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

Area of Science:

• Machine Learning
• Statistical Modeling
• Computational Statistics

Background:

• Discrete Markov Random Fields (MRFs) present computational challenges for learning due to NP-hard inference.
• Efficient learning necessitates sparse regularization and approximate inference techniques.
• Existing methods often struggle with the exact gradient evaluation required for maximum likelihood estimation.

Purpose of the Study:

• To develop and analyze a stochastic learning framework for L1-regularized maximum likelihood estimation in discrete MRFs.
• To provide theoretical guarantees for the quality of gradient approximations used in learning.
• To introduce an empirically effective learning strategy for improving model performance.

Main Methods:

• Utilizing a stochastic proximal gradient (SPG) algorithm, an inexact proximal gradient method.
• Employing Gibbs sampling as a stochastic oracle for approximating gradients.
• Developing verifiable bounds to quantify and control gradient approximation error.
• Proposing the tighten asymptotically (TAY) learning strategy.

Main Results:

• Novel verifiable bounds for gradient approximation quality in SPG were established.
• The proposed TAY learning strategy demonstrated improved performance of SPG.
• The framework addresses the challenges of sparse regularization and approximate inference in MRF learning.

Conclusions:

• The stochastic learning framework provides a scalable approach for discrete MRFs.
• Verifiable bounds offer crucial insights into controlling approximation errors.
• The TAY strategy enhances the practical utility of SPG for MRF learning.