Introduction to Bayesian Learning for Machine Learning 5.4 - 5.7

「ベイズ推論による機械学習入門」輪読会 #4 - connpass https://reading-circle-beginners.connpass.com/event/136714/ の発表資料です

Transcript

1. ʮϕΠζਪ࿦ʹΑΔػցֶशೖ໳ʯྠಡձ #4
   5.4 - 5.7
   

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2. ࣗݾ঺հ
   • ਿࢁ Ѩ੟
   • Software Engineer (Machine Learning ؔ܎ͷॾʑ)
   • ػցֶशਤؑ ڞஶ
   

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3. ͜͜ͰֶͿ͜ͱ
   • ҰൠʹػցֶशͰߦΘΕΔΞϧΰϦζϜΛϕΠζਪ࿦Ͱݟ௚͢
   (͜͜Ͱ৮ΕΔେମͷΞϧΰϦζϜ͸ྫ͑͹ scikit-learn
   ʹ࣮૷͞Ε͍ͯΔ)
   

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4. ํ਑
   • ໰୊ઃఆͷ֬ೝΛߦ͏
   • άϥϑΟΧϧϞσϧͷ֬ೝΛߦ͏
   • ਺ࣜͷ֬ೝ͸௥͍ٻΊͳ͍
   1.ຊʹׂͱஸೡʹॻ͍ͯ͋ΔͨΊ
   2.ຊΛهड़͕ͳ͍͜ͱΛ௥͍ٻΊΑ͏ͱ͢Δͱ্هͷϙΠϯτ
   ʹϑΥʔΧε͖͠Εͳ͍ͨΊ
   

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5. ໨࣍
   1.τϐοΫϞσϧ (5.4)
   2.ςϯιϧ෼ղ (5.5)
   3.ϩδεςΟοΫճؼ (5.6)
   4.χϡʔϥϧωοτϫʔΫ (5.7)
   

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6. Point
   ಺༰ (section) Point
   τϐοΫϞσϧ (5.4) ࣗવݴޠॲཧͷάϥϑΟΧϧϞσϧ
   ςϯιϧ෼ղ (5.5) ࣌ܥྻσʔλʹରͯ͠ͷڠௐϑΟϧλ
   ϦϯάͷάϥϑΟΧϧϞσϧ
   ϩδεςΟοΫճؼ (5.6) ࠶ύϥϝʔλʔԽ
   χϡʔϥϧωοτϫʔΫ (5.7) ޡࠩٯ఻೻๏
   

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7. τϐοΫϞσϧ (5.4)
   

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8. τϐοΫϞσϧ (5.4) ཁ໿
   1.LDA (Latent Dirichlet Allocation) Λѻ͏
   2.LDA Ͱ͸࣍ͷ 2 ͭΛಉ࣌ʹߦ͏
   • จষ͔ΒͷτϐοΫͷநग़
   • ֤τϐοΫͰग़ݱ͢Δ୯ޠͷੜ੒Ϟσϧͷֶश
   3.ֶश͸ม෼ਪ࿦ɾ่յܕΪϒεαϯϓϦϯάͰՄೳ
   

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9. τϐοΫϞσϧ ಺༰
   1.എܠɾ໰୊ઃఆ
   2.Ϟσϧͷఆٛ
   3.ֶश
   

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10. τϐοΫϞσϧͰѻ͏σʔλ
    • ࣗવݴޠͰॻ͔Εͨจষͷղੳ
    • จষ͸ू߹ͱͯ͠ѻ͍ɺ୯ޠͷग़ݱॱং͸ߟྀ͠ͳ͍
    • χϡʔεهࣄͷจষͷΑ͏ʹจষʹ͸τϐοΫ (੓࣏ɺܳೳɺ
    etc.) ͕͋ΓɺτϐοΫ͝ͱʹग़ݱ͢Δޠ͕۟ҧ͏ͱ૝ఆ͢Δ
    • ྫ : ʮྟ࣌ࠃձʯ͸ʮ੓࣏ʯτϐοΫͰ͸ग़ݱ͠΍͘͢ɺ
    ʮܳೳʯτϐοΫͰ͸ग़ݱ͠ʹ͍͘
    • τϐοΫ͕Կ͔͸ ۩ମతʹ͸஌Βͳ͍ ΋ͷͱ͢Δ
    

