ソーシャルメディア上のテキスト情報を考慮した社会ネットワーク分析モデル

ソーシャルメディア上のテキスト情報を考慮した社

会ネットワーク分析モデル

著者

五十嵐 未来, 照井 伸彦

雑誌名

DSSR Discussion Papers

号

J-7

ページ

1-27

発行年

2020-05

URL

http://hdl.handle.net/10097/00127725



Data Science and Service Research

Discussion Paper

Discussion Paper No.J-7

ࢯ࣮ࢩ࣓ࣕࣝࢹ࢕࢔ୖࡢࢸ࢟ࢫࢺ᝟ሗࢆ⪃៖ࡋࡓ ♫఍ࢿࢵࢺ࣮࣡ࢡศᯒࣔࢹࣝ

஬༑ᔒᮍ᮶ ↷஭ఙᙪ

2020 ᖺ ᭶

Center for Data Science and Service Research Graduate School of Economic and Management

Tohoku University 27-1 Kawauchi, Aobaku

ιʔγϟϧϝσΟΞ্ͷςΩετ৘ใΛߟྀͨ͠

ࣾձωοτϫʔΫ෼ੳϞσϧ

ޒेཛྷະདྷ

*

রҪ৳඙

„

2020 ೥ 5 ݄

Abstract ۙ೥ɼࣾձωοτϫʔΫΛϞσϧԽͯ͠෼ੳ͢ΔࡍʹɼωοτϫʔΫ৘ใ͚ͩͰͳ͘ɼ ਓʑ͕ιʔγϟϧϝσΟΞ্ͳͲͰੜ੒͢ΔςΩετ৘ใΛߟྀͯ͠ίϛϡχςΟߏ଄Λ ଊ͑Δ͜ͱͷॏཁੑ͕૿͍ͯ͠ΔɽςΩετ৘ใΛߟྀ͢Δ͜ͱʹΑΓɼωοτϫʔΫ ্ͰີʹΤοδ͕ܗ੒͞Ε͍ͯΔߏ଄ͷதʹɼਓʑ͕࣋ͭڵຯ΍ؔ৺ʹԠͨ͡ෳ਺ͷ· ͱ·Γ͕ଘࡏ͢Δͱ͍͏Α͏ͳෳࡶͳίϛϡχςΟߏ଄Λ࣋ͭࣾձωοτϫʔΫͷ෼ੳ ͕ՄೳͱͳΔɽຊݚڀͰ͸ɼ͜ΕΛϞσϧԽͨ͠ Igarashi and Terui (2020) ʹΑΔωο τϫʔΫσʔλͱςΩετσʔλͷಉ࣌ར༻ϞσϧΛ֦ு͠ɼΤοδੜ੒֬཰Λؔ܎͢ Δϊʔυ͝ͱʹҟͳΔΑ͏ʹఆࣜԽ͢Δ͜ͱͰɼϊʔυͷ࣍਺෼෍͕΂͖৐ଇʹै͏ͱ ͍͏ࣾձωοτϫʔΫ͕࣋ͭҰൠతͳੑ࣭Λߟྀ͢ΔϞσϧΛఏҊ͍ͯ͠ΔɽTwitter Λ ༻͍࣮ͨূ෼ੳͰ͸ɼఏҊϞσϧΛ༻͍࣮ͨσʔλ΁ͷԠ༻ྫΛࣔ͢ͱͱ΋ʹɼઌߦݚ ڀʹ͓͚ΔطଘϞσϧΑΓ΋༏Εͨ༧ଌੑೳΛ࣋ͭ͜ͱΛࣔ͢ɽ Keywords: ࣾձωοτϫʔΫ෼ੳɾίϛϡχςΟݕग़ɾςΩετղੳɾτϐοΫϞσ ϦϯάɾϕΠζਪఆɾϊʔυ࣍਺ͷҟ࣭ੑ *_{౦๺େֶେֶӃܦࡁֶݚڀՊɹത࢜ޙظ՝ఔɿ˟980-8576ɹٶ৓ݝઋ୆ࢢ੨༿۠઒಺27ʵ1ʢE-mailɿ} [email protected]ʣɽຊݚڀ͸JSPSՊݚඅ18J20698ͷॿ੒Λड͚ͨ΋ͷͰ͢ɽ

„_{౦๺େֶେֶӃܦࡁֶݚڀՊɹڭतʢE-mailɿ[email protected]ʣɽຊݚڀ͸JSPSՊݚඅ(A) 17H01001}

1

ং࿦

Social Networking Sites (SNS) ͷྲྀߦ΍e-ίϚʔεαΠτͷ୆಄ͳͲʹΑΓɼফඅऀΛऔΓ רࣾ͘ձωοτϫʔΫΛ෼ੳ͠ɼͦͷߏ଄Λ೺Ѳ͢Δ͜ͱ͸ɼاۀͷϚʔέςΟϯά׆ಈʹ ͓͚ΔॏཁͳҐஔΛ઎ΊΔΑ͏ʹͳ͍ͬͯΔɽࣾձωοτϫʔΫ෼ੳͷख๏͸ɼ౷ܭֶ΍ࣾ ձֶͷ෼໺Λத৺ʹ௕೥ݚڀ͞Ε͓ͯΓɼωοτϫʔΫߏ଄Λଊ͑ΔͨΊͷ౷ܭϞσϧ͕ଟ

͘ఏҊ͞Ε͍ͯΔ(e.g., Snijders and Nowicki, 1997; Airoldi et al., 2008)ɽ͜ΕΒͷϞσϧͰ

͸ɼωοτϫʔΫ্ͷϊʔυͱΤοδΛ؍ଌσʔλͱͯ͠ѻ͍ɼ͔ͦ͜ΒίϛϡχςΟߏ଄ Λநग़͢Δ͜ͱΛ໨తͱ͍ͯ͠Δɽ·ͨɼࣾձωοτϫʔΫʹ͓͍ͯɼϊʔυ͸ਓʑͷ͜ͱ Λද͓ͯ͠Γɼਓʑͷଐੑ΍ߦಈͱ͍ͬͨ෇ਵతͳσʔλΛߟྀ͢Δ͜ͱͰɼωοτϫʔΫ

Ϟσϧͷਫ਼៛ԽΛ໨ࢦ͢ݚڀ΋೤৺ʹऔΓ૊·Ε͍ͯΔ(e.g., Handcock et al., 2007)ɽதͰ

΋ɼۙ೥͸ɼιʔγϟϧϝσΟΞͷྲྀߦ΍ޱίϛػೳΛ౥ࡌͨ͠e-ίϚʔεαΠτͷ୆಄ͳ

ͲʹΑΓɼϢʔβʔੜ੒ίϯςϯπ(User-Generated-ContentsɼUGC)ɼಛʹςΩετ৘ใ

ΛωοτϫʔΫͱ૊Έ߹ΘͤͨࣾձωοτϫʔΫ෼ੳϞσϧ͕ଟ͘ఏҊ͞Ε͍ͯΔ(e.g., Liu

et al., 2009; Bouveyron et al., 2018)ɽ

ωοτϫʔΫ৘ใ͚ͩͰͳ͘ςΩετ৘ใ΋ߟྀͨ͠ϞσϧΛߏங͢Δ͜ͱͷར఺ͱ͠ ͯ͸ɼҰํͷ৘ใ͚ͩͰ͸ଊ͑Δ͜ͱ͕೉͍͠ίϛϡχςΟߏ଄Λநग़Ͱ͖Δͱ͍͏఺͕ڍ ͛ΒΕΔɽྫ͑͹ɼ͋ΔֶߍͷಉڃੜͰߏ੒͞ΕΔίϛϡχςΟΛ૝ఆ͢Δɽͦ͜Ͱ͸ɼֶ ੜΒ͸ޓ͍ʹԿΒ͔ͷؔ܎ੑΛ࣋ͬͨີ౓ͷߴ͍ωοτϫʔΫ͕ܗ੒͞Ε͍ͯΔ͸ͣͰ͋Δɽ ͕ͨͬͯ͠ɼωοτϫʔΫ৘ใͷΈΛߟྀͨ͠ϞσϧΛ༻͍ΔͱɼͦͷΑ͏ͳωοτϫʔΫ ্ʹ͸ɼҰͭͷίϛϡχςΟ͕ଘࡏ͍ͯ͠Δͱೝࣝ͞ΕΔɽ͔͠͠ɼͦΕͱಉ࣌ʹɼֶੜΒ ͸Իָ΍ಡॻɼεϙʔπͱ͍༷ͬͨʑͳझຯΛ͍࣋ͬͯΔ͜ͱ͕ߟ͑ΒΕΔͨΊɼڞ௨ͷझ ຯΛֶ࣋ͬͨੜΒΛ·ͱΊͯෳ਺ͷίϛϡχςΟ͕ଘࡏ͢ΔͱΈͳ͢ํ͕ɼΑΓҙຯͷ͋Δ

ηάϝϯςʔγϣϯͱͳΔՄೳੑ͕͋ΔɽIgarashi and Terui (2020)Ͱ͸ɼͦͷΑ͏ͳίϛϡ

χςΟΛτϐοΫϕʔεɾίϛϡχςΟͱ໊෇͚ɼωοτϫʔΫͱςΩετΛߟྀͨ͠Ϟσ ϧʹΑΔݕग़ΛఏҊ͍ͯ͠ΔɽιʔγϟϧϝσΟΞʹ୅ද͞ΕΔΦϯϥΠϯ্ͷࣾձωοτ ϫʔΫͰ͸ɼݱ࣮ੈքʹ͓͚Δࣾձతͳͭͳ͕Γ͚ͩͰͳ͘ɼڵຯ΍ؔ৺ͳͲʹج͍ͮͨͭ ͳ͕Γɼͭ·ΓτϐοΫϕʔεɾίϛϡχςΟ͕఺ࡏ͍ͯ͠Δ͜ͱ͕ߟ͑ΒΕΔͨΊɼϝσΟ

Ξ্ʹੜ੒͞ΕͨςΩετίϯςϯπ͔ΒͦͷϢʔβʔͷڵຯ΍ؔ৺Λਪఆ͢Δ͜ͱͰɼࣾ ձωοτϫʔΫ෼ੳϞσϧΛਫ਼៛Խͤ͞Δ͜ͱ͕Ͱ͖Δɽ ·ͨɼࣾձωοτϫʔΫ͕࣋ͭੑ࣭ͷҰͭͱͯ͠ɼ࣍਺෼෍͕΂͖৐ଇʹै͏ͱ͍͏ੑ ࣭͕͋Δɽ͜Ε͸ɼ͘͝গ਺ͷਓʑ͕ଟ͘ͷਓʑͱωοτϫʔΫ্Ͱؔ܎Λ࣋ͪɼͦͷଞେ ੎ͷਓʑ͸ɼ͘͝গ਺ͷਓʑͱͷΈؔ܎ੑΛ࣋ͭ܏޲ʹ͋Δͱ͍͏ੑ࣭Ͱ͋ΔɽͦͷΑ͏ʹɼ ݱ࣮ͷࣾձωοτϫʔΫʹ͓͍ͯɼ࣍਺͸ϊʔυ͝ͱʹҟ࣭Ͱ͋Δ͕ɼ֬཰తϒϩοΫϞσ ϧ(Snijders and Nowicki, 1997)ͳͲ୅දతͳωοτϫʔΫϞσϧͷଟ͕ͦ͘͏Ͱ͋ΔΑ͏ ʹɼIgarashi and Terui (2020)Ͱ͸ɼ࣍਺ͷҟ࣭ੑΛߟྀ͍ͯ͠ͳ͍ɽ

