Algebraic Structure in Hidden Variable Models

Elina Robeva, MIT - Massachusetts Institute of Technology

Wednesday, February 13, 2019 - 3:30pm

Hidden variable models are ubiquitous tools in modern data science. This talk explores some of the rich, diverse mathematical structure arising in discrete and continuous settings. The first part of the talk focuses on the discrete setting, where the joint distribution of d random variables can be described by an order d tensor. The rank of this tensor is related to the dependence between the random variables, and the decomposition contains information about the latent parameters. We will see that one way a low rank tensor can be decomposed is via orthogonal tensor decomposition. We show that orthogonally decomposable tensors retain many of the nice properties of matrices. In particular, we describe all of their eigenvectors, and we give a characterization via quadratic equations of the set of all orthogonally decomposable tensors.

In the second part of the talk, we turn our attention to directed Gaussian graphical models with hidden variables. We give a necessary combinatorial criterion which characterizes the model corresponding to a given graph, and we show that this criterion is also sufficient for a specific family of graphs, which includes the set of ancestral graphs.

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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