TITLE: Blind Regression, Recommendation System and Collaborative Filtering

ABSTRACT:

We discuss the framework of Blind Regression (also known as Latent Variable Model) motivated by the problem of Matrix Completion for recommendation systems: given n users and m movies, the goal is to predict the unknown rating of a user for a movie using known observations, i.e. completing the partially observed matrix. We posit that each user and movie is associated with latent features, and the rating of a user for a movie equals the noisy version of latent function applied to the associated latent features. The goal is to predict such a function value for user-movie pairs for which ratings are unknown, just like the classical regression setting. However, unlike the setting of regression, features are not observed here — hence the term Blind Regression. Such a model arises as a canonical characterization due to multi-dimensional exchangeability property a la Aldous and Hoover (early 1980s). 

In this talk, using inspiration from the classical Taylor’s expansion for differentiable functions, we shall propose a prediction algorithm that is consistent for all Lipschitz continuous functions. We provide finite sample analysis that suggests that even when observing a vanishing fraction of the matrix, the algorithm produces accurate predictions. We discuss relationship with spectral algorithm for matrix completion, and the collaborative filtering. 

The talk is based on joint works with Christina Lee, Yihua Li and Dogyoon Song (MIT).

BIO: 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 Social Data Processing. His work has been recognized through prize paper awards in Machine Learning, Operations Research and Computer Science, as well as 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.