ຊݚڀͰ͸ɼIgarashi and Terui (2020)ͷϞσϧΛ֦ு͠ɼϒϩοΫϞσϧʹଈͨ͠Το

δੜ੒֬཰Λϊʔυ͝ͱʹҟ࣭ͳΤοδ֬཰ͱ͠ɼ࣍਺ͷҟ࣭ੑΛߟྀͨ͠ϞσϧΛఏҊ͢ Δɽຊݚڀͷ࣮ূ෼ੳͰ͸ɼ࣍਺ͷҟ࣭ੑΛߟྀͨ͠ఏҊϞσϧΛɼҰൠతͳ֬཰ϒϩοΫ Ϟσϧͱಉ༷ʹҟ࣭ੑΛߟྀ͠ͳ͍ࠩ෼Ϟσϧͱൺֱ͠ɼ֎૷༧ଌʹ͓͍ͯఏҊϞσϧͷํ ͕༏Ε͍ͯΔ͜ͱΛࣔ͢ɽ ҎԼɼ2અͰ͸ɼࣾձωοτϫʔΫ෼ੳʹؔ܎͢ΔઌߦݚڀΛ·ͱΊɼຊݚڀͷ໨తͱҐ ஔ͚ͮΛ໌֬ʹ͢Δɽ3અͰ͸ɼఏҊϞσϧΛઆ໌͠ɼ4અͰ͸ͦͷਪఆ๏Λಋग़͢Δɽଓ ͍ͯɼ5અͰ͸ɼTwitterσʔλΛར༻࣮ͨ͠ূݚڀΛใࠂ͠ɼ࠷ޙʹɼ6અͰ݁࿦ͱࠓޙͷ ՝୊Λड़΂Δɽ

2

ઌߦݚڀ

2.1

ࣾձωοτϫʔΫ෼ੳϞσϧͷਐల

౷ܭֶ΍ࣾձֶͳͲΛத৺ͱͯ͠ɼݹ͔͘ΒࣾձωοτϫʔΫΛϞσϧԽ͠ɼͦͷߏ଄Λ೺ Ѳ͢ΔͨΊͷݚڀ͕ଓ͍͍ͯΔɽதͰ΋୅දతͳ΋ͷ͕ɼ֬཰తϒϩοΫϞσϧ(Stochastic

Block Models, SBM, Wang and Wong, 1987; Snijders and Nowicki, 1997)Ͱ͋ΔɽSBM͸ɼ

ϊʔυ͕KݸͷίϛϡχςΟͷ͏ͪҰ͚ͭͩʹଐ͢Δ͜ͱΛԾఆ͓ͯ͠Γɼϊʔυi͕ଐ͢

ΔίϛϡχςΟΛzi ∈ {1, . . . , K}ͱ͢ΔͱɼϊʔυiͱjͷؒʹΤοδ͕ੜ੒͞ΕΔ֬཰͸ɼ

λͰ͋Δɽ

SBM͸ɼϞσϧ͕ఏҊ͞ΕͯҎ߱ɼ༷ʑͳจ຺ͰϞσϧͷ֦ு͕औΓ૊·Ε͓ͯΓɼྫ

͑͹ɼAiroldi et al. (2008)͸ɼSBMͷ֦ுϞσϧͱͯࠞ͠߹ϝϯόʔγοϓ֬཰తϒϩο ΫϞσϧ (Mixed Membership Stochastic Blockmoldels, MMSB) ΛఏҊ͍ͯ͠ΔɽSBM͕ɼ

ϊʔυʹ୯ҰͷϝϯόʔγοϓΛԾఆ͍ͯͨ͠ͷʹର͠ɽMMSBͰ͸ɼ֤ϊʔυ͸ɼଞϊʔ υͱͷؔ܎ੑຖʹෳ਺ͷίϛϡχςΟʹଐ͢Δ͜ͱ͕ڐ༰͞Ε͍ͯΔɽϊʔυi͔Βjͷؔ܎ ੑʹ͓͍ͯɼϊʔυi͕ଐ͢ΔίϛϡχςΟΛsijɼϊʔυj͕ଐ͢ΔίϛϡχςΟΛrjiͱ͢ Δͱɼ྆ऀͷؒʹΤοδ͕ੜ੒͞ΕΔ֬཰͸ɼψs_ijrjiͰද͞ΕΔɽ͜ͷ֦ுʹΑΓɼMMSB ͸ίϛϡχςΟͷॏͳΓΛߟྀ͢Δ͜ͱ͕Ͱ͖ʢSBMͰ͸ίϛϡχςΟ͕ॏͳΔ͜ͱ͸ͳ ͍ʣɼΑΓݱ࣮ʹଈͨ͠ϞσϦϯά͕Մೳͱͳ͍ͬͯΔɽ ·ͨɼࣾձֶͷจ຺Ͱ͸ɼϊʔυؒͷؔ܎ੑ͕ੑผ΍೥ྸͱ͍ͬͨϊʔυݻ༗ͷಛ௃ྔͷ

ӨڹΛड͚ܾͯ·Δ͜ͱ΋஌ΒΕ͍ͯΔ(Hoff et al., 2002; Handcock et al., 2007; Krivitsky

et al., 2009)ɽ͔͠͠ɼຊݚڀͰ͸ɼιʔγϟϧϝσΟΞʹ୅ද͞ΕΔΑ͏ͳΦϯϥΠϯ্ͷ ࣾձωοτϫʔΫʹண໨͍ͯ͠ΔͨΊɼͦͷΑ͏ͳಛ௃ྔ͸ߟྀ͠ͳ͍ɽTwitterͷΑ͏ͳ ಗ໊ܕιʔγϟϧϝσΟΞͰ͸ɼϢʔβʔ͸೥ྸ΍ੑผͱ͍ͬͨݸਓ৘ใΛӅͨ͠ঢ়ଶͰΞ Χ΢ϯτΛొ࿥͢Δ͜ͱ͕Ͱ͖ɼͦͷΑ͏ͳঢ়گʹ͓͍ͯଞऀͱؔ܎Λ݁ͿࡍʹߟྀͰ͖Δ ৘ใ͸ɼ૬ख͕ܗ੒͍ͯ͠ΔωοτϫʔΫͱϝσΟΞ্ʹ౤ߘͨ͠ίϯςϯπͷΈͰ͋Δɽ ͜ΕΒͷσʔλ͕ར༻ՄೳͰ͋Ε͹ɼఏҊϞσϧʹऔΓࠐΉ͜ͱ͸༰қͰ͋Γɼࣾձֶతࢹ ఺͔Βͷ෼ੳ΋ՄೳͰ͋Δɽ

2.2

ωοτϫʔΫͱςΩετ৘ใͷಉ࣌ϞσϦϯάʹؔ͢Δݚڀ

લઅͰڍ͛ͨࣾձωοτϫʔΫϞσϧʹؔ͢ΔݚڀͰ͸ɼωοτϫʔΫ৘ใͷΈʹண໨ͯ͠ ϞσϧΛఏҊ͍ͯ͠Δ͕ɼۙ೥ɼTwitter΍Facebookͱ͍ͬͨΦϯϥΠϯ্ͷࣾձωοτ ϫʔΫߏ଄ΛΑΓਂ͘ཧղ͢ΔͨΊʹɼωοτϫʔΫͱςΩετ৘ใΛͲͪΒ΋ߟྀ͢ΔϞ

σϧ͕੝Μʹݚڀ͞Ε͍ͯΔɽྫ͑͹ɼChang and Blei (2010)͸ɼϊʔυʹݻ༗ͷςΩε

τ৘ใʹରͯ͠τϐοΫϞσϧΛద༻͠ɼϊʔυͷςΩετʹׂΓ౰ͯΒΕͨτϐοΫׂ߹

Topic Model, RTM) ΛఏҊ͍ͯ͠Δɽͨͩ͠ɼRTMͷ໨త͕ɼωοτϫʔΫ৘ใΛՃຯ͠ ͯςΩετ৘ใʹ͓͚ΔτϐοΫΛਪఆ͢Δ͜ͱͰ͋Δͷʹରͯ͠ɼຊݚڀͷ໨త͸ςΩε τ৘ใΛߟྀͯ͠ωοτϫʔΫ্ͷίϛϡχςΟߏ଄Λ೺Ѳ͢Δ͜ͱͰ͋ΔΑ͏ʹରরతͳ ΋ͷͰ͋Δɽ

Chang and Blei (2010)ͷΑ͏ʹςΩετ৘ใΛજࡏతσΟϦΫϨ഑෼๏(latent Dirichlet allocation, LDA, Blei et al., 2003)΍ͦͷ֦ுϞσϧΛ༻͍ͯωοτϫʔΫϞσϧʹऔΓࠐ

Ήͱ͍͏ํ๏͸ଞʹ΋͍͔ͭ͘ͷݚڀͰݟΒΕΔɽྫ͑͹ɼLiu et al. (2009)͸ɼTopic-Link

LDAΛఏҊ͓ͯ͠Γɼϊʔυݻ༗ͷςΩετ৘ใΛߟྀͯ͠ίϛϡχςΟߏ଄Λݕग़͢Δͱ ͍͏఺Ͱຊݚڀͱಉ͡໨తΛ͍࣋ͬͯΔɽͨͩ͠ɼSBMͱಉ༷ʹɼϊʔυ͕୯Ұͷίϛϡχ ςΟʹଐ͢Δ͜ͱΛԾఆ͍ͯ͠Δ෦෼͸ຊݚڀͱҟͳΔ఺Ͱ͋Δɽ·ͨɼLiu et al. (2009) Ͱ͸ɼΤοδੜ੒֬཰͕ɼϊʔυݻ༗ͷτϐοΫٴͼίϛϡχςΟׂ߹ͷྨࣅ౓ʹΑͬͯఆ ٛ͞Ε͍ͯΔͨΊɼର৅ͱ͢ΔωοτϫʔΫΛແ޲άϥϑͱͯ͠ѻ͏͜ͱΛ૝ఆ͍ͯ͠Δͷ ʹର͠ɼຊݚڀΛؚΊͨϒϩοΫϞσϧʹ͓͍ͯ͸ɼK× KߦྻͷΤοδ֬཰ύϥϝʔλΛ ༻͍ͨωοτϫʔΫϞσϦϯάʹΑΓɼάϥϑͷํ޲ੑʹ͔͔ΘΒͣϞσϧΛద༻ՄೳͰ͋ Δɽଞʹ΋ɼBouveyron et al. (2018)͸ɼSBMʹςΩετ৘ใͷϞσϧΛՃ͑Δ͜ͱͰ֦ு

