Graphical models are widely used to model stochastic dependences among largecollections of variables. We introduce a new method of estimating undirectedconditional independence graphs based on the score matching loss, introduced byHyvarinen (2005), and subsequently extended in Hyvarinen (2007). Theregularized score matching method we propose applies to settings withcontinuous observations and allows for computationally efficient treatment ofpossibly non-Gaussian exponential family models. In the well-explored Gaussiansetting, regularized score matching avoids issues of asymmetry that arise whenapplying the technique of neighborhood selection, and compared to existingmethods that directly yield symmetric estimates, the score matching approachhas the advantage that the considered loss is quadratic and gives piecewiselinear solution paths under $\ell_1$ regularization. Under suitableirrepresentability conditions, we show that $\ell_1$-regularized score matchingis consistent for graph estimation in sparse high-dimensional settings. Throughnumerical experiments and an application to RNAseq data, we confirm thatregularized score matching achieves state-of-the-art performance in theGaussian case and provides a valuable tool for computationally efficientestimation in non-Gaussian graphical models.
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