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11. τϐοΫϞσϧͰୡ੒͍ͨ͜͠ͱ
    1.จষͷଐ͢ΔτϐοΫʹ͍ͭͯɺ෼ੳऀ͕໌ࣔతʹࢦఆ͢Δ͜
    ͱͳ͘σʔλͦͷ΋ͷ͔Βநग़͍ͨ͠
    • நग़ͨ͠τϐοΫ͕ԿΛҙຯ͢Δͷ͔͸෼ੳऀ͕൑அ͢Δ
    • จষ͸ʮ੓࣏ 0.9, ܳೳ 0.1ʯͷΑ͏ʹෳ਺ͷτϐοΫʹ
    ଐ͢Δ΋ͷͱ͢Δ
    2.୯ޠ͕ଐ͢ΔτϐοΫʹ͍ͭͯจ຺Λߟྀ͍ͨ͠
    • ʮυϥΠϒʯ͸ं͔Β΋ςΫϊϩδʔ͔Β΋ग़ݱ͢Δ
    

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12. એ఻
    ػցֶशਤؑͰѻ͍ͬͯΔͷͰ಺༰Λ֬ೝ
    

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13. ༨ஊ
    • ࿦จ1 Ͱ͸ूஂҨ఻ֶͰͷԠ༻ʹ͍ͭͯड़΂͍ͯΔ
    1.ར֐ؔ܎Λ࣋ͭूஂΛݟ͚ͭɺͦΕΒͷؔ܎ੑΛௐ΂͍ͨ
    2.֤ूஂ͔Β࠾औͨ͠ DNA ͔Βڞ௨ͷ૆ઌΛௐ΂͍ͨ
    • σʔλ͔Β෼ੳऀͷओ؍ʹΑΒͳ͍ʮӅ͞Εͨʯߏ଄Λநग़͠
    ͍ͨɺͱ͍͏ͷ͕Ϟνϕʔγϣϯ
    1 Pritchard, J. K.; Stephens, M.; Donnelly, P. (June 2000). "Inference of population structure
    using multilocus genotype data". Genetics. 155 (2): pp. 945–959. ISSN 0016-6731.
    

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14. τϐοΫϞσϧ ಺༰
    1.എܠɾ໰୊ઃఆ
    2.Ϟσϧͷఆٛ
    3.ֶश
    

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15. ه߸ͷ४උ
    

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17. τϐοΫ਺ 1 ͷ৔߹
    • ࣗ໌ͳྫΛѻͬͯɺه߸ͷ֬ೝΛ·ͣߦ͏
    • τϐοΫ਺ 1 ͱ͢Δͱɺ1 ͭͷτϐοΫʹ͢΂ͯͷจষ͕ଐ
    ͢Δ͜ͱʹͳΔ
    • ͭ·ΓɺҰൠʹ೔ຊޠͷจষʹ͍ͭͯͷੜ੒ϞσϧΛѻ͏
    

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19. τϐοΫ਺ 2 ͷ৔߹
    • εύϜϝʔϧ൑ఆͷΑ͏ͳ΋ͷΛѻ͏
    • ਖ਼͘͠͸࣍
    1.ϝʔϧ͕ 2 छྨʹ෼͚ΒΕͦ͏ͳ͜ͱ͸ͳ͔ͥ஌͍ͬͯΔ
    2.݁Ռ͕Ͳ͏෼͔ΕΔ͔͸஌Βͳ͍
    3.্هͷঢ়ଶͰΫϥελϦϯάΛߦ͍͍ͨ
    

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21. τϐοΫϞσϧ ಺༰
    1.എܠɾ໰୊ઃఆ
    2.Ϟσϧͷఆٛ
    3.ֶश
    

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22. τϐοΫϞσϧͷֶश
    • ม෼ਪ࿦ʹ͍ͭͯ͸লུ
    • ॻ੶ʹׂͱஸೡʹهड़͞Ε͍ͯΔͨΊ
    • ่յܕΪϒεαϯϓϦϯάʹ͍ͭͯѻ͏
    