ͨ͠ɼStochastic Topic Block Model (STBM) ΛఏҊ͍ͯ͠Δɽ

͜ΕΒ͸୯ҰͷϝϯόʔγοϓΛԾఆͨ͠SBMͷ֦ுϞσϧͰ͋Δ͕ɼZhu et al. (2013) ͸ɼϊʔυͷࠞ߹ϝϯόʔγοϓΛԾఆ͠ɼςΩετͱωοτϫʔΫ৘ใͷ྆ऀΛߟྀ͢Δ ωοτϫʔΫ෼ੳϞσϧΛఏҊ͍ͯ͠Δɽ͜ͷ఺ʹ͓͍ͯຊݚڀʹ͓͚ΔఏҊϞσϧͱ΋ࣅ ͨߏ଄Λ༗͍ͯ͠Δ͕ɼओͳ૬ҧ఺͸ɼΤοδʹׂΓ౰ͯΒΕΔίϛϡχςΟͱ୯ޠʹׂΓ ౰ͯΒΕΔτϐοΫ͕ಉҰͷ෼෍ʹै͍ͬͯΔͱ͍͏఺Ͱ͋Δɽݴ͍׵͑Ε͹ɼZhu et al. (2013)͸ίϛϡχςΟͱτϐοΫͷ࣍ݩΛಉҰͷ΋ͷͱͯ͠ѻ͍ͬͯΔͱ͍͑Δɽ͔͠͠ɼݱ ࣮ͷࣾձωοτϫʔΫͰ͸ɼίϛϡχςΟͱτϐοΫ͕ඞͣ͠΋ޓ͍ʹରԠ͍ͯ͠Δͱ͸ݶ Βͳ͍ɽྫ͑͹ɼԻָͱεϙʔπʹڵຯͷ͋Δϝϯόʔ͕ີͳϦϯΫߏ଄Λ͍࣋ͬͯΔωο τϫʔΫΛߟ͑Δɽ͜ͷΑ͏ͳίϛϡχςΟΛZhu et al. (2013)ͷϞσϧͰݕग़ͨ͠ͱ͢ ΔͱɼҰͭͷίϛϡχςΟʹରͯ͠ɼԻָͱεϙʔπͱ͍͏ෳ਺ͷҙຯత·ͱ·ΓΛ΋ͭτ ϐοΫ͕ରԠͯ͠͠·͍ɼτϐοΫͷղऍੑʹ͚ܽΔɽҰํͰɼຊݚڀͰ͸ɼίϛϡχςΟ

ͱτϐοΫ͕ͦΕͧΕҟͳΔ෼෍ʹै͏͜ͱΛԾఆ͓ͯ͠Γɼ্هͷΑ͏ͳωοτϫʔΫʹ ରͯ͠΋ɼҰͭͷίϛϡχςΟͱɼԻָτϐοΫٴͼεϙʔπτϐοΫͷΑ͏ʹผʑʹෳ਺

τϐοΫΛରԠͤ͞Δ͜ͱ͕Ͱ͖Δɽ3અͰ͸ɼͦͷৄࡉͳఆࣜԽΛઆ໌͢Δɽ

͜ΕΒͷطଘϞσϧΛ౿·͑ͯɼIgarashi and Terui (2020)Ͱ͸ɼϊʔυͷࠞ߹ϝϯόʔ

γοϓΛԾఆͨ͠ωοτϫʔΫͱςΩετͷಉ࣌ϞσϦϯάΛఏҊ͍ͯ͠ΔɽຊݚڀͰ͸ɼ ͜ͷϞσϧΛ֦ு͠ɼΤοδ֬཰Λϊʔυ͝ͱʹҟ࣭ͳύϥϝʔλͱ͢ΔϞσϧΛݕ౼͢Δɽ ͜ΕʹΑΓɼࣾձωοτϫʔΫ͕Ұൠతʹ༗͢Δ࣍਺෼෍ͷҟ࣭ੑΛߟྀͨ͠ϞσϦϯά͕

ՄೳͱͳΔɽઌߦݚڀʹ͓͍ͯ͸ɼKarrer and Newman (2011)͕ɼSBMͰఆٛ͞ΕΔΑ͏

ͳϊʔυʹ͍ͭͯಉ࣭తͳΤοδੜ੒֬཰Λద༻͢ΔͷͰ͸ͳ͘ɼϊʔυ͝ͱͷظ଴࣍਺Λ ύϥϝʔλͱͯ͠ಋೖ͠ɼؔ܎͢ΔϊʔυʹԠͯ͡Τοδੜ੒֬཰͕ҟ࣭ͱͳΔΑ͏ͳิਖ਼ Λߦ͏ϞσϧΛఏҊ͍ͯ͠Δɽຊݚڀʹ͓͚ΔఆࣜԽͰ͸ɼΤοδੜ੒֬཰ࣗମΛϊʔυ͝

ͱʹҟ࣭ͳύϥϝʔλͱͯ͠ఆ͓ٛͯ͠ΓɼKarrer and Newman (2011)ͱ΋ҟͳΔΞϓϩʔ

νΛͱ͍ͬͯΔɽ ද1Ͱ͸ɼ͜͜·Ͱʹٞ࿦ͨ͠ຊݚڀͱઌߦݚڀͱͷൺֱΛ·ͱΊ͍ͯΔɽ·ͣɼωοτ ϫʔΫ΍ςΩετͲͪΒ͔ͷΈΛ؍ଌσʔλͱͯ͠ѻ͏Ϟσϧͱൺֱ͢ΔͱɼຊݚڀͰఏҊ ͢ΔϞσϧ͸ɼͦͷ྆ऀΛߟྀͯࣾ͠ձωοτϫʔΫ෼ੳΛߦ͏΋ͷͰ͋Γɼલड़ͨ͠Α͏ ʹͲͪΒ͔Ұํͷ৘ใ͚ͩͰ͸ัଊ͢Δ͜ͱ͕೉͍͠ωοτϫʔΫߏ଄Λ໌Β͔ʹग़དྷΔՄ ೳੑ͕͋Δɽ·ͨɼͦͷ྆৘ใΛѻ͏طଘϞσϧͱൺֱ͢Δͱɼϊʔυʹࠞ߹ϝϯόʔγο ϓΛڐ༰͍ͯ͠Δ఺ɼάϥϑͷ༗޲ແ޲ʹ͔͔ΘΒͣద༻Մೳͳ఺ɼͦͯࣾ͠ձωοτϫʔ Ϋʹ͓͚Δ࣍਺ͷҟ࣭ੑΛߟྀͨ͠ϞσϦϯάΛߦ͍ͬͯΔ఺͕ຊݚڀͷಛ৭ͱݴ͑Δɽ͜ ΕΒͷൺֱΛ௨ͯ͠ɼ5અͰ͸ɼఏҊϞσϧ͔Β࣍਺ͷҟ࣭ੑͷߟྀΛআ͍ͨϞσϧʹ͋ͨ

ΔIgarashi and Terui (2020)ɼٴͼςΩετ৘ใΛߟྀ͠ͳ͍Ϟσϧʹ૬౰͢ΔAiroldi et al. (2008)ΛൺֱϞσϧͱͯͦ͠ΕΒͷ༧ଌੑೳΛݕূ͍ͯ͠Δɽ

3

Ϟσϧ

ຊઅͰ͸ɼ·ͣఏҊϞσϧͷجૅͱͳΔIgarashi and Terui (2020)ͷϞσϧΛ঺հ͠ɼ࣍ʹ

ͦͷࠩҟΛ໌Β͔ʹ͠ͳ͕ΒຊݚڀͰ࢖༻͢ΔϞσϧͷઆ໌Λߦ͏ɽ·ͨɼ྆ϞσϧͰڞ௨ ͯ͠ɼ؍ଌ͞ΕΔσʔλ͸ɼωοτϫʔΫ৘ใΛද͢ྡ઀ߦྻAɼٴͼϊʔυʹݻ༗ͷςΩ ετ৘ใΛද͢୯ޠͷBag-of-Wordsू߹W ͷೋͭͰ͋Δɽ ·ͣɼDݸͷϊʔυΛ࣋ͭ༗޲άϥϑΛߟ͑Δͱɼͦͷྡ઀ߦྻA͸ɼD× DߦྻͰ͋ Γɼߦྻͷ֤ཁૉ͸ϊʔυؒͷؔ܎ੑΛࣔ͢ೋ஋ม਺Ͱ͋Δɽͭ·Γɼaij = 0͸Τοδ͕ ଘࡏ͠ͳ͍͜ͱΛද͠ɼaij = 1͸ଘࡏ͢Δ͜ͱΛද͢ɽ·ͨɼࣗݾϧʔϓ͸ߟ͑ͳ͍͜ͱ

ͱ͠ɼશͯͷiʹ͍ͭͯaii = 0Ͱ͋ΔɽIgarashi and Terui (2020)Ͱ͸ɼϊʔυi͔Βj΁

ͷؔ܎ੑʹ͓͍ͯɼͦͷૹΓखi͕જࡏతͳίϛϡχςΟsij ∈ {1, . . . , K}ʢK͸ίϛϡχ ςΟ਺ʣʹଐ͠ɼड͚खj͸જࡏίϛϡχςΟrji ∈ {1, . . . , K} ʹଐ͢Δ͜ͱΛԾఆ͢Δɽ· ͨɼ͜ΕΒજࡏίϛϡχςΟͷߦྻදݱΛS = (sij), R = (rji)ͱ͢ΔɽϞσϧͷੜ੒աఔʹ ͓͍ͯɼૹΓखٴͼड͚खͷίϛϡχςΟ͸ΧςΰϦΧϧ෼෍ɼsij | ηi ∼ Categorical (ηi)ɼ rji| ηj ∼ Categorical (ηj)ʹै͏ɽͨͩ͠ɼηi = (ηi1, . . . , ηiK)͸ϊʔυiͷίϛϡχςΟॴ ଐׂ߹Λද͢ύϥϝʔλͰ͋Γɼ_kηik= 1Λຬͨ͢ɽ͜ͷίϛϡχςΟ෼෍ͷߦྻදݱ͸ H = (η₁, . . . , ηD)Ͱද͞ΕΔɽHͷࣄલ෼෍͸σΟϦΫϨ෼෍ηi | γ ∼ Dirichlet(γ)ʹै͏ ͜ͱΛԾఆ͓ͯ͠Γɼγ = (γ₁, . . . , γK)͸ਪఆʹ͋ͨͬͯௐ੔͕ඞཁͳϋΠύʔύϥϝʔλ Ͱ͋Δɽ

