Stochastic Learning for Sparse Discrete Markov Random Fields with Controlled Gradient Approximation Error

• URL: http://arxiv.org/abs/2005.06083v1
• Date: Tue, 12 May 2020 22:48:42 GMT
• Title: Stochastic Learning for Sparse Discrete Markov Random Fields with Controlled Gradient Approximation Error
• Authors: Sinong Geng, Zhaobin Kuang, Jie Liu, Stephen Wright, David Page
• Abstract summary: We study the $L_$-regularized maximum likelihood estimator/estimation (MLE) problem for discrete Markov random fields (MRFs) To address these challenges, we consider a verifiable learning framework called proximal gradient (SPG) We provide novel verifiable bounds to inspect and control the quality of the gradient approximation.
• Score: 10.381976180143328
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the $L_1$-regularized maximum likelihood estimator/estimation (MLE) problem for discrete Markov random fields (MRFs), where efficient and scalable learning requires both sparse regularization and approximate inference. To address these challenges, we consider a stochastic learning framework called stochastic proximal gradient (SPG; Honorio 2012a, Atchade et al. 2014,Miasojedow and Rejchel 2016). SPG is an inexact proximal gradient algorithm [Schmidtet al., 2011], whose inexactness stems from the stochastic oracle (Gibbs sampling) for gradient approximation - exact gradient evaluation is infeasible in general due to the NP-hard inference problem for discrete MRFs [Koller and Friedman, 2009]. Theoretically, we provide novel verifiable bounds to inspect and control the quality of gradient approximation. Empirically, we propose the tighten asymptotically (TAY) learning strategy based on the verifiable bounds to boost the performance of SPG.

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