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23. ΪϒεαϯϓϦϯά (4.2)
    ͋Δ֬཰෼෍ ͔Βαϯϓϧ
    Λಘ͍ͨ৔߹ɺ࣍ͷΑ͏ʹ৚݅෇͖֬཰෼෍͔Βஞ࣍αϯϓϦϯά
    ͢Δ͜ͱͰɺۙࣅతʹ΋ͱͷ෼෍ʹै͏αϯϓϧྻΛಘΒΕΔɻ
    

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24. ่յܕΪϒεαϯϓϦϯά (4.2)
    ͋Δ֬཰෼෍ ͔Βαϯϓϧ Λ
    ಘ͍ͨ৔߹ɺ࣍ͷΑ͏ʹपลআڈ͔ͯ͠ΒαϯϓϦϯά͢Δɻ
    

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25. τϐοΫϞσϧ΁ͷԠ༻
    1.่յܕΪϒεαϯϓϦϯάΛ༻͍ͯ ΛαϯϓϦϯά͠ɺ࣮
    ݱ஋ ΛಘΔ
    2.࣮ݱ஋ Λ࢖ͬͯ୯ޠΛτϐοΫʹ෼͚ɺ ൪໨ͷτϐοΫ
    ͔Βग़ݱͨ͠୯ޠू߹ ΛಘΔ
    3. ͔Β Λߋ৽͢Δ
    4. ͔Β֤จষͷτϐοΫൺ཰ΛٻΊɺ Λߋ
    ৽͢Δ
    

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26. पลআڈͨ͠άϥϑΟ
    ΧϧϞσϧ
    • पลআڈ͢Δͱ׬શάϥϑ͕Ͱ͖Δ
    (ӈਤ)
    • τϐοΫϞσϧͰ΋पลআڈΛ͢Δͱ
    ׬શάϥϑ͕Ͱ͖͕͋Δ
    

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27. Ϛϧίϑϒϥϯέοτ
    (1.5)
    • , , , , , , ͷؒʹ͸ґଘ
    ؔ܎͕͋Δ
    • ͜ͷઌʹ͋Δϊʔυ͸͢΂ͯ ͱಠཱ
    

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28. ৚݅෇͖ಠཱੑͷ֬ೝ
    • ͱ , ͸৚݅෇͖ಠཱ
    • ਤ 4.8 ͱಉٞ͡࿦
    • ͱ ͸৚݅෇͖ಠཱ
    • ڞಉ਌ͷؔ܎ʹͳ͍ͨΊ
    • ্هΛ࢖͏ͱ ͷ෼෍͸࣍ͷΑ͏
    ʹͰ͖Δ
    

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29. Ҏ߱লུ
    

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30. ςϯιϧ෼ղ (5.4)
    

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31. ςϯιϧ෼ղ ཁ໿
    1.τϨϯυΛߟྀͨ͠ڠௐϑΟϧλϦϯάΛѻ͏
    2.ڠௐϑΟϧλϦϯάͰ͸ϢʔβʔͱΞΠςϜͷ྆ํΛߟྀͨ͠
    ϨʔςΟϯάΛߦ͏
    3.ֶश͸ม෼ਪ࿦ͰՄೳ (ΪϒεαϯϓϦϯά͸ݴٴͳ͠)
    

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32. ςϯιϧ෼ղ ಺༰
    1.എܠɾ໰୊ઃఆ
    2.Ϟσϧͷఆٛ
    3.ֶश
    

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33. ໰୊ઃఆ: ۺ԰ͷधཁ༧ଌ2(1/2)
    • قॳͷ஫จͱաڈͷ஫จཤྺ͔Βࠓقͷधཁ༧ଌΛ͍ͨ͠
    • ҠಈฏۉϞσϧ (ARMA) ͸࢖͑ͳ͍ɺͳͥͳΒ৽͍͠ΞΠςϜ
    ʹ͍ͭͯաڈͷσʔλ͸ͳ͍
    • ճؼϞσϧ͸࢖͑ͳ͍ɺͳͥͳΒυϝΠϯ஌͕ࣝෳࡶ͗͢Δ͠
    ϙϦγʔʹ൓͢Δ (?)
    2 L.Xiong,X.Chen,T.K.Huang,J.Schneider,andJ.G.Carbonell.Temporal collaborative filtering with
    Bayesian probabilistic tensor factorization. In Proceeding sof the 2010 SIAM International
    Conferenceon Data Mining, pages 211-222, 2010.
    