ϊʔυiͱjؒͷؔ܎ੑaij͸ɼsijͱrji͕ॴ༩ͷ࣌ɼϕϧψʔΠ෼෍ɼaij | sij = k, rji=

k, Ψ ∼ Bernoulli (ψkk)ʹै͏͜ͱΛԾఆ͢Δɽͨͩ͠ɼψkk ͸ɼૹΓखͷίϛϡχςΟ ͕kɼड͚खͷίϛϡχςΟ͕kͷ࣌ʹΤοδ͕ੜ੒͞ΕΔ֬཰Λࣔ͢ɽ·ͨɼΤοδ֬཰ ͷK× Kߦྻදݱ͸Ψ = (ψkk)Ͱද͞Εɼߦྻͷ֤ཁૉ͸ɼࣄલ෼෍ͱͯ͠ϕʔλ෼෍ɼ ψkk | δkk, kk ∼ Beta(δkk, kk)Λ࣋ͭɽ͜ͷͱ͖ɼδ, ͸Ψͱಉ࣍͡ݩΛ࣋ͭϋΠύʔύϥ ϝʔλͰ͋Δɽ ैͬͯɼίϛϡχςΟ෼෍HΛॴ༩ͱͨ͠ͱ͖ͷωοτϫʔΫσʔλʹର͢Δ৚݅෇໬

౓͸ҎԼͰఆٛ͞ΕΔɽ p(A, S, R, Ψ| H) = p(A| S, R, Ψ)p(S | H)p(R | H)p(Ψ | δ, ) = D  i=1  _D  j=1,j=i

{p(aij | sij, rji, Ψ)p(sij | ηi)p(rji| ηj)}

 _K  k=1 K  k₌₁ p(ψkk | δkk, _kk). (1) ଓ͍ͯɼϊʔυݻ༗ͷςΩετίϯςϯπʹ͍ͭͯߟ͑Δɽ͜͜Ͱ͸ɼϊʔυi͕ੜ੒͠ ͨςΩετʹ͍ͭͯɼจষ಺ͷ୯ޠͷॱ൪Λແࢹͯ͠ɼͭ·ΓBag-of-WordsͷܗࣜͰอଘ͠ ͨMiݸͷ୯ޠΛ؍ଌσʔλͱ͢Δɽϊʔυiʹؔ͢Δm൪໨ͷ୯ޠwim͸જࡏతͳίϛϡχ ςΟxim∈ {1, . . . , K}ٴͼτϐοΫzim∈ {1, . . . , L}ʢL͸τϐοΫ਺ʣΛ࣋ͭ͜ͱΛԾఆ͢ Δɽ୯ޠίϛϡχςΟͱ୯ޠτϐοΫͷ഑ྻදݱ͸ͦΕͧΕXͱZͰද͞Εɼ֤഑ྻͷཁૉ ͸Mi࣍ݩͷϕΫτϧͰ͋ΔɽϞσϧͷੜ੒աఔʹ͓͍ͯɼ୯ޠίϛϡχςΟxim͸ΧςΰϦ

Χϧ෼෍xim | ηi∼ Categorical(ηi)ʹै͏ɽ͜͜Ͱɼηi͕୯ޠίϛϡχςΟxim͚ͩͰͳ͘ɼ

ϊʔυίϛϡχςΟsij, rjiΛੜ੒͢ΔύϥϝʔλͰ͋ͬͨ͜ͱΛࢥ͍ग़͢ͱɼηi͸ωοτϫʔ

ΫσʔλͱςΩετσʔλͷϞσϧʹڞ௨͢ΔύϥϝʔλͰ͋Γɼ྆ऀͷ৘ใΛͭͳ͛Δ໾ ׂΛՌ͍ͨͯ͠ΔɽҰํɼ୯ޠτϐοΫ͸୯ޠίϛϡχςΟ͕ॴ༩ͷঢ়ଶͰΧςΰϦΧϧ෼ ෍zim | xim = k, Θ∼ Categorical(θk)ʹै͏ɽ͜ͷͱ͖ɼθk = (θk1, . . . , θkL)͸ɼίϛϡχ ςΟkʹؔ͢ΔτϐοΫׂ߹Λࣔ͢ύϥϝʔλͰ͋Γɼ_lθkl = 1Λຬͨ͢ɽ͜ͷτϐοΫ ෼෍ͷߦྻදݱ͸Θ = (θ₁, . . . , θk)Ͱ͋Γɼࣄલ෼෍͸σΟϦΫϨ෼෍θk | α ∼ Dirichlet(α) ʹै͏ɽ ୯ޠτϐοΫzimΛॴ༩ͱͯ͠ɼͦΕʹରԠ͢Δ୯ޠwim ∈ {1, . . . , V }ʢV ͸૯୯ޠ਺ʣ ͸ɼ୯ޠτϐοΫʹରԠ͢ΔΧςΰϦΧϧ෼෍wim | zim = l, Φ ∼ Categorical(φl)ʹै͏ɽ ͨͩ͠ɼφl= (φ_l1, . . . , φlV)͸ɼͦͷτϐοΫʹ͓͍ͯ୯ޠ͕ੜ੒͞ΕΔ֬཰Λද͢୯ޠ෼ ෍Ͱ͋Γɼ_vφlv = 1Λຬͨ͢ɽ୯ޠ෼෍ͷߦྻදݱ͸Φ = (φ₁, . . . , φL)Ͱ͋Γɼͦͷࣄલ ෼෍͸σΟϦΫϨ෼෍φl ∼ Dirichlet(β)ʹै͏ɽ ैͬͯɼςΩετσʔλʹର͢Δ৚݅෇໬౓͸ɼಉ͘͡ίϛϡχςΟ෼෍HΛॴ༩ͱ͠

ͯɼҎԼͰఆٛ͞ΕΔɽ p(W, X, Z, Θ, Φ| H) = p(W | Z, Φ)p(Z | X, Θ)p(X | H)p(Θ | α)p(Φ | β) = D  i=1 _Mi  m=1

{p(wim| zim, Φ)p(zim| xim, Θ)p(xim | ηi)}

 _K  k=1 p(θk | α) L  l=1 p(φl| β). (2) ίϛϡχςΟ෼෍HΛॴ༩ͱ͢Δ͜ͱͰɼࣜʢ1ʣٴͼʢ2ʣͷ৚݅෇໬౓͕ಠཱͱͳΔԾఆ

Λஔ͍͍ͯΔͨΊɼIgarashi and Terui (2020)ͷ݁߹෼෍͸ɼࣜʢ1ʣͱʢ2ʣٴͼHͷີ౓

Λֻ͚߹ΘͤΔ͜ͱͰҎԼͷΑ͏ʹಘΒΕΔɽ p(A, W, S, R, X, Z, H, Ψ, Θ, Φ) = D  i=1  _D  j=1,j=i

{p(aij | sij, rji, Ψ)p(sij | ηi)p(rji| ηj)} Mi



m=1

{p(wim | zim, Φ)P (zim| xim, Θ)p(xim | ηi)}

 × D  i=1 p(ηi | γ) K  k=1 K  k₌₁ p(ψkk | δkk, kk) K  k=1 p(θk | α) L  l=1 p(φl | β). (3)

Igarashi and Terui (2020)ͷϞσϧͰ͸ɼϢʔβʔ͕ੜ੒ͨ͠ςΩετίϯςϯπΛߟྀ ͠ͳ͕ΒωοτϫʔΫ্ͷίϛϡχςΟߏ଄Λ೺Ѳ͢Δɼͭ·ΓτϐοΫϕʔεɾίϛϡχ ςΟΛݟ͚ͭΔ͜ͱΛ໨తͱ͍ͯ͠Δɽ͜ͷͱ͖ɼϊʔυؒʹΤοδ͕ੜ੒͞ΕΔ֬཰Λɼ

aij = 1 | sij = k, rji = k ∼ Bernoulli(ψkk)ͱͯ͠શͯͷϊʔυʹରͯ͠ಉ࣭తͰ͋Δ͜ͱ

ΛԾఆ͍ͯ͠Δɽ͔͠͠ɼલઅͰ΋આ໌ͨ͠Α͏ʹɼݱ࣮ͷࣾձωοτϫʔΫʹ͓͍ͯ͸ɼ

࣍਺͕ϊʔυʹΑͬͯେ͖͘ҟͳΔ͜ͱ͕ҰൠతͰ͋ΓɼIgarashi and Terui (2020)Ͱ͸ɼ͜

ͷੑ࣭ΛߟྀͰ͖͍ͯͳ͍ͨΊɼݱ࣮ͷωοτϫʔΫσʔλʹରͯ͠े෼ʹϑΟοςΟϯά Ͱ͖ͳ͍Մೳੑ͕͋Δɽ ຊݚڀͰ͸ɼ͜ͷ໰୊Λղܾ͢ΔͨΊʹɼΤοδੜ੒֬཰ͷ෦෼Λaij = 1| sij = k, rji= k ∼ Bernoulli(ψjkk)ͱͯ͠ϞσϧΛ֦ு͢Δɽ͜ͷͱ͖ɼψjkk͸ɼૹΓखͷίϛϡχςΟ ͕kͰɼड͚खͷίϛϡχςΟ͕kͷ࣌ʹΤοδ͕ੜ੒͞ΕΔ֬཰Λࣔ͠ɼड͚खͷϊʔυ jʹґଘ͢Δҟ࣭ͳύϥϝʔλͰ͋Δɽ͜ͷఆࣜԽʹΑΓɼྫ͑͹ɼड͚खj͕ίϛϡχςΟ

kͷதͰଟ͘ͷΤοδΛूΊΔɼ͍ΘΏΔϋϒϊʔυͰ͋Δ৔߹ʹɼψjkk͕େ͖ͳ஋ΛऔΔ ͜ͱͰͦΕΛදݱ͢Δɽ͜ΕʹΑΓɼఏҊϞσϧ͸ɼࣾձωοτϫʔΫʹ͓͚Δ࣍਺෼෍ͷ ҟ࣭ੑΛ൓ө͠ɼϊʔυ͝ͱͷ࣍਺ͷଟՉʹԠͯ͡Τοδ֬཰ύϥϝʔλΛҟ࣭తʹਪఆ͢ Δ͜ͱͰɼΑΓݱ࣮ͷࣾձωοτϫʔΫʹଈͨ͠ϞσϦϯά͕ՄೳͱͳΔɽ·ͨɼΤοδ֬ ཰ͷK× Kߦྻදݱ͸Ψi = (ψikk)Ͱද͞Εɼߦྻͷ֤ཁૉ͸ɼࣄલ෼෍ͱͯ͠ϕʔλ෼ ෍ɼψikk | δkk, kk ∼ Beta(δkk, kk)ʹै͏͜ͱΛԾఆ͢Δɽ

