Latent variable models: from spectral methods to non-convex optimization

Kaizheng Wang, Princeton

Wednesday, January 22, 2020 - 3:30pm

Latent variable models lay the statistical foundation for data science problems with unstructured, incomplete and heterogeneous information. For the sake of computational efficiency, heuristic algorithms are proposed to extract the latent low-dimensional structures for downstream tasks. Despite their huge success in practice, theoretical understanding is lagging far behind and that hinders further advancement. In this talk, I will first present an $\ell_p$ theory of eigenvector analysis that yields optimal recovery guarantees for spectral methods in many challenging problems. Then I will discuss a more general framework for clustering based on non-convex optimization and provide its theoretical guarantees under statistical models. The results find applications in dimensionality reduction, mixture models, network analysis, recommendation systems, ranking and beyond.

Seminars generally take place in 116 Old Chemistry Building on Fridays from 3:30 - 4:30 pm. For additional information contact: karen.whitesell@duke.edu or phone 919-684-8029. Sorry, but we do not have reprints available. Please feel free to contact the authors by email for follow-up information, articles, etc. Reception following seminar in 203B Old Chemistry.

Old Chemistry 116

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