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Abstract:
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We discuss a variety of results concerning structure estimation for graphical models. Our results are motivated by well-known theory for Gaussian graphical models; however, a key insight is that methods such as the graphical Lasso and nodewise linear regression may be statistically consistent for edge recovery even when data are non-Gaussian. In the first part of the talk, we outline theoretical results relating the support of generalized inverse covariance matrices to the edge structure of undirected graphs for discrete-valued variables, and also discuss the significance of the inverse covariance matrix in the case of linear structural equation models. In the second part of the talk, we turn our attention to settings where data are missing, contaminated, or systematically corrupted. We show how the graphical Lasso may be adjusted to yield statistically consistent estimators even when data possess some form of systematic corruption, and also discuss theoretical guarantees for a robust version of the graphical Lasso when data are subject to cellwise contamination.
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