ຊݚڀͰ༻͍ΔϞσϧ͸ɼ্ड़ͨ͠఺Ҏ֎͸Igarashi and Terui (2020)ͱಉ͡ఆࣜԽΛ

Ծఆ͍ͯ͠ΔͨΊɼίϛϡχςΟ෼෍HΛॴ༩ͱͨ͠ͱ͖ͷωοτϫʔΫσʔλʹର͢Δ໬ ౓ɼࣜ(1)͕ҎԼͷΑ͏ʹมߋ͞ΕΔɽ p(A, S, R, Ψ| H) = p(A| S, R, Ψ)p(S | H)p(R | H)p(Ψ | δ, ) = D  i=1  _D  j=1,j=i

{p(aij | sij, rji, Ψj)p(sij | ηi)p(rji| ηj)} K  k=1 K  k₌₁ p(ψikk | δkk, _kk)  . (4)

4

৚݅෇͖ࣄޙ෼෍ͱύϥϝʔλਪఆ

ઌߦݚڀʹ͓͍ͯɼτϐοΫϞσϧΛਪఆ͢ΔͨΊͷख๏͸ɼม෼ϕΠζ๏΍ஞֶ࣍श๏ͳ Ͳଟ͘ఏҊ͞Ε͍ͯΔɽͦͷதͰ΋࠷΋޿͘࢖ΘΕ͍ͯΔ΋ͷͷҰ͕ͭɼ่յܕΪϒεαϯ ϓϦϯά(collapsed Gibbs sampling, CGS, Griffiths and Steyvers, 2004)Ͱ͋Δɽ͜Ε͸ɼ જࡏม਺ͷࣄޙ෼෍Λಋग़͢ΔաఔͰϞσϧύϥϝʔλΛੵ෼ফڈ͠ɼαϯϓϦϯάΛޮ཰ తʹߦ͏ख๏Ͱ͋ΔɽҎԼͰ͸ɼຊݚڀͷఏҊϞσϧʹର͢ΔCGSͷͷͨΊͷ৚݅෇͖ࣄ ޙ෼෍Λಋग़͢Δɽ ఏҊϞσϧʹ͓͚ΔɼίϛϡχςΟ෼෍HɼΤοδ֬཰ΨɼτϐοΫ෼෍Θɼ୯ޠ෼෍Φ ͷ4ͭͷύϥϝʔλʹ͍ͭͯ͸ɼࣄલ෼෍ͱͷڞ໾ੑʹج͖ͮɼ৚݅෇͖ࣄޙ෼෍Λط஌ͷ ෼෍ͱͯ͠ಋग़͢Δ͜ͱ͕Ͱ͖Δɽͨͩ͠ɼͦͷৄࡉͳಋग़աఔ͸Appendix AʹৡΔɽ· ͨɼͦΕҎ֎ͷજࡏม਺ͱͯ͠ɼૹΓखٴͼड͚खͷજࡏίϛϡχςΟS, Rɼ୯ޠͷજࡏί ϛϡχςΟXٴͼજࡏτϐοΫZͷ4͕ͭ͋Δ͕ɼ͜ΕΒͷ৚݅෇͖ࣄޙ෼෍͸ɼAppendix

AͰಋग़ͨ͠ࣄޙ෼෍Λ༻͍ͯҎԼͷΑ͏ʹಋग़͞ΕΔɽ

p(sij = k, rji = k | aij, A\ij, S\ij, R\ji, X, γ, δ, ) ∝

 

p(sij = k | ηi)p(rji = k | ηj)p(xi | ηi)p(xj | ηj)p(ηi | S\ij, R\ji, X, γ) p(ηj | S\ij, R_\ji, X, γ)dηidηj×



p(aij | ψjkk)p(ψjkk | A\ij, S_\ij, R_\ji, δ, )dψjkk

= Nik\ij + Mik+ γk t  N_it\ij+ Mit+ γt × Njk_\ji+ M_jk+ γ_k  t  N_jt\ji+ Mjt+ γt× n(+)_jkk_\ij+ δkk I(aij=1) n(−)_jkk_\ij + kk I(aij=0) n(+)_jkk_\ij + n(−)_jkk_\ij + δkk+ kk , (5)

p(xim = k, zim= l | W, S, R, X\im, Z\im, α, β, γ) ∝



p(si, ri | ηi)p(xim = k | ηi)p(ηi | S, R, X\im, γ)dηi×

 p(zim= l | θk) p(θk | X\im, Z\,im, α)dθk×  p(wim = v | φl)p(φl | W\im, Z\im, β)dφl = Nik+ Mik\im+ γk t  Nit+ M_it\im+ γt × M_kl\im+ αl  q  M_kq\im+ αq × M_lv\im+ βv  u  M_lu\im+ βu. (6) ͨͩ͠ɼࣜʢ5ʣʹ͓͚ΔNik͸ɼϊʔυi͕࣋ͭD− 1ݸͷؔ܎ੑʹ͓͍ͯɼૹΓखٴͼड ͚खͷજࡏίϛϡχςΟͱͯ͠kׂ͕Γ౰ͯΒΕͨճ਺Λද͠ɼMik͸ɼϊʔυiͷ୯ޠί ϛϡχςΟʹkׂ͕Γ౰ͯΒΕͨճ਺Λද͢ɽn(+)_ikk͸ɼϊʔυiʹؔ͢ΔD− 1ݸͷؔ܎ੑ ͷ͏ͪɼίϛϡχςΟk, kׂ͕Γ౰ͯΒΕͨΤοδ͕ੜ੒͞Ε͍ͯΔؔ܎ੑͷ਺ɼn(−)_ikk ͸ɼ Τοδ͕ੜ੒͞Ε͍ͯͳ͍ؔ܎ੑͷ਺Λද͢ɽࣜʢ6ʣʹ͓͚ΔMkl͸ɼίϛϡχςΟkׂ͕ Γ౰ͯΒΕͨ୯ޠͷ͏ͪτϐοΫlׂ͕Γ౰ͯΒΕͨճ਺ɼMlv͸ɼޠኮvʹτϐοΫlׂ͕ Γ౰ͯΒΕͨճ਺Λද͢ɽ·ͨɼఴ͑ࣈͷ_\͸͜ΕΒͷΧ΢ϯτ͔Βɼ౰֘σʔλΛআ͘͜ ͱΛҙຯ͢Δɽ CGSͰ͸ɼࣜʢ5ʣٴͼʢ6ʣʹैͬͯɼ֤ؔ܎ੑٴͼ୯ޠʹରͯ͠જࡏίϛϡχςΟͱ τϐοΫΛ܁Γฦ͠αϯϓϦϯά͢Δɽ࠷ऴతʹɼॳظ஋ʹґଘ͢ΔՔಇظؒΛআ͍ͨαϯ ϓϧΛ༻͍ͯɼੵ෼ফڈ͍ͯͨ͠4ͭͷύϥϝʔλͷظ଴஋Λܭࢉ͢Δ͜ͱͰਪఆ஋ΛಘΔɽ

5

࣮ূ෼ੳ

5.1

࢖༻σʔλ

͜͜Ͱ͸ɼݱ࣮ͷΦϯϥΠϯࣾձωοτϫʔΫʹରͯ͠ɼఏҊϞσϧΛ༻͍ͨ෼ੳ͕༗ӹͰ ͋Δ͜ͱΛࣔͨ͢ΊʹɼTwitterσʔλΛ࢖࣮ͬͨূ෼ੳΛߦ͏ɽຊઅͰ͸ɼ·ͣ෼ੳʹ༻͍ ͨσʔληοτͷ֓ཁͱલॲཧʹ͍ͭͯઆ໌͢ΔɽຊݚڀͰ͸ɼ೚ఱಊגࣜձ͕ࣾTwitter ্Ͱอ͍࣋ͯ͠Δӳޠ൛ެࣜΞΧ΢ϯτΛத৺ͱ͢ΔωοτϫʔΫΛର৅ͱͯ͠ɼҎԼͷख ॱͰσʔλΛऩूٴͼՃ޻ͨ͠ɽ ·ͣɼ2018೥5݄1೔࣌఺ͰͷϑΥϩʔؔ܎ʹैͬͯɼ೚ఱಊͷΞΧ΢ϯτΛϑΥϩʔ͠ ͍ͯΔϢʔβʔ͔ΒϥϯμϜʹαϯϓϦϯάΛߦͬͨɽଓ͍ͯɼαϯϓϧ͞ΕͨϢʔβʔΛ ϑΥϩʔ͍ͯ͠ΔผͷϢʔβʔ͔Β΋ϥϯμϜʹαϯϓϦϯάΛߦͬͨɽͦͯ͠ɼͦΕΒͷ ϢʔβʔͰܗ੒͞ΕΔωοτϫʔΫʹ͓͍ͯɼೖ࣍਺ͱग़࣍਺ͷฏۉ͕3ҎԼͷϢʔβʔΛ ֎Ε஋ͱΈͳͯ͠σʔληοτ͔Βআ֎ͨ͠ɽ݁Ռͱͯ͠ɼ3,500ਓͷϢʔβʔ͕࢒Γɼωο τϫʔΫ಺ʹ͓͚ΔΤοδͷ૯਺͸68,949ຊͰ͋ͬͨɽ͜ΕΒͷϢʔβʔͰܗ੒͞ΕΔ༗޲ άϥϑΛωοτϫʔΫ৘ใͱͯ͠࢖༻͢Δɽ ࣍ʹɼςΩετσʔλͷ࡞੒ํ๏Λઆ໌͢Δɽ·ͣɼ্Ͱαϯϓϧ͞Εͨ3,500ਓ෼ͷΞ Χ΢ϯτʹରͯ͠ɼ2017೥9݄1೔͔Β2018೥ͷ2݄28೔1·Ͱʹ౤ߘͨ͠౤ߘ಺༰͔Β ςΩετ෦෼Λશͯൈ͖ग़ͨ͠ɽ͜ΕΒͷςΩετσʔλʹରͯ͠ɼจষ͔Β୯ޠू߹΁ͷ ෼ղɼখจࣈ΁ͷ౷Ұɼ਺ࣈɼه߸ɼٴͼओཁͳετοϓϫʔυʢaɼtheɼIͳͲʣͷ࡟আɼ ׆༻ܗ͔Βޠװ΁ͷ౷ҰʢstemmingʣͷॱʹલॲཧΛߦͬͨɽ͞ΒʹɼॲཧࡁΈͷςΩετ σʔλͷ͏ͪɼίʔύε಺Ͱͷස౓͕20ҎԼɼ͋Δ͍͸20ਓҎԼͷϢʔβʔʹ͔͠࢖ΘΕ ͍ͯͳ͍௿ස౓ͷ୯ޠͱɼ50ਓҎ্ͷϢʔβʔʹ࢖ΘΕ͍ͯΔߴස౓ͷ୯ޠΛɼτϐοΫਪ ఆ΁ͷѱӨڹΛආ͚ΔͨΊʹσʔληοτ͔Βআ͍ͨɽ݁Ռͱͯ͠ɼίʔύε಺ʹ͸9,001 छྨͷ୯ޠ͕࢒Γɼϊʔυ͝ͱͷฏۉ୯ޠ਺͸98.2Ͱ͋ͬͨɽ࣍અͰ͸ɼఏҊϞσϧʹ͓͚ ΔίϛϡχςΟ਺ɼτϐοΫ਺ͷܾఆํ๏Λઆ໌ͨ͠ͷͪɼ࡞੒ͨ͠σʔληοτʹର͢Δ 1_{ςΩετσʔλͷલॲཧͷஈ֊Ͱɼେ൒ͷϢʔβʔ͕ɼ2018೥3݄ʹ։͔ΕͨNintendo Directͱ͍͏} ৽঎඼ൃදΠϕϯτʹؔ͢Δ౤ߘΛߦ͍ͬͯΔ͜ͱ͕൑໌ͨ͠ɽ͕ͨͬͯ͠ɼຊݚڀͰ͸ɼ͜ͷΑ͏ͳଟ͘ͷ ϢʔβʔͰڞ௨͢ΔಉҰͷࣄ৅ʹର͢Δ౤ߘ͕τϐοΫͷਪఆʹ༩͑ΔӨڹΛආ͚ΔͨΊɼςΩετσʔλͷ ؍ଌظؒΛ2018೥2݄28೔·Ͱͱͨ͠ɽ

