Abstract:
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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 Hyvarinen. Our regularized score matching method avoids issues of asymmetry that arise when applying the technique of neighbourhood selection. Compared to existing methods that directly yield symmetric graph estimates, our approach has the advantage that the considered loss is quadratic and gives piecewise linear solution paths under l1 regularization. These properties hold generally for exponential family models comprising continuous distributions. Focusing on the Gaussian setting in this paper, we confirm through numerical experiments that the performance of regularized score matching is state-of-the-art, compared with existing methods. We further show that, under suitable irrepresentability conditions, regularized score matching is able to recover a true sparse conditional independence graph with high probability even in high dimensions.
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