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34. ໰୊ઃఆ: ۺ԰ͷधཁ༧ଌ (2/2)
    • యܕతͳڠௐϑΟϧλϦϯάͰ͸ෆे෼ɺͳͥͳΒσβΠϯ΍
    ফඅऀͷ޷ΈͷྲྀߦΛߟྀͰ͖ͳ͍
    • ͦ͜Ͱզʑ͸࣌ܥྻΛߟྀͨ͠ BPTF (Bayesian
    Probabilistic Tensor Factorization) ΛఏҊ͢Δ
    • Netflix ͷࢹௌཤྺσʔλ3Ͱݕূͨ͠ͱ͜Ζɺ࣌ܥྻΛߟྀ
    ͠ͳ͍Ϟσϧʹൺ΂͔ͯ֬ʹվળ͞Εͨ
    3 Netflix Prise data https://www.kaggle.com/netflix-inc/netflix-prize-data
    

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35. ༨ஊ
    • ڠௐϑΟϧλϦϯά͸ɺΞΠςϜͱϢʔβʔΛ ࣍ݩϕΫτϧ
    ʹຒΊࠐΜͰ͍ΔͱղऍͰ͖Δ
    • ਂ૚ֶश੎͔Β͸ embedding Λಘ͍ͨͷͳΒ auto
    encoder ͱ͔ word2vec ͱ͔࢖͑͹͍͍Μ͡Όͳ͍͔ɺͱ
    ͳΔ (͔΋)
    • ࣮ࡍɺචऀ͕ VAE ͱͷؔ࿈ʹ͍ͭͯϒϩάهࣄ4Λॻ͍͍ͯΔ
    4 ઢܗճؼΛ̍ͭ̍ͭվ଄ͯ͠ม෼ΦʔτΤϯίʔμʢVAEʣΛ࡞Δ - ࡞ͬͯ༡Ϳػցֶशɻ
    

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36. ςϯιϧ෼ղ ಺༰
    1.എܠɾ໰୊ઃఆ
    2.Ϟσϧͷఆٛ
    3.ֶश
    

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37. ڠௐϑΟϧλϦϯά (1/2)
    • ԣํ޲ʹΞΠςϜɺॎํ޲ʹϢʔβʔΛฒ΂ͨߦྻ Λѻ͏
    • ͸Ϣʔβʔ ͷΞΠςϜ ʹର͢ΔϨʔςΟϯά
    • ػցֶशʹ͓͍ͯ࣍ͷΑ͏ʹߟ͑Δ͜ͱ͕ଟ͍ (ཁग़య)
    • ϕΫτϧ : 1 ࣍ݩ഑ྻ
    • ߦྻ : දɺςʔϒϧ
    • ςϯιϧ : ෳ਺ͷද (ϛχόονͱ͔)
    

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38. ڠௐϑΟϧλϦϯά (2/2)
    • ϨʔςΟϯάΛ࣍ͷΑ͏ʹ෼ղ͢Δ
    • , ,
    ͱͯ͠
    • ੒෼Ͱॻ͘ͱ࣍ͷࣜ
    • ࣍ݩ࡟ݮʹΑΔܽଛ஋ͷิ׬ʹಉ͡
    (5.1)
    

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39. ࣌ܥྻ΁ͷ֦ு
    • ͋Δ࣌ؒ ʹ͓͚Δಛ௃ ͷྲྀߦ౓
    ͷΑ͏ͳ΋ͷ (ݪจϚϚ) Λಋೖ
    ͢Δ
    • ϢʔβʔͱΞΠςϜͷ಺ੵΛɺྲྀߦ౓ʹ
    ΑΔॏΈ෇͖Ͱܭࢉ͍ͯ͠Δ
    

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41. ςϯιϧ෼ղ ಺༰
    1.എܠɾ໰୊ઃఆ
    2.Ϟσϧͷఆٛ
    3.ֶश
    

