Generalized Score Matching for Non-Negative Data

• Activity Number: 627 - Advances in Stochastics and Distribution Theory
• Type: Contributed
• Date/Time: Thursday, August 2, 2018 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Shiqing Yu* and Mathias Drton and Ali Shojaie
• Companies: University of Washington and University of Washington and University of Washington
• Keywords: Graphical model; Exponential family ; Score matching; Positive data; Sparsity

Abstract

A common challenge in estimating parameters of probability density functions from data is the intractability of the normalizing constant. This happens when the proposed density is only known up to a multiplicative constant that does not have a closed form. While in such cases maximum likelihood estimation may be implemented using techniques from numerical integration, the approach becomes very computationally intensive. In contrast, the score matching proposal of Hyv\"arinen (2005) avoids direct calculation of the normalizing constant and yields closed-form estimates for exponential families of continuous distributions over R^m. Hyv\"arinen (2007) extended the approach to distributions supported on the nonnegative orthant R_+^m. In this work, we give a generalized form of score matching for non-negative data that improves estimation efficiency. We also generalize the regularized score matching method introduced in Lin et al (2016) for non-negative Gaussian graphical models, with improved theoretical guarantees.