High Dimensional Inference of Graphical Models Using Regularized Score Matching
Advisor: Mathias Drton
Undirected graphical models, also known as Markov random fields, are widely used to model stochastic dependences among large collections of variables. We introduce a new method of estimating sparse undirected conditional independence graphs based on the score matching loss, introduced by HyvÃ¤rinen (2005), and subsequently extended in HyvÃ¤rinen (2007). The regularized score matching method we propose applies to settings with continuous observations and allows for computationally efficient treatment of possibly non-Gaussian exponential family models. In the well-explored Gaussian setting, regularized score matching avoids issues of asymmetry that arise when applying neighborhood selection. In addition, compared to existing methods that directly yield symmetric estimates, the score matching approach has the advantage that the considered loss is quadratic and gives piecewise linear solution paths under l1 regularization. Under suitable irrepresentability conditions, we show that l1-regularized score matching is consistent for graph estimation in high-dimensional settings. Through numerical experiments and an application to RNAseq data, we confirm that regularized score matching achieves state-of-the-art performance in the Gaussian case and provides a valuable, computationally efficient tool for inference in non-Gaussian graphical models.