Recsysษڧձ2015 [4b-1] Dynamic Poisson Factorization ! L. Charlin, R. Ranganath, J. Mclnerney, D. M. Blei ٠ాངฏ diracdiego@gmail.com https://www.facebook.com/yohei.kikuta.3
 2015/10/17

ݚڀͷഎܠͱ࣮ࢪࣄ߲ [4b-1] ٠ాངฏ 2/6 ʲഎܠʳ ɾજࡏม਺Λ༻͍ΔϨίϝϯυϞσϧ͸੩తΛԾఆ ɾݱ࣮ੈք͸ಈత ɹɹ−ݚڀऀͷڵຯ͸൒೥΋͋Ε͹มΘΔ(ຊจΑΓҾ༻) ɾϨίϝϯυ΋࣌ؒൃల͢΂͖ʂ ! ʲ࣮ࢪࣄ߲ʳ ɾϢʔβͱΞΠςϜΛΨ΢εϚϧίϑաఔͰ࣌ؒൃల ɾϨʔςΟϯά͸ϙΞιϯ෼෍Ͱදݱ ɹɹ−ϢʔβͱΞΠςϜΛexponentiateͨ͠΋ͷ͕Ҿ਺ ɾELBOΛL-BFGSͰoptimize͢Δ͜ͱͰਪఆ


Ϟσϧͷεέον [4b-1] ٠ాངฏ 3/6 u0 u1 uT vT v1 v0 y0 y1 yT ¯ u ¯ v unk,t |unk,t 1 ⇠ N ( unk,t 1 , 2 u) | ⇠ N vmk,t |vmk,t 1 ⇠ N ( vmk,t 1 , 2 v) ynm,t ⇠ Poisson ( P K k =1 e( unk,t+¯ unk)e( vmk,t+¯ vmk) ) · · · · · · µu, u µ¯ u, ¯ u µ¯ v, ¯ v µv, v global factor global factor

Item 4663: “The Google Similarity Distance” 2005 2006 2007 2008 2009 2010 2011 2012 Access frequency 1.0 1.5 2.0 2.5 3.0 3.5 User 755 2005 2006 2007 2008 2009 2010 2011 2012 Click frequency 2 3 4 5 6 7 8 9 ݁Ռ [4b-1] ٠ాངฏ 4/6 ਤ͸ݪ࿦จΑΓҾ༻ ͋ΔϢʔβͷ raw click data ͋ΔΞΠςϜ΁ͷ raw access frequency 2005 2006 2007 2008 2009 2010 2011 2012 Factor expression 2005 2006 2007 2008 2009 2010 2011 2012 Factor expression dynamic Poisson FactorizationʹΑΔ෼ղ ͜ͷϢʔβͷؔ৺෼໺ ͜ͷΞΠςϜͷඃӾཡ෼໺ જࡏม਺ͷ࣌ؒൃల σʔληοτ arXiv.org users clicking on computer science articles

݁Ռ2 [4b-1] ٠ాངฏ 5/6 Recall@50 MAR MRR NDCG dPF 0.035 21822 0.0062 0.186 PF-all [6] 0.032 22402 0.0056 0.182 PF-last [6] 0.023 25616 0.0040 0.168 Table 3: Performance of dPF versus baselines on arXiv. Bold num- bers indicate the top performance for each metric. [ Figure 2: dPF performs well across a large range of variances (2– 50) by MRR in a pilot study of a single timestep of the arXiv data. Computational Complexity Machine Learning & Information Theory Quantum Computing Community Detection Monte Carlo & Simulation Probability & Statistics for Graphs Computational Geometry Information Theory Mathematical Statistics Computability Classes Physics & Society Quantum Information Theory Quantum Logic Quantum Algorithms General Interest CS Graph Theory Information Theory Message Passing Algorithms Condensed Matter & Computing Network Analysis 04/05 10/05 04/06 04/07 04/08 04/09 04/10 04/11 03/12 10/06 10/07 10/08 10/09 10/10 10/11 0.0 0.2 0.4 0.6 0.8 1.0 Figure 3: Evolution of latent factors, corresponding to research ar- eas, as discovered by dPF from the raw click data. We see that network analysis has been a growing area of research in computer science over the past decade. Table Bold dPF d PF-a erenc 3.5 Ther we h to ex can b date arXiv In tors u from mode ϨʔςΟϯάਫ਼౓΋޲্ ࣌ؒ৘ใͷॏཁੑΛࣔࠦ ਤද͸ݪ࿦จΑΓҾ༻ arXiv-cs-statsʹ͓͚Δ20ݸͷજࡏม਺ͷ࣌ؒൃల ݚڀ෼໺͸੒ख़͍ͯͯ͠େมಈ͸ͳ͍͕NetworkͳͲ͸৳ு

ϨϏϡʔ [4b-1] ٠ాངฏ 6/6 ʲ৽نੑɾಠ૑ੑʳ4఺/5఺ ɾϢʔβͱΞΠςϜ͕࣌ؒൃల͢ΔॳΊͯͷϞσϧ ɹɹ−ݸผͷൃలΛ௥੻Ͱ͖Δ఺ͷ৽نੑ͕ߴ͍ ɾ࣌ؒൃలΛѻ͏ࡍʹੜ͡ΔෆఆੑΛѻ͏֬཰తϑϨʔϜ ɹϫʔΫΛద੾ʹߏங ! ʲ༗ޮੑɾॏཁੑʳ4఺/5఺ ɾϨίϝϯυʹ͓͚Δ࣌ؒґଘੑͷॏཁੑΛڧࣔࠦ͘ ɾࠓޙͷൃలՄೳੑ͕޿ൣ ɹɹ−࿈ଓ࣌ؒ΁ͷ֦ு΍ҟͳΔ࣌ܥྻϞσϧͷద༻ͳͲ