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42. ֶश (লུ)
    • ม෼ਪ࿦ͰՄೳ (ৄࡉ͸লུ)
    • ࣍ͷ݁Ռʹ஫໨͢Δ
    • ͸Ϣʔβʔ͝ͱʹݸผͷ஋ֶ͕श͞ΕΔ
    • ͸Ϣʔβʔ͝ͱʹڞ௨ͷ஋ֶ͕श͞ΕΔ
    • ΋ಉ༷
    • ਫ਼౓ߦྻ , , ͸ʮେ͖͘ʯͳ͍ͬͯΔ
    

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43. ϩδεςΟοΫճؼ (5.6)
    

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44. ϩδεςΟοΫճؼ ཁ໿
    1.ϩδεςΟοΫճؼͰ͸ Softmax ؔ਺Λ༻͍ΔͨΊɺࠓ·Ͱ
    ͷΑ͏ʹղੳղ͕ٻΊΒΕͳ͍
    2.࠷దͳύϥϝʔλʔΛٻΊΔͨΊʹɺ৽ͨʹޯ഑๏Λಋೖ͢Δ
    3.ޯ഑ͷܭࢉΛۙࣅతʹߦ͏ͨΊɺ࠶ύϥϝʔλʔԽτϦοΫΛ
    ߦͬͯܭࢉ͢Δ
    

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45. ϩδεςΟοΫճؼ ಺༰
    1.എܠɾ໰୊ઃఆ
    2.Ϟσϧͷఆٛ
    3.ֶश
    

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46. ϩδεςΟοΫճؼ (ඇϕΠζ)
    ػցֶशਤؑͰѻ͍ͬͯΔͷͰ֬ೝ
    

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47. ϕΠζʹ͢ΔͱԿ͕خ͍͠ͷ͔
    • ਤ 5.15
    • Կݸ΋ϩδεςΟοΫճؼϞσϧΛ࡞ͬͯΞϯαϯϒϧ͢Δ͜
    ͱͰ͍͍ײ͡ͷग़ྗ͕ಘΒΕΔ
    

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48. ϩδεςΟοΫճؼ ಺༰
    1.എܠɾ໰୊ઃఆ
    2.Ϟσϧͷఆٛ
    3.ֶश
    

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49. ϩδεςΟοΫճؼ
    ଟ࣍ݩϕΫτϧ ͕࣍ͷΑ͏ͳΧςΰϦ෼෍ʹैͬͯग़ྗ͞Ε
    Δ΋ͷͱ͢Δɻ
    ͜͜Ͱɺ ͸ඇઢܗؔ਺Ͱɺࠓճ͸ Softmax ؔ਺Λ༻͍Δɻ
    

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50. ༨ஊ ιϑτϚοΫεؔ਺ͷඍ෼
    

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52. ϩδεςΟοΫճؼ ֶश
    • ೖྗ஋ͱग़ྗ஋ͷσʔληοτ ͔Β ͷࣄޙ෼෍Λ
    ܭࢉ
    ϩδεςΟοΫճؼ ਪ࿦
    • ৽نͷೖྗσʔλ ͕༩͑ΒΕͨͱ͖ͷग़ྗ஋ ͷܭࢉ
    

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53. ϩδεςΟοΫճؼ ಺༰
    1.എܠɾ໰୊ઃఆ
    2.Ϟσϧͷఆٛ
    3.ֶश
    

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54. ࠓ͔Βઆ໌͢Δ಺༰
    • ม෼ਪ࿦Λߦ͍͍͕ͨɺ୯७ͳฏۉ৔ۙࣅͰ͸ෆՄೳ
    • ϞϯςΧϧϩ๏Ͱ΋ՄೳͰ͸͋Δ͕ɺ͏·͍͔͘ͳ͍͜ͱ͕஌
    ΒΕ͍ͯΔ
    • ࠶ύϥϝʔλʔԽτϦοΫΛ࢖ͬͨޯ഑๏ͰɺϞϯςΧϧϩ๏
    Λճආ͢Δ
    

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55. ม෼ਪ࿦
    • ͱ͢Δ
    • KLμΠόʔδΣϯε Λ࠷খԽ͢Δ
    

