খ͍̺͞ V ⇤ Steffen Rendle, Factorization Machines [ICDM 2010]
58. CTR༧ଌʹؔͯ͠ิ଍ Logistic Regression ͷઆ໌ม਺͸booleanͰ͋Δ͜ͱ͕ଟ͍ ࿈ଓ஋Λઆ໌ม਺ͱͯ͠࢖͍͍ͨ৔߹ ܾఆ໦ܥͷΞϯαϯϒϧֶशͰΧςΰϦʹม׵ͯ͠࢖͏ͷ͕ྲྀߦΓ ม׵ͨ͠ޙͷ࣍ݩ͸ ਺ेʙ਺ेສ͘Β͍ͷ࣍ݩɽ ΫϦοΫ՝ۚҎ֎ʹ΋༷ʑํ๏Ͱ޿ࠂ͸औҾ͞Ε͍ͯ·͢ɽ 58 Xu, Huang, Weinberger and Zheng. Gradient Boosted Feature Selection [KDD 2014]
59. ޿ࠂޮՌΛܭଌͯ͠ ࠷దͳҙࢥܾఆΛߦ͏ 59
60. ؍ଌ͞ΕΔσʔλʢച্ɼࢪࡦ౤ೖྔʣͷࢄ෍ਤ ͜ͷσʔλΛݩʹདྷظͷ࠷దࢪࡦ౤ೖྔΛܾΊ͍ͨ ͳͥϞσϦϯάʁ 60
61. ϞσϦϯάͷ݁Ռ͕ҙࢥܾఆͷ൑அࡐྉʹͳΔɽ ͳͥϞσϦϯάʁ 61 ࠷దͳࢪࡦ౤ೖྔ
62. ޿ࠂࢪࡦͷϙʔτϑΥϦΦ ࢪࡦ̍ͱࢪࡦ̎΁ͷ౤ೖֹۚ ͱKPIΛϞσϦϯά͢Δͱɽ ࢪࡦ̍ɼ̎͸ྫ͑͹Ϛε޿ࠂͱΦϯϥΠϯ޿ࠂ ϞσϧͷԼͰ࠷దͳ༧ࢉ഑෼͕ܭࢉग़དྷΔ [1]ࢪࡦʹର͢Δ༧ࢉ഑෼໰୊ 62 x1 x2 x1 x2 ༧ࢉ੍໿ ࢪࡦͷ΋ͱͰͷKPI
63. [1]ࢪࡦʹର͢Δ༧ࢉ഑෼໰୊ 63 y = X i ✓i log(xi + 1) + ✓0 Optim Modeling ※Ϟσϧࣜ͸μϛʔ ঎ࡐʹ߹Θͤͯద੾ʹ σβΠϯ͢Δ y = X i ✓i log(xi + 1) + ✓0 y = X i ✓i log(xi + 1) + ✓0 Optim Modeling y = X i ✓i log(xi + 1) + ✓0 ͜ΕΛ܁Γฦͯ͠࠷దͳ༧ࢉ഑෼Λ୳Δ ʦ໰୊ʧച্Λ֫ಘͭͭ͠ɼޮ཰Α͘୳ࡧ͢Δʹ͸ʁ
64. [2] ಉ͡ࢪࡦ͸ܧଓͯ͠ߦ͏ͱޮՌ͸చݮ͢Δͷ͔ʁ ʮि຤ͷࢪࡦɼ࠷ۙޮՌѱ͘ແ͍Ͱ͔͢ʁʁʯ 64
65. [2] ಉ͡ࢪࡦ͸ܧଓͯ͠ߦ͏ͱޮՌ͸చݮ͢Δͷ͔ʁ 65 ࢪࡦʹΑΔޮՌ͕చݮ͍ͯ͠Δࣄ͕Θ͔Δ ࢪࡦΛ౤ೖ͍ͯ͠ͳ͍ظؒͷ܎਺͕ਪఆग़དྷ͍ͯΔ
66. [2] ಉ͡ࢪࡦ͸ܧଓͯ͠ߦ͏ͱޮՌ͸చݮ͢Δͷ͔ʁ 66 ࢪࡦʹΑΔޮՌ͕చݮ͍ͯ͠Δࣄ͕Θ͔Δ Ͳ͏΍ͬͨʁʁ ಈతઢܗϞσϧͷಋೖ
