Dynamic Poisson Factorization
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1 Dynamic Poisson Factorization Laurent Charlin Joint work with: Rajesh Ranganath, James McInerney, David M. Blei McGill & Columbia University Presented at RecSys 2015
2 2
3 Click Data for a paper 3.5 Item 4663: The Google Similarity Distance Access frequency The Google Similarity effect arxiv: cs/ Year
4 arxiv evolves over time Click data evolves over time Popularity of papers change over time Users interests change over time The same is also true of other datasets 4
5 Recommendations should evolve over time
6 3.5 Raw Data Item 4663: The Google Similarity Distance Modeled Data (e.g., Matrix Factorization) 0.14 Access frequency The Google Similarity effect arxiv: cs/ DDtD 6tructures GrDSh Theory ComSresseG 6eQsiQg 4uDQtum CryStogrDShy
7 3.5 Raw Data Item 4663: The Google Similarity Distance Modeled Data (e.g., Matrix Factorization) 0.14 Access frequency The Google Similarity effect arxiv: cs/ DDtD 6tructures GrDSh Theory ComSresseG 6eQsiQg 4uDQtum CryStogrDShy Time-aware Modeled Data Factor expression
8 Objectives Understand click data over time Better predictions of future user interests Explore how (large) datasets evolve over time Motivated by the arxiv Study other datasets 7
9 Technical approach Dynamic model of user preferences Poisson matrix factorization [Gopalan et al. UAI 15] User and item latent factors evolve over time Develop inference procedure Fit this model using data Explore fits 8
10 Data (e.g., clicks) Recommendations Generative Model a, b u y M Learning & Inference Exploration (latent factors) c, d v N Factor expression
11 Background 10
12 Gaussian Matrix Factorization [Salakhutdinov et al. 15] a, b u y M c, d v N [wikipedia] 11
![15] a, b u Poisson Matrix](/docs-images/88/116355982/images/13-2.jpg "Factorization (PF) [Gopalan et al.")
13 Gaussian Matrix Factorization [Salakhutdinov et al. 15] a, b u Poisson Matrix Factorization (PF) [Gopalan et al. 15] y M c, d v N [wikipedia] 11 [wikipedia]
14 Properties of PF Suitable for implicit and explicit data Model can be fit to massive datasets 12
15 9 User Click frequency
16 Dynamic Poisson factorization 14
17 Users preferences evolve over time Item popularity evolves over time Ratings are not exchangeable over time 15
18 Dynamic Matrix Factorization (DPF) 16
19 Dynamic Matrix Factorization (DPF) y 0 y 1... y T 16
20 Dynamic Matrix Factorization (DPF) u 0 u 1... u T y 0 y 1... y T M v 0 v 1... v T N 16
21 Dynamic Matrix Factorization (DPF) a, b u 0 u 1... u T y 0 y 1... y T M c, d v 0 v 1... v T N Modeling: Smooth evolution through time 16
22 Smooth Evolution through time Gaussian time series model Exponentiate to obtain positive Poisson rates 17
23 Local and Global factors Two levels of modeling: Local factors: model evolution through time Global factors: model constant preferences wrt time µū, ū ū µ u, u u 0 u 1... u T y 0 y 1... y T M µ v, v v 0 v 1... v T v N µ v, v 18
24 Local and Global factors Two levels of modeling: Local factors: model evolution through time Global factors: model constant preferences wrt time µū, ū ū µ u, u u 0 u 1... u T y 0 y 1... y T M µ v, v v 0 v 1... v T v N µ v, v 18
25 Local and Global factors Two levels of modeling: Local factors: model evolution through time Global factors: model constant preferences wrt time µū, ū ū µ u, u u 0 u 1... u T y 0 y 1... y T M µ v, v v 0 v 1... v T v N µ v, v 18
26 A 3 timeslice Dynamic PF µū, ū ū µ u, u u 0 u 1 u 2 y 0 y 1 y 2 M µ v, v v 0 v 1 v 2 v N µ v, v
27 Inference Variational inference algorithm Mean-field (factorized) approximation Non-conjugacy between and Use an additional approximation See the paper for details on the algorithm Scales linearly in time, we provide a parallel implementation 20
