Graphical Models for NonNegative Data Using Generalized Score Matching
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Proceedings of the TwentyFirst International Conference on Artificial Intelligence and Statistics, PMLR 84:17811790, 2018.
Abstract
A common challenge in estimating parameters of probability density functions is the intractability of the normalizing constant. While in such cases maximum likelihood estimation may be implemented using numerical integration, the approach becomes computationally intensive. In contrast, the score matching method of Hyvärinen (2005) avoids direct calculation of the normalizing constant and yields closedform estimates for exponential families of continuous distributions over $\mathbb{R}^m$. Hyvärinen (2007) extended the approach to distributions supported on the nonnegative orthant $\mathbb{R}_+^m$. In this paper, we give a generalized form of score matching for nonnegative data that improves estimation efficiency. We also generalize the regularized score matching method of Lin et al. (2016) for nonnegative Gaussian graphical models, with improved theoretical guarantees.
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