67. ௨ৗͷਖ਼نઢܗϞσϧ ಈతઢܗϞσϧ ͜ͷa_t, b ,σ Λਪఆ͢Ε͹ྑ͍ ΑΓҰൠతʹ͸ঢ়ଶۭؒϞσϧ Ͳ͏΍ͬͯܭࢉ͢Ε͹͍͍͔ʁ 67 [2] ಉ͡ࢪࡦ͸ܧଓͯ͠ߦ͏ͱޮՌ͸చݮ͢Δͷ͔ʁ yt ⇠ N( axt + b, 2) yt ⇠ N( atxt + b, 2) at ⇠ N(at 1, 2 a )
68. ϕΠζਪ࿦ͱStan ϕΠζͷఆཧ ͜ͷࣄޙ෼෍͸ܭࢉࠔ೉ ఆৗ෼෍͕͜ͷࣄޙ෼෍ͱͳΔܥྻ Λੜ੒͢Δ͜ͱ͕ग़དྷΔ ʹʼ Ϛϧίϑ࿈࠯Ϟϯς Χϧϩ๏ 68 p(✓|Y, X) = p(X, Y |✓)p(✓) R p(X, Y |✓)p(✓)d✓ ✓1, ✓2, · · ·
69. 69 ϕΠζਪ࿦ͱStan ๯಄ͷಈతઢܗϞσϧ
70. ϕΠζਪ࿦ιϑτ΢ΣΞ Stan ࣄޙ෼෍͔ΒαϯϓϧΛಘΔ͜ͱ͕ग़དྷΔ R/ Python/ MatLabʹຒΊࠐΜͰ࢖͑ΔDSL 70 ࢀߟɿ॓ധ͢ΔϗςϧͷόελΦϧ ϕΠζਪ࿦ͱStan
71. Stanͷϓϩάϥϛϯά 71 log p ( ✓|Y, X ) = log p ( X, Y |✓ ) + log p ( ✓ ) C p(✓|Y, X) = p(X, Y |✓)p(✓) R p(X, Y |✓)p(✓)d✓ ೖྗ ग़ྗ ϕΠζਪ࿦ͱStan
72. 72 Y ✓ log p ( Y |✓ ) + log p ( ✓ ) ͷએݴ ͷએݴ Λهड़ ϕΠζਪ࿦ͱStan
73. 73 Y ✓ log p ( Y |✓ ) + log p ( ✓ ) ͷએݴ ͷએݴ Λهड़ ϕΠζਪ࿦ͱStan
74. ·ͱΊ 74
75. ·ͱΊ 75 ޿ࠂͷ༷ʑͳ՝୊Λ਺ཧతͳ໰୊ʹؼணͤ͞Δྫ ΦʔΫγϣϯͷཧ࿦ Ձ஋ͷਪఆ ޮՌͷܭଌ ػցֶशιϑτ΢ΣΞ TensorFlow, ApacheSpark, scikit-learn, Mahout, XGBoost… ౷ܭϞσϦϯάιϑτ΢ΣΞ Stan, Jags, WinBUGS, glm@R, Statsmodels@Python
76. ലେͳ࣮σʔλΛอ༗ ΦʔΫγϣϯऔҾϩά νϟοτର࿩ϩά ଞɽɽɽ ࠃ಺༗਺ͷ༏लͳΤϯδχΞଟ਺ ཁૉٕज़ͷϚωλΠζ࣮੷ ࢈ֶ࿈ܞਪਐத 76 ༷ʑͳઐ໳ྖҬ ͇
77. ஫ྗ෼໺ 77 ΦʔΫγϣϯͷཧ࿦ ࣗવݴޠॲཧٕज़ ඇߏ଄σʔλॲཧʢը૾ɾԻ੠ɾԻָʣ ϚʔέςΟϯάαΠΤϯε Ϗοάσʔλॲཧج൫ ·ͣ͸͓ଧͪ߹Θ͔ͤΒʂ
78. Hiroki Mizukami mizukami_hiroki@cyberagent.co.jp “͝੩ௌ͋Γ͕ͱ͏͍͟͝·ͨ͠”