Latent Variable Model, Matrix Estimation and Collaborative Filtering
Estimating a matrix based on partial, noisy observations is prevalent in a variety of modern applications with recommendation system being a prototypical example. The non-parametric latent variable model provides canonical representation for such matrix data when the underlying distribution satisfies “exchangeability” with graphons and stochastic block model being recent examples of interest. Collaborative filtering has been a successfully utilized heuristic in practice since the dawn of e-commerce. In this talk, I will argue that collaborative filtering (and its variants) solve matrix estimation for a generic latent variable model with near optimal sample complexity.
The talk is based on joint works with
- Christina Lee (MSR), Yihua Li (MS) and Dogyoon Song (MIT)
- Christina Borgs (MSR), Jennifer Chayes (MSR) and Christina Lee (MIT)
Devavrat Shah is a Professor with the department of Electrical Engineering and Computer Science at Massachusetts Institute of Technology. His current research interests are at the interface of Statistical Inference and Stochastic Networks. His work has been recognized through career prizes including 2010 Erlang prize from the INFORMS Applied Probability Society and 2008 ACM Sigmetrics Rising Star Award. He is a distinguished young alumni of his alma mater IIT Bombay.