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Latent Variable Model, Matrix Estimation and Collaborative Filtering

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Estimating a matrix based on partial, noisy observations is prevalent in 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 estimationfor a generic latent variable model with near optimal sample complexity.

The talk is based on joint works with (a) Christina Lee (MSR), Yihua Li (MS) and Dogyoon Song (MIT), and (b) Christina Borgs (MSR), Jennifer Chayes (MSR) and Christina Lee (MIT).

This talk is part of the Computer Laboratory Wednesday Seminars series.

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