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56. ղੳతͳղΛಘΒΕͳ͍߲ͷܭࢉ
    • ࠷ޙͷ໬౓ͷظ଴஋Λͱ͍ͬͯΔ߲ͷܭࢉ͕ࠔ೉
    • ϞϯςΧϧϩ๏ʹΑΔܭࢉ͕ՄೳͰ͸͋Δ
    • ͔͠͠ɺ ΛαϯϓϦϯά͢Δͱ࠷దԽ͍ͨ͠ύϥϝʔλʔ
    ͕࢒Βͳ͍
    

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57. ࠶ύϥϝʔλʔԽτϦοΫ
    • ΛαϯϓϦϯάͯ͠ Λಘͨͱ͢Δ
    • ͔ΒαϯϓϦϯάͨ͠ͱߟ͑Δͱɺ࠷దԽͨ͠
    ͍ύϥϝʔλʔ͕͔ࣜΒফ͑ͯޯ഑๏͕࣮ߦͰ͖ͳ͍
    • ͷ࣮ݱ஋ ͕ಘΒΕͨͷͩͱΈͳ͢
    ( ΛαϯϓϦϯάͨ͠ͷͩͱߟ͑Δ)
    • 1ճͷαϯϓϦϯάͰޯ഑ͷܭࢉͱɺॏΈͷߋ৽͕Ͱ͖Δ
    

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58. View Slide

59. ࣜ 5.236 Ҏ߱ͷهड़ʹ͍ͭͯ
    • ޯ഑͕ܭࢉͰ͖ͨͷͰɺύϥϝʔλʔΛߋ৽Ͱ͖Δ
    • ͋ͱ͸Կ౓΋αϯϓϦϯάͱύϥϝʔλʔͷߋ৽ΛؤுΔ
    

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60. ਪ࿦
    • ࠷దͳύϥϝʔλʔ͕ٻΊΒΕͨͷͰ࣍ͷΑ͏ʹۙࣅͰ͖Δ
    • ϥϕϧͷظ଴஋͸࣍ͷΑ͏ʹۙࣅͰ͖Δ
    

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61. χϡʔϥϧωοτϫʔΫ (5.7)
    

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62. লུ
    

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63. লུ͢Δཧ༝
    1.໰୊ઃఆ͸ϩδεςΟοΫճؼʹ΄΅ಉ͡
    2.Ϟσϧ͸ϩδεςΟοΫճؼΛॏͶΔ͚ͩ
    3.ֶशͰಋೖ͢Δޡࠩٯ఻೻๏ʹ͍ͭͯɺ͜Ε͚ͩͷઆ໌ͰΘ͔
    Δਓ͸͍ͳ͍
    

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64. ༨ஊ
    • χϡʔϥϧωοτϫʔΫͷॏΈΛখ͞ͳཚ਺ͰॳظԽ͠ޯ഑߱
    Լ๏Ͱܭࢉͤ͞Δɺͱ͍͏ͷ͸Ұൠత
    • ͜͜·ͰདྷΔͱʮଟ਺ͷॏΈΛ͔͚߹Θͤͯ଍͢ʯͱ͍͏ͷ
    ͸ɺظ଴஋ΛͱΔૢ࡞ʹݟ͑ͯ͘Δ
    • ޯ഑๏Λ༻͍ͯߋ৽ͨ͠ॏΈͷ஋Λར༻͢Δͷ͸ɺࣄޙ෼෍͔
    ΒαϯϓϦϯά͍ͯ͠ΔΑ͏ʹݟ͑ͯ͘Δ
    • ࣮ࡍɺਂ૚ֶश͸Ψ΢εաఔͱΈͳͤΔ͜ͱ͕஌ΒΕ͍ͯΔ
    

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65. Recap
    ಺༰ (section) Point
    τϐοΫϞσϧ (5.4) ࣗવݴޠॲཧͷάϥϑΟΧϧϞσϧ
    ςϯιϧ෼ղ (5.5) ࣌ܥྻσʔλʹରͯ͠ͷڠௐϑΟϧλ
    ϦϯάͷάϥϑΟΧϧϞσϧ
    ϩδεςΟοΫճؼ (5.6) ࠶ύϥϝʔλʔԽ
    χϡʔϥϧωοτϫʔΫ (5.7) ޡࠩٯ఻೻๏ (লུ)
    

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