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論文紹介:Probabilistic Matrix Factorization
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KenjiH
April 28, 2017
Technology
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論文紹介:Probabilistic Matrix Factorization
機械学習勉強会(2017/04/29)での発表資料
KenjiH
April 28, 2017
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Transcript
1SPCBCJMJTUJD.BUSJY'BDUPSJ[BUJPO /*14 จհ Kenji Hayashida
*OUSPEVDUJPO 3 65 7 1SFGFSFODF.BUSJY 6TFS$PF⒏DJFOU .BUSJY 'BDUPS.BUSJY º
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*OUSPEVDUJPO طଘख๏࣮༻తʹޭͱݴ͑ͳ͍ ڊେͳσʔληοτʹରͯ͠͏·͘εέʔϧͰ͖ͳ͍ ධՁͷճ͕গͳ͍ϢʔβͷQSFEJDUJPOʹۤઓ ౾ࣝ $'ͷίϛϡχςΟͰධՁͷճ͕গͳ͍ϢʔβΛ͋Β͔͡ Ίআڈͯ͠σʔληοτΛ࡞͍ͬͯΔʢͨʁʣΒ͍͠ FY .PWJF-FOTɺ&BDI.PWJF /FUqJYͷσʔληοτϨϏϡʔ͕݅গͳ͍ʢ݅ະຬʣϢʔβؚΉ
ΑΓݱ࣮తͳσʔληοτʂ
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1SPCBCJMJTUJD.BUSJY'BDUPSJ[BUJPO 1.' Ψε ີؔ ରີؔ f(x) = 1 p 2⇡
2 exp ✓ (x µ) 2 2 2 ◆ ln f ( x ) = 1 2 ln 2 ⇡ 2 ( µ x )2 2 2 ରࣄޙ֬
1SPCBCJMJTUJD.BUSJY'BDUPSJ[BUJPO 1.' ϋΠύʔύϥϝʔλΛݻఆ͠ɺࣄޙ֬࠷େԽ ҎԼͷؔ&ͷ࠷େԽͱಉ ͨͩ͠ ࠷ٸ߱Լ๏Ͱہॴղ͕͑ΒΕΔ
1SPCBCJMJTUJD.BUSJY'BDUPSJ[BUJPO 1.' QSFEJDUJPOͷͱ͖ʹ͕< ,>ͷൣғʹೖΒͳ͍ͱࠔΔͷͰɺϩδεςΟοΫؔ Λ͔·ͤΔ ͞ΒʹධՁҎԼͷΑ͏ʹϚοϐϯά͓ͯ͘͜͠ͱͰɺඞͣൣғʹ͓͞·Δ
"VUPNBUJD$PNQMFYJUZ$POUSPM GPS1.'.PEFMT Ϟσϧͷෳࡶͷௐ͕ඞཁ જࡏϕΫτϧͷ࣍ݩΛม͑Δํ๏ɺσʔληοτ͕ภ͍ͬͯΔ߹ʢϢʔβʹ ΑͬͯධՁ͕ҟͳΔʣɺෆదɻ Е6ɺЕ7ͰෳࡶΛίϯτϩʔϧ͢Δํ͕ॊೈ $SPTT7BMJEBUJPOతʹύϥϝʔλαʔν͢Δͷܭࢉ࣌ؒతʹͭΒ͍
ϋΠύʔύϥϝʔλʹࣄલΛಋೖ ύϥϝʔλɺϋΠύʔύϥϝʔλ྆ํΛಈ͔ͯ͠."1ਪఆ͢Δ͜ͱͰࣗಈνϡʔ χϯά͕Ͱ͖Δʢઌߦݚڀ͋Γʣ
"VUPNBUJD$PNQMFYJUZ$POUSPM GPS1.'.PEFMT ͨͩ͠ɺ 7 6ͷࣄલͷύϥϝʔλ ɺ 6 7ͷࣄલɺฏۉɺٿঢ়ͷࢄΛͭਖ਼نͱͯ͜͠Ε·ͰΛਐ Ί͕ͨɺࣄલͷύϥϝʔλ͕ՄมʹͳΔ ࣄલʹΨεΛ͑ɺ࠷దͳϋΠύʔύϥϝʔλղੳతʹٻΊΒΕΔɻ
ʢ6 7Λݻఆͨ͠߹ʣ ύϥϝʔλͷVQEBUFɺϋΠύʔύϥϝʔλͷVQEBUFΛަޓʹ܁Γฦ͠ͳ͕Β࠷ٸ ߱Լ๏Λߦ͑0,
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$POTUSBJOFE1.' ࠨଆ͕1.'ͷάϥϑΟΧϧϞσϧɺӈଆ͕DPOTUSBJOFE1.'ͷάϥϑΟΧϧϞσϧɻ ˞ਤ3FGFSFODFͷ'JHVSFΑΓൈਮ
&YQFSJNFOUBM3FTVMUT /FUqJY%BUB ܇࿅σʔλ ݅ͷϨϏϡʔ ςετσʔλ
݅ͷϢʔβөըͷΈ߹Θͤ ܇࿅σʔλʹଘࡏ͢ΔϢʔβͷ࠷ۙͷϨϏϡʔ͔ΒαϯϓϦϯά τΠσʔλ ຊจͷݕূͷͨΊɺҎԼͷςετσʔλू߹Λ࡞ ݅ͷϨϏϡʔ͔ΒͳΔ܇࿅σʔλ ܇࿅σʔλͷҎ্ͷϢʔβະຬͷϨϏϡʔ͔͍ͯ͠͠ͳ͍
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&YQFSJNFOUBM3FTVMUT ϢʔβͷϨϏϡʔ͕গͳ͍߹ɺDPOTUSBJOFE1.'͕༗༻ ˞ਤ3FGFSFODFͷ'JHVSFΑΓൈਮ
&YQFSJNFOUBM3FTVMUT 1.'ͷ߹ɺϨϏϡʔ͕গͳ͍Ϣʔβʹର͢ΔQSFEJDUJPOϨϏϡʔͷฏۉΛ ฦ͍ͯ͠Δͷͱಉ͡ $POTUSBJOFE1.'ʹ͢Δ͜ͱͰΑ͍݁Ռ͕͑ΒΕΔ ςετσʔλͷதʹͲͷʢϢʔβ өըʣͷλϓϧؚ͕·ΕΔͷͰɺͦͷใΛ܇ ࿅࣌ʹར༻͢Δ͜ͱͰύϑΥʔϚϯε্͕ ˞ਤ3FGFSFODFͷ'JHVSFΑΓൈਮ
4VNNBSZBOE%JTDVTTJPO 1SPCBCJMJTUJD.BUSJY'BDUPSJ[BUJPOΛఏҊ "EPQUJWF1SJPS1.' $POTUSBJOFE1.' ڊେͳөըධՁσʔληοτΛ༻͍ͯɺϞσϧͷ༗༻ੑΛ࣮ূ ·ͱΊ
՝ ύϥϝʔλͷਪఆΛܭࢉ͕ͨ͠ɺύϥϝʔλͷܭࢉ͍ͯ͠ͳ͍ શͳϕΠζΞϓϩʔνΛऔΓ͍ͨ߹ɺ.$.$͢Δ ܭࢉίετେ͖͍͕ɺੑೳ্͕ݟࠐ·ΕΔ
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