ఏҊϞσϧͷਪఆ݁Ռʹ͍ͭͯٞ࿦͢Δɽ

5.2

෼ੳ݁Ռ

ఏҊϞσϧΛؚΊͯɼҰൠʹϒϩοΫϞσϧΛ༻͍ͯ෼ੳ͢Δࡍʹ͸ɼࣄલʹίϛϡχςΟ ਺ʢٴͼຊݚڀͰ͸ͦΕʹՃ͑ͯτϐοΫ਺ʣΛܾΊΔඞཁ͕͋ΔɽઌߦݚڀͰ͸ɼίϛϡχ

ςΟ਺ͷܾఆΛ৘ใྔج४Λ༻͍ͨϞσϧൺֱͱͯ͠ଊ͑ɼBICʹΑΔํ๏(Handcock et al.,

2007; Salda˜na et al., 2017)ɼintegrated completed likelihoodʹΑΔํ๏(Daudin et al., 2008; Bouveyron et al., 2018)ɼม෼ϕΠζʹΑΔํ๏(Latouche et al., 2012)ͳͲ༷ʑͳख๏͕ ఏҊ͞Ε͍ͯΔɽ͔͠͠ɼຊݚڀͰ͸ɼۙ೥৽ͨͳ৘ใྔج४ͱͯ͠ఏҊ͞ΕɼݱࡏͰ͸਺

ଟ͘ͷྖҬͰ࢖ΘΕ͍ͯΔ޿͘࢖͑Δ৘ใྔج४(widely applecable information criterion,

WAIC, Watanabe, 2010)ΛϞσϧൺֱͷج४ͱͯ͠࠾༻ͨ͠ɽఏҊϞσϧʹର͢ΔWAIC

ͷৄࡉ͸Appendix BʹৡΔɽද2͸ɼίϛϡχςΟ਺ٴͼτϐοΫ਺Λ5͔Β10ͷൣғͰ ઃఆ͠ɼ5.1અͰ࡞੒ͨ͠σʔληοτʹରͯ͠WAICΛܭࢉͨ݁͠ՌͰ͋Δɽͨͩ͠ɼ͜ͷ ࣌ͷ܁Γฦ͠਺͸5,000ճͰ͋Γɼͦͷ͏ͪ2,000ճΛॳظ஋ʹґଘ͢ΔՔಇظؒͱͯ͠আ͍ ͨɽ·ͨɼϋΠύʔύϥϝʔλͷઃఆ͸ɼͦΕͧΕɼαl= 0.1,∀lɼβv = 0.1,∀vɼγk = 1.0,∀kɼ δkk = kk = 0.1,∀k, kͰ͋Δɽͦͷ݁ՌɼίϛϡχςΟ਺7ɼτϐοΫ਺7ͷϞσϧ͕બ͹ ΕͨͨΊɼҎ߱Ͱ͸͜ͷϞσϧΛ༻͍ͨTwitterσʔλͷ෼ੳ݁ՌΛٞ࿦͢Δɽ ·ͣɼϊʔυʹґଘ͠ͳ͍άϩʔόϧύϥϝʔλΛݟΔ͜ͱͰɼਓʑ͕ݕग़͞Εͨίϛϡ χςΟ಺ͰͲͷΑ͏ͳ͜ͱʹؔ৺Λ͍࣋ͬͯΔͷ͔͕෼͔Δɽਤ2͸ɼਪఆ͞Εͨ୯ޠ෼ ෍ͷ஋͕࠷΋ߴ্͍Ґ10ݸͷ୯ޠΛτϐοΫຖʹฒ΂ͨ΋ͷͰ͋Γɼ͜ΕʹΑͬͯτϐο ΫͷҙຯΛղऍ͢Δ͜ͱ͕Ͱ͖Δɽ֤τϐοΫͷҙຯͱ୅දతͳ୯ޠ͸ҎԼͷ௨ΓͰ͋Δɽ τϐοΫ1͸Ξχϝʔγϣϯʹؔ͢ΔτϐοΫʢ୅දతͳ୯ޠ͸blackclovɼhunterxhuntɼ jojosbizarreadventurͳͲʣɼτϐοΫ2͸ετϦʔϛϯά഑৴શൠʹؔ͢ΔτϐοΫʢ୅ද

తͳ୯ޠ͸teamemmmmsiɼtwitchkittenɼrokuͳͲʣɼτϐοΫ3͸Իָʹؔ͢ΔτϐοΫ

ʢ୅දతͳ୯ޠ͸vevoɼsprinrillaͳͲʣɼτϐοΫ4͸ήʔϜετϦʔϛϯά഑৴ʹؔ͢Δτ

ϐοΫʢ୅දతͳ୯ޠ͸critical roleɼzeldathonͳͲʣɼτϐοΫ5͸ಡॻʹؔ͢ΔτϐοΫ

ΔτϐοΫʢ୅දతͳ୯ޠ͸digitalmarketɼsmmɼcontentmarketͳͲʣɼͦͯ͠τϐοΫ 7͸εϙʔπʹؔ͢ΔτϐοΫʢ୅දతͳ୯ޠ͸oilerɼtfcͳͲʣͱݴ͑Δɽ·ͨɼਤ3͸ɼ ਪఆ͞Ε֤ͨίϛϡχςΟͷτϐοΫ෼෍Ͱ͋Γɼ֤ίϛϡχςΟ಺ʹ͓͚ΔτϐοΫͷׂ ߹Λ֬ೝ͢Δ͜ͱ͕Ͱ͖Δɽ ࣍ʹɼ֤ϊʔυʹ͍ͭͯҟ࣭ͳϩʔΧϧύϥϝʔλͷਪఆ݁ՌΛ֬ೝ͢Δɽਤ4ٴͼ5 ͸ɼϊʔυ൪߸1൪ͱ237൪ʹؔ͢ΔΤοδ֬཰ͱίϛϡχςΟ෼෍ͷਪఆ݁ՌͰ͋Δɽ· ͨɼϊʔυ1ͷೖ࣍਺͸6ɼग़࣍਺͸0Ͱ͋Γɼϊʔυ237ͷೖ࣍਺͸657ɼग़࣍਺͸37Ͱ ͋Δɽਪఆ݁Ռ͸ɼ͜ͷ྆ϊʔυͷ࣍਺த৺ੑͷҧ͍Λ೗࣮ʹද͓ͯ͠Γɼϊʔυ1͕ओʹ ଐ͢ΔίϛϡχςΟʢίϛϡχςΟ1ͱ6ʣʹؔ͢ΔΤοδ֬཰͸௿͍஋Ͱਪఆ͞Ε͍ͯΔͷ ʹରͯ͠ɼϊʔυ237͕ओʹଐ͢ΔίϛϡχςΟʢίϛϡχςΟ1ͱ5ʣʹؔ͢ΔΤοδ֬཰ ͸ߴ͍஋Ͱਪఆ͞Ε͍ͯΔɽ͜ͷΑ͏ʹɼΤοδ֬཰ͷύϥϝʔλ͕Τοδͷܨ͕Γ΍͢͞ ʹؔ͢Δҟ࣭ੑΛଊ͑ΒΕΔΑ͏ͳԾఆΛಋೖ͢Δ͜ͱͰɼΑΓॊೈʹωοτϫʔΫϞσϧ ΛදݱͰ͖ΔΑ͏ʹͳΓɼςετσʔλʹର͢Δ༧ଌੑೳ΋޲্͢Δ͜ͱ͕ظ଴͞ΕΔɽ࣍ અͰ͸ɼ͜ΕΛݕূ͢ΔͨΊʹɼઌߦݚڀʹ͓͚ΔطଘϞσϧͱڞʹൺֱ࣮ݧΛߦ͏ɽ

5.3

༧ଌੑೳͷݕূ

ຊઅͰ͸ɼఏҊϞσϧͷςετσʔλʹର͢Δ༧ଌੑೳΛɼൺֱϞσϧͱڞʹݕূ͢Δɽൺ

ֱϞσϧͱͯ͠ɼઌߦݚڀʹ͓͚ΔطଘϞσϧ͔ΒɼAiroldi et al. (2008)ͱIgarashi and

Terui (2020)ΛબΜͩɽAiroldi et al. (2008)ͷϞσϧ͸ɼIgarashi and Terui (2020)ͷϞσϧ

͔ΒςΩετ৘ใͷߟྀΛআ͍ͨϞσϧʹ૬౰͢ΔͨΊɼ͜ΕΒΛൺֱ͢Δ͜ͱͰɼςΩε τ৘ใΛߟྀ͢Δ͜ͱʹΑΔ༧ଌੑೳ΁ͷӨڹΛݟΔ͜ͱ͕Ͱ͖Δɽ͞ΒʹɼIgarashi and Terui (2020)ͷϞσϧ͸ɼຊݚڀͷϞσϧ͔ΒΤοδ֬཰ͷҟ࣭ੑΛআ͍ͨಉ࣭ϞσϧͰ͋ Γɼҟ࣭ੑͷߏ଄͕༧ଌੑೳ΁༩͑ΔӨڹΛݟΔ͜ͱ͕Ͱ͖Δɽ 5.2અͰ͸ɼશͯͷωοτϫʔΫɼςΩετσʔλΛֶशσʔλͱͯ͠ϞσϧͷਪఆΛߦͬ ͕ͨɼ͜͜Ͱ͸ɼ֤ϊʔυ͕࣋ͭD− 1ݸͷؔ܎ੑͷ͏ͪɼ90%Λֶशσʔλͱͯ͠Ϟσϧ ͷਪఆʹ࢖͍ɼ࢒Γͷ10%Λςετσʔλͱͨ͠͠ɽςΩετσʔλʹ͍ͭͯ͸ɼલઅಉ༷ શͯͷσʔλΛֶशσʔλͱͯ͠༻͍ͨɽ·ͨɼ܁Γฦ͠਺΍ϋΠύʔύϥϝʔλͷઃఆ΋