28 Empirical results 21
29 Explicit data Augmented matrix factorization [Koren 10, Li 11, Gultekin 14] Tensor factorization [Karatzoglou 10] Bayesian Tensor Probabilistic Factorization [Xiong 10] Implicit data HMM [Sahoo 12] Gamma process MF [Acharya 15] DPF (us): User and item dynamicity Implicit and explicit Scalable 22
30 Experimental setup Test on multiple time steps Train data: clicks up to time slice t Predict held-out clicks at time t+1 Metrics for implicit data Ranking-based (NDCG, Recall, MAR, MRR) 23
31 Netflix-time MAR MRR NDCG dpf BPTF [Xiong 10] PF-all [Gopalan 15] PF-last [Gopalan 15] K users, 3.6K items, 2M non-zero ratings, binarized 3 months per time slice 24
32 Netflix MAR MRR NDCG dpf PF-all [Gopalan 15] PF-last [Gopalan 15] K users, 14K items, 6.9M non-zero ratings, binarized 6 months per time slice 25
33 arxiv MAR MRR NDCG dpf PF-all [Gopalan 15] PF-last [Gopalan 15] K users, 5K items, 1.3M clicks 18 months per time slice 26
34 Usage Data DPF Factors 3.5 The Google Similarity effect arxiv: cs/ Item 4663: The Google Similarity Distance Factor expression 3.0 Access frequency GOobDO fdctor exsressioq DPF Global Factors GrDSh Theory 4uDQtuP & &ops. &opsoexity DDtD 6tructures & ProbDbiOity GeQerDO 0Dth 2StiPizDtioQ
35 Paper Selected at Random FaFtor expression
36 FaFtor expression
37 FaFtor expression he entrrpy frrmuld frr the 5icci flrw Dnd its germetric DpplicDtiRns (mdth/ ) 6 5 Access fretuency DDte
38 FaFtor expression he entrrpy frrmuld frr the 5icci flrw Dnd its germetric DpplicDtiRns (mdth/ ) 6 5 Access fretuency DDte
39 FaFtor expression Perelman 6 declines the 5 Fields Medal Access fretuency 4 3 7he entrrpy frrmuld frr the 5icci flrw Dnd its germetric DpplicDtiRns (mdth/ ) DDte
40 FaFtor expression Perelman 6 declines the 5 Fields Medal Access fretuency 4 3 7he entrrpy frrmuld frr the 5icci flrw Dnd its germetric DpplicDtiRns (mdth/ ) Perelman rejects the Millenium Prize DDte
41 Usage Data DPF Factors 9 User Click frequency Factor expression
42 Fields evolve over time Computability Classes Physics & Society Quantum Information Theory Quantum Logic Quantum Algorithms General Interest CS Graph Theory Information Theory Message Passing Algorithms Mathematical Statistics Information Theory Computational Geometry Probability & Statistics for Graphs Monte Carlo & Simulation Community Detection Quantum Computing Machine Learning & Information Theory Computational Complexity Condensed Matter & Computing Network Analysis 04/05 10/05 04/06 10/06 04/07 10/07 04/08 10/08 04/09 10/09 04/10 10/10 04/11 10/11 03/12 31
43 Fields evolve over time Computability Classes Physics & Society Quantum Information Theory Quantum Logic Quantum Algorithms General Interest CS Graph Theory Information Theory Message Passing Algorithms Mathematical Statistics Information Theory Computational Geometry Probability & Statistics for Graphs Monte Carlo & Simulation Community Detection Quantum Computing Machine Learning & Information Theory Computational Complexity Condensed Matter & Computing Network Analysis 04/05 10/05 04/06 10/06 04/07 10/07 04/08 10/08 04/09 10/09 04/10 10/10 04/11 10/11 03/12 31
44 Conclusions Dynamic Poisson factorization (DPF) 9 User Click frequency Factor expression Implicit data, scalable Open source implementation is available: github.com/blei-lab/ Future work: levels of granularities, continuous time 32
45 Thank you! Dynamic Poisson factorization (DPF) 9 User Click frequency Factor expression Implicit data, scalable Open source implementation is available: github.com/blei-lab/ Future work: levels of granularities, continuous time 32
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