Poisson Matrix Factorization Task

See: Gaussian Matrix Factorization, Collective Bayesian Poisson Factorization.

References

http://www.hongliangjie.com/2015/08/17/poisson-matrix-factorization/
- QUOTE: Recently, Prem Gopalan et al. [3, 4, 5, 6] have proposed a new model called Poisson Factorization (PF) to address these two issues. The central idea is to replace Gaussian assumption with Poisson distribution: [math]\displaystyle{ X_{i,j} ∼ Poisson(θ^T_iϕ_j)(5) }[/math] where θ_i and ϕ_j are drawn from user specific and item specific Gamma distributions.

(Gopalan et al., 2013) ⇒ Prem Gopalan, Jake M. Hofman, and David M. Blei. (2013). “Scalable Recommendation with Poisson Factorization." arXiv preprint arXiv:1311.1704.
- ABSTRACT: We develop a Bayesian Poisson matrix factorization model for forming recommendations from sparse user behavior data. These data are large user/item matrices where each user has provided feedback on only a small subset of items, either explicitly (e.g., through star ratings) or implicitly (e.g., through views or purchases). In contrast to traditional matrix factorization approaches, Poisson factorization implicitly models each user's limited attention to consume items. Moreover, because of the mathematical form of the Poisson likelihood, the model needs only to explicitly consider the observed entries in the matrix, leading to both scalable computation and good predictive performance. We develop a variational inference algorithm for approximate posterior inference that scales up to massive data sets. This is an efficient algorithm that iterates over the observed entries and adjusts an approximate posterior over the user/item representations. We apply our method to large real-world user data containing users rating movies, users listening to songs, and users reading scientific papers. In all these settings, Bayesian Poisson factorization outperforms state-of-the-art matrix factorization methods.