લઅͱಉ͡৚݅Ͱਪఆ͍ͯ͠Δɽ͜ΕΒͷ৚݅ͷԼͰֶशσʔλʹର͢ΔਪఆΛߦ͍ɼ֤ύ ϥϝʔλͷਪఆ஋Λಘͨɽਪఆ͞ΕͨίϛϡχςΟ෼෍ͱΤοδ֬཰Λ_{H, ˆ}ˆ _{Ψͱද͢ͱɼྫ} ͑͹ఏҊϞσϧʹ͍ͭͯ͸ɼςετσʔλaij ∈ Atestʹର͢Δ༧ଌ֬཰͸ҎԼͰܭࢉͰ͖Δɽ p(aij = 1) = K  k=1 K  k₌₁ ˆ ηikηjkˆ ψjkkˆ  (7)

Airoldi et al. (2008)ͱIgarashi and Terui (2020)ͷϞσϧʹ͍ͭͯ΋ಉ༷ʹɼίϛϡχςΟ ෼෍ͱΤοδ֬཰ͷੵʹΑͬͯ༧ଌ֬཰ΛܭࢉͰ͖Δɽ

ද3͸ɼίϛϡχςΟ਺ͱτϐοΫ਺ΛͦΕͧΕ5͔Β10·ͰมԽͤͨ͞ͱ͖ͷ֤Ϟσ

ϧͷArea Under the CurveʢAUCʣͷ஋Ͱ͋Δɽ͜ΕΛݟΔͱɼ΄΅શͯͷ૊Έ߹Θͤʹͭ

͍ͯఏҊϞσϧʢද಺Ͱ͸Heteroʣ͕ൺֱϞσϧͰ͋ΔIgarashi and Terui (2020)ʢද಺Ͱ

͸HomoʣΑΓ΋༏Ε͍ͯΔ͜ͱ͕෼͔ΔɽΑͬͯɼࣾձωοτϫʔΫʹҰൠతʹΈΒΕΔ

࣍਺ͷҟ࣭ੑΛߟྀ͠ɼΤοδ͕ੜ੒͞ΕΔ֬཰͸ϊʔυ͝ͱʹಉ࣭తͰ͸ͳ͍ͱ͍͏Ծఆ

Λஔ͍ͨϞσϧͷํ͕༧ଌੑೳ͕༏ΕͨϞσϧͰ͋Δͱ͍͑Δɽ·ͨɼAiroldi et al. (2008)

ʢද಺Ͱ͸MMSBʣͱIgarashi and Terui (2020)Λൺֱ͢ΔͱɼίϛϡχςΟͷ਺͕গͳ͍

ͱ͖ʢK = 5, 6ʣʹ͸Airoldi et al. (2008)ͷํ͕AUC͕શମతʹߴ͘ɼίϛϡχςΟͷ਺͕

ଟ͍ͱ͖ʢK = 8, 9, 10ʣ͸Igarashi and Terui (2020)ͷํ͕શମతʹAUC͕ߴ͍ͱ͍͏݁

ՌͰ͋ͬͨɽ͜ͷ݁Ռ͔ΒɼຊݚڀͰ༻͍ͨTwitterωοτϫʔΫ͸ɼେ·͔ʹίϛϡχςΟ Λ෼͚Δࡍʹ͸ωοτϫʔΫ৘ใͷΈΛߟྀ͢Δ͚ͩͰॆ෼Ͱ͋Δ͕ɼΑΓࡉ͔ͳίϛϡχ ςΟʹ෼͚Δ৔߹ʹ͸ɼςΩετ৘ใΛ༻͍ͯτϐοΫͷ·ͱ·ΓΛߟྀ͠ͳ͕Β෼͚ͨํ ͕ΑΓྑ͍ΫϥελϦϯάͱͳΔωοτϫʔΫͰ͋Δͱ͍͑Δɽͭ·Γɼ1અͰ΋ड़΂ͨΑ ͏ʹɼֶߍ΍ಉڃੜͱ͍ͬͨେ͖ͳ·ͱ·ΓͷίϛϡχςΟͷத͔ΒɼԻָ΍εϙʔπͷΑ ͏ʹझຯ΍ؔ৺ࣄ͕ڞ௨͍ͯ͠Δ·ͱ·ΓɼτϐοΫϕʔεɾίϛϡχςΟΛݟ͚͍ͭͯ͘ ϞσϦϯά͕ɼΑΓਫ਼៛ͳωοτϫʔΫ෼ੳͷͨΊʹ͸༗ӹͰ͋Δͱ͍͏͕ࣔࠦಘΒΕͨɽ

6

݁࿦

ຊݚڀͰ͸ɼࣾձωοτϫʔΫ෼ੳΛΑΓݱ࣮ʹଈͨ͠༗ҙٛͳ෼ੳͱ͢ΔͨΊʹɼωοτ ϫʔΫ৘ใ͚ͩͰͳ͘ɼਓʑͷڵຯ΍ؔ৺Λද͢ιʔγϟϧϝσΟΞ্ͷςΩετ৘ใΛߟ ྀ͠ɼ͞ΒʹɼࣾձωοτϫʔΫʹಛ༗ͷ࣍਺ͷҟ࣭ੑΛՃຯͨ͠ϞσϧΛఏҊͨ͠ɽઌߦ ݚڀʹ͓͚ΔطଘϞσϧͱൺֱͨ͠ͱ͖ɼຊݚڀͰఏҊ͢ΔϞσϧͷಛ৭ͱͯ͠͸ɼωοτ ϫʔΫ্ͷ֤ϊʔυ͕࣋ͭςΩετ৘ใΛར༻͍ͯ͠Δ఺ɼϊʔυ͕ͦΕͧΕͷؔ܎ੑʹ Ԋͬͯෳ਺ͷίϛϡχςΟʹଐ͢Δ͜ͱΛڐ༰͍ͯ͠Δ఺ɼແ޲άϥϑ͔༗޲άϥϑʹ͔͔ ΘΒͣద༻Ͱ͖Δ఺ɼͦͯ࣍͠਺ͷҟ࣭ੑΛߟྀ͠ɼΤοδ֬཰ͷύϥϝʔλ͕ϊʔυ͝ͱ ʹҟ࣭Ͱ͋Δ͜ͱΛԾఆ͍ͯ͠Δ఺͕ڍ͛ΒΕΔɽ͜ΕʹΑͬͯɼ࣍਺͕ϊʔυʹΑͬͯେ ͖͘ҟͳΔҰൠతͳࣾձωοτϫʔΫʹରͯ͠΋े෼ͳϑΟοςΟϯάੑೳΛ༗͠ͳ͕Βɼ Τοδ͕ີʹू·͓ͬͯΓɼ͔ͭੜ੒͞ΕͨςΩετͷτϐοΫ͕ಉҰͷ෼෍͔Βੜ੒͞Ε ΔɼτϐοΫϕʔεɾίϛϡχςΟͷݕग़͕ՄೳͱͳΔɽ ࣮ূ෼ੳͷ݁Ռɼ่յܕΪϒεαϯϓϦϯάʹΑͬͯਪఆ͞ΕΔఏҊϞσϧ͸ɼݱ࣮ͷ Twitterσʔλʹରͯ͠ɼҙຯͷ͋ΔίϛϡχςΟٴͼτϐοΫߏ଄Λଊ͑Δ͚ͩͰͳ͘ɼͲ ͷΑ͏ͳίϛϡχςΟ਺ɼτϐοΫ਺ͷ૊Έ߹ΘͤͰ͋ͬͯ΋طଘϞσϧΑΓ΋༏Εͨ༧ଌ ੑೳΛ͓࣋ͬͯΓɼ࣍਺ͷҟ࣭ੑΛߟྀͯ͠Τοδ֬཰Λਪఆ͢ΔϞσϦϯά͸ɼ༧ଌੑೳ ʹ͓͍ͯ༏Ε͍ͯΔ͜ͱ͕ࣔ͞Εͨɽ͞Βʹɼ͜ͷ݁Ռ͔ΒɼΦϯϥΠϯͷࣾձωοτϫʔ Ϋ෼ੳʹ͓͍ͯɼωοτϫʔΫ্ͷେ·͔ͳίϛϡχςΟߏ଄Λ௒͑ͯɼ͞Βʹࡉ͔͘Ϋϥ ελʔΛ෼ੳ͍ͯ͘͠৔߹͸ɼ֤ϊʔυ͕࣋ͭςΩετ৘ใΛՃຯͯ͠τϐοΫϕʔεɾί ϛϡχςΟΛݟ͚͍ͭͯ͘ϞσϦϯά͕༗ӹͰ͋ΔͱͷࣔࠦΛಘΔ͜ͱ͕Ͱ͖ͨɽ ຊݚڀͰ͸ɼΦϯϥΠϯ্ͷࣾձωοτϫʔΫʹண໨ͨͨ͠Ίɼਓʑ͕ଞͱωοτϫʔ ΫΛܗ੒͢Δࡍʹ͸ɼ૬खͷωοτϫʔΫ৘ใͱςΩετ৘ใͷΈΛߟྀ͢Δͱ͍͏ԾఆΛ ஔ͖ɼ૬खͷ೥ྸ΍ੑผͱ͍ͬͨଐੑ৘ใɼ͋Δ͍͸ߦಈ΍ଶ౓ͱ͍ͬͨ৘ใ͸ɼ͜ΕΒͷ σʔλ͕ར༻Ͱ͖ͳ͍͜ͱ͔ΒఏҊϞσϧͷߟྀ͔Β֎͍ͯͨ͠ɽҰํͰɼࣾձωοτϫʔ Ϋ෼ੳʹؔ͢Δઌߦݚڀͷจ຺Ͱ͸ɼͦͷΑ͏ͳϊʔυݻ༗ͷʢ͋Δ͍͸ೋ߲ɼࡾ߲ؒͷʣಛ ௃ྔ͕ωοτϫʔΫܗ੒ʹӨڹ͍ͯ͠Δ͜ͱ͕ଟ͘ͷݚڀͰࣔ͞Ε͍ͯΔ(Hoff et al., 2002; Handcock et al., 2007)ɽຊݚڀͰ͸ɼΤοδܗ੒ͷؔ਺͕ɼؔ܎ੑΛ݁Ϳ྆ऀͷίϛϡχςΟ

