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Introduction to Bayesian Learning for Machine L...

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

Asei Sugiyama

July 07, 2019
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  1. Point ಺༰ (section) Point τϐοΫϞσϧ (5.4) ࣗવݴޠॲཧͷάϥϑΟΧϧϞσϧ ςϯιϧ෼ղ (5.5) ࣌ܥྻσʔλʹରͯ͠ͷڠௐϑΟϧλ

    ϦϯάͷάϥϑΟΧϧϞσϧ ϩδεςΟοΫճؼ (5.6) ࠶ύϥϝʔλʔԽ χϡʔϥϧωοτϫʔΫ (5.7) ޡࠩٯ఻೻๏
  2. τϐοΫϞσϧ (5.4) ཁ໿ 1.LDA (Latent Dirichlet Allocation) Λѻ͏ 2.LDA Ͱ͸࣍ͷ

    2 ͭΛಉ࣌ʹߦ͏ • จষ͔ΒͷτϐοΫͷநग़ • ֤τϐοΫͰग़ݱ͢Δ୯ޠͷੜ੒Ϟσϧͷֶश 3.ֶश͸ม෼ਪ࿦ɾ่յܕΪϒεαϯϓϦϯάͰՄೳ
  3. 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.
  4. Ϛϧίϑϒϥϯέοτ (1.5) • , , , , , , ͷؒʹ͸ґଘ

    ؔ܎͕͋Δ • ͜ͷઌʹ͋Δϊʔυ͸͢΂ͯ ͱಠཱ
  5. ৚݅෇͖ಠཱੑͷ֬ೝ • ͱ , ͸৚݅෇͖ಠཱ • ਤ 4.8 ͱಉٞ͡࿦ •

    ͱ ͸৚݅෇͖ಠཱ • ڞಉ਌ͷؔ܎ʹͳ͍ͨΊ • ্هΛ࢖͏ͱ ͷ෼෍͸࣍ͷΑ͏ ʹͰ͖Δ
  6. ໰୊ઃ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.
  7. ໰୊ઃ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
  8. 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
  9. ڠௐϑΟϧλϦϯά (1/2) • ԣํ޲ʹΞΠςϜɺॎํ޲ʹϢʔβʔΛฒ΂ͨߦྻ Λѻ͏ • ͸Ϣʔβʔ ͷΞΠςϜ ʹର͢ΔϨʔςΟϯά •

    ػցֶशʹ͓͍ͯ࣍ͷΑ͏ʹߟ͑Δ͜ͱ͕ଟ͍ (ཁग़య) • ϕΫτϧ : 1 ࣍ݩ഑ྻ • ߦྻ : දɺςʔϒϧ • ςϯιϧ : ෳ਺ͷද (ϛχόονͱ͔)
  10. ࣌ܥྻ΁ͷ֦ு • ͋Δ࣌ؒ ʹ͓͚Δಛ௃ ͷྲྀߦ౓ ͷΑ͏ͳ΋ͷ (ݪจϚϚ) Λಋೖ ͢Δ •

    ϢʔβʔͱΞΠςϜͷ಺ੵΛɺྲྀߦ౓ʹ ΑΔॏΈ෇͖Ͱܭࢉ͍ͯ͠Δ
  11. ֶश (লུ) • ม෼ਪ࿦ͰՄೳ (ৄࡉ͸লུ) • ࣍ͷ݁Ռʹ஫໨͢Δ • ͸Ϣʔβʔ͝ͱʹݸผͷ஋ֶ͕श͞ΕΔ •

    ͸Ϣʔβʔ͝ͱʹڞ௨ͷ஋ֶ͕श͞ΕΔ • ΋ಉ༷ • ਫ਼౓ߦྻ , , ͸ʮେ͖͘ʯͳ͍ͬͯΔ
  12. Recap ಺༰ (section) Point τϐοΫϞσϧ (5.4) ࣗવݴޠॲཧͷάϥϑΟΧϧϞσϧ ςϯιϧ෼ղ (5.5) ࣌ܥྻσʔλʹରͯ͠ͷڠௐϑΟϧλ

    ϦϯάͷάϥϑΟΧϧϞσϧ ϩδεςΟοΫճؼ (5.6) ࠶ύϥϝʔλʔԽ χϡʔϥϧωοτϫʔΫ (5.7) ޡࠩٯ఻೻๏ (লུ)