෼෍ɼٴͼؔ܎ੑΛड͚औΔଆͷΤοδ֬཰Ͱߏ੒͞Ε͍͕ͯͨɼઌߦݚڀΛࢀর͢Δͱɼ ͜͜ʹଐੑ΍ߦಈ৘ใͱ͍ͬͨϊʔυݻ༗ͷಛ௃ྔΛ૊ΈࠐΉ֦ு͸༗ҙٛͰ͋Γɼ͜ΕΒ ͷ৘ใΛϞσϧʹऔΓࠐΉ͜ͱ͸௚઀తʹՄೳͰ͋Δɽσʔλͷར༻Մೳੑͱ߹Θͤͯࠓޙ ͷ՝୊ͱ͍ͨ͠ɽ

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Tables

ද 1: ఏҊϞσϧͱطଘϞσϧͷൺֱ

؍ଌσʔλ ϝϯόʔγοϓ άϥϑͷํ޲ੑ ࣍਺ͷҟ࣭ੑ Blei et al. (2003) ςΩετͷΈ ࠞ߹ - -Snijders and Nowicki (1997) ωοτϫʔΫͷΈ ୯Ұ ྆ํՄೳ ߟྀͤͣ Airoldi et al. (2008) ωοτϫʔΫͷΈ ࠞ߹ ྆ํՄೳ ߟྀͤͣ Chang and Blei (2010) ωοτϫʔΫʗςΩετ ࠞ߹ ແ޲άϥϑͷΈ ߟྀͤͣ Liu et al. (2009) ωοτϫʔΫʗςΩετ ୯Ұ ແ޲άϥϑͷΈ ߟྀͤͣ Bouveyron et al. (2018) ωοτϫʔΫʗςΩετ ୯Ұ ྆ํՄೳ ߟྀͤͣ Zhu et al. (2013) ωοτϫʔΫʗςΩετ ࠞ߹ ྆ํՄೳ ߟྀͤͣ Igarashi and Terui (2020) ωοτϫʔΫʗςΩετ ࠞ߹ ྆ํՄೳ ߟྀͤͣ Karrer and Newman (2011) ωοτϫʔΫͷΈ ୯Ұ ྆ํՄೳ ϊʔυ͝ͱͷظ଴࣍਺ύϥϝʔλΛಋೖ ຊݚڀ ωοτϫʔΫʗςΩετ ࠞ߹ ྆ํՄೳ Τοδ֬཰Λҟ࣭ύϥϝʔλͱͯ͠ఆٛ

ද 2: WAICʹΑΔϞσϧൺֱɿK͸ίϛϡχςΟ਺ΛɼL͸τϐοΫ਺Λද͠ɼଠࣈ͸࠷ খͷ஋Λҙຯ͢Δɽ L=5 L=6 L=7 L=8 L=9 L=10 K=5 4422206.32 4340879.93 4321068.95 4333535.35 4354814.11 4553144.83 K=6 4333313.32 4333488.66 4351008.38 4309479.01 4302773.27 4280703.13 K=7 4313265.58 4285253.01 4272682.48 4346780.91 4301005.75 4414800.13 K=8 4320416.87 4282485.37 4326300.05 4324393.23 4321806.29 4426226.19 K=9 4429170.84 4329997.66 4439594.82 4407656.85 4296128.61 4301655.85 K=10 4361219.83 4342899.53 4282056.30 4306509.44 4306244.12 4406655.34

ද 3: AUCʹΑΔ༧ଌੑೳͷൺֱʀ֤Ϟσϧͷ໊લ͸ͦΕͧΕɼMMSB͕Airoldi et al. (2008)ɼHomo͕Igarashi and Terui (2020)ɼHetoro͕ຊݚڀͷϞσϧΛࢦ͠ɼଠࣈ͸֤ί

ϛϡχςΟ਺ʢKʣɼτϐοΫ਺ʢLʣͷ૊Έ߹Θͤʹ͓͚Δ࠷େͷAUCΛද͢ɽ L 5 6 7 8 9 10 K=5 MMSB 0.897 0.897 0.897 0.897 0.897 0.897 Homo 0.896 0.900 0.890 0.883 0.905 0.890 Hetero 0.917 0.920 0.924 0.921 0.923 0.924 K=6 MMSB 0.913 0.913 0.913 0.913 0.913 0.913 Homo 0.904 0.908 0.910 0.909 0.908 0.906 Hetero 0.925 0.930 0.922 0.930 0.923 0.921 K=7 MMSB 0.907 0.907 0.907 0.907 0.907 0.907 Homo 0.920 0.900 0.895 0.900 0.903 0.911 Hetero 0.929 0.926 0.929 0.930 0.929 0.931 K=8 MMSB 0.904 0.904 0.904 0.904 0.904 0.904 Homo 0.925 0.918 0.916 0.921 0.897 0.916 Hetero 0.928 0.930 0.927 0.930 0.929 0.928 K=9 MMSB 0.912 0.912 0.912 0.912 0.912 0.912 Homo 0.920 0.922 0.918 0.917 0.922 0.920 Hetero 0.922 0.923 0.925 0.927 0.927 0.922 K=10 MMSB 0.906 0.906 0.906 0.906 0.906 0.906 Homo 0.923 0.926 0.923 0.925 0.920 0.917 Hetero 0.923 0.921 0.926 0.925 0.923 0.930

Figures

A S R η γ X Z W Bernoulli

Multi Multi Multi

Dir Multi Multi ψ δ  θ α φ β Beta Dir Dir ∀k, k_{∈ K} ∀j ∈ D, j = i ∀1 ≤ n ≤ Mi ∀i ∈ D ∀k ∈ K ∀l ∈ L ਤ 1: ఏҊϞσϧͷάϥϑΟΧϧදݱ

nonfollow blackclov hunterxhunt jojosbizarreadventur mkleosaga wnf hori mdva hyrulesaga nyxl teamemmmmsi dokkan twitchkitten vgc roku wizebot ryzen freebiefriday streamersconnect nbaliv trapadr vevo ddrive leed spinrilla ifb gainwithpyewaw gainwithxtiandela horford suav criticalrol zeldathon orton fursuitfriday dramaalert sdlive htgawm sml robloxdev yoongi iartg amread erotica asmsg momlif hemp writerslif bookreview kindleunlimit bookboost growthhack digitalmarket gdpr smm contentmarket gamedesign podernfamili socialmediamarket bigdata emailmarket savvi lube foodporn oiler austria tfc crowdfir tranc tock thexfil Topic 1 Topic 2 Topic 3 Topic 4 Topic 5 Topic 6 Topic 7

Community 5 Community 6 Community 7

Community 1 Community 2 Community 3 Community 4

1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00 Topic To pic distr ib ution ਤ 3: ֤ίϛϡχςΟͷτϐοΫ෼෍ʹؔ͢Δਪఆ݁Ռ

1 2 3 4 5 6 7 1 2 3 4 5 6 7 Receiver Community Sender Comm unity 0.25 0.50 0.75 Edge Probability 0.0 0.2 0.4 0.6 1 2 3 4 5 6 7 Community Comm unity Distr ib ution ਤ4: ϊʔυ1ͷΤοδ֬཰ͱίϛϡχςΟ෼෍ʹؔ͢Δਪఆ݁Ռ

1 2 3 4 5 6 7 1 2 3 4 5 6 7 Receiver Community Sender Comm unity 0.25 0.50 0.75 Edge Probability 0.0 0.2 0.4 0.6 1 2 3 4 5 6 7 Community Comm unity Distr ib ution ਤ 5: ϊʔυ237ͷΤοδ֬཰ͱίϛϡχςΟ෼෍ʹؔ͢Δਪఆ݁Ռ

Appendices

A

৚݅෇͖ࣄޙ෼෍ͷಋग़

??અͰ͸ɼજࡏίϛϡχςΟٴͼજࡏτϐοΫͷ৚݅෇͖ࣄޙ෼෍Λಋग़ͨ͠ʢࣜ5ɼ6ʣɽ ͜ΕΒͷࣄޙ෼෍ΛಘΔͨΊʹ͸ɼ·ͣɼίϛϡχςΟ෼෍ɼΤοδ֬཰ɼτϐοΫ෼෍ɼ୯ ޠ෼෍ͷ4ͭͷύϥϝʔλʹ͍ͭͯɼ৚݅෇͖ࣄޙ෼෍Λಋग़͢Δඞཁ͕͋Δɽࣄલ෼෍ͱ ͷڞ໾ੑʹج͍ͮͯɼ͜ΕΒͷࣄޙ෼෍͸ҎԼͷΑ͏ʹಋग़͞ΕΔɽ p(ηi | S, R, X, γ) = Γ (  kNik+ Mik+ γk)  kΓ(Nik+ Mik+ γk) K  k=1 ηNik+Mik+γk ik (8) p(ψikk | A, S, R, δ, ) = Γ(n (+) ikk+ n(−)_ikk + δkk+ kk) Γ(n(+)_ikk + δkk)Γ(n(−)_ikk + _kk)× ψ I(aij=1)

ikk (1− ψikk)I(aij=0) (9) p(θk | X, Z, α) = Γ (  lMkl + αl) ΠlΓ(Mkl+ αl) L  l=1 θMkl+αl kl (10) p(φl| W, Z, β) = Γ (  vMlv+ βv) ΠvΓ(Mlv+ βv) V  v=1 φMlv+βv lv , (11)

B

ఏҊϞσϧʹର͢Δ

WAIC

ͷఆٛࣜ

ఏҊϞσϧʹର͢ΔWAICͷఆٛࣜ͸ҎԼͷ௨ΓͰ͋Δɽ lpd(i) = log 1 G G  g=b+1 D  j=1 p aij | H(g), Ψ(g)_j Mi  m=1 pwim| H(g), Θ(g), Φ(g)  (12) p(i)_waic = G G− 1 1 G G  g=b+1 _D  j=1 log p aij | H(g), Ψ(g)_j 2+ Mi  m=1 log pwim | H(g), Θ(g), Φ(g)2  − 1 G G  g=b+1 _D  j=1 log p aij | H(g), Ψ(g)j + M_i  m=1 log pwim| H(g), Θ(g), Φ(g) 2⎞ ⎠ (13) W AIC =−2 D  i=1

ͨͩ͠ɼp aij | H(g), Ψ(g)j ͱpwim| H(g), Θ(g), Φ(g)͸ɼCGSʹΑΔαϯϓϧͷ͏ͪgճ ໨ͷ܁Γฦ͠ʹ͓͚ΔαϯϓϧͰਪఆͨ͠ύϥϝʔλΛ༻͍ͯܭࢉ͞ΕΔ໬౓Ͱ͋ΓɼҎԼ Ͱఆٛ͞Ε͍ͯΔɽ p aij | H(g), Ψ(g)_j = K  k=1 K  k₌₁

ηik· η_jk(g) · ψjkk(g)I(a ij=1)· (1 − ψjkk)(g)I(aij=0) (15)

pwim | H(g), Θ(g), Φ(g)= K  k=1 L  l=1 η_ik(g)· θ_kl(g)· φ(g)_lwim. (16)