Graphical Models for Non-Negative Data Using Generalized Score Matching

Shiqing Yu, Mathias Drton, Ali Shojaie
Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, PMLR 84:1781-1790, 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 closed-form estimates for exponential families of continuous distributions over $\mathbb{R}^m$. Hyvärinen (2007) extended the approach to distributions supported on the non-negative orthant $\mathbb{R}_+^m$. In this paper, we give a generalized form of score matching for non-negative data that improves estimation efficiency. We also generalize the regularized score matching method of Lin et al. (2016) for non-negative Gaussian graphical models, with improved theoretical guarantees.

Cite this Paper


BibTeX
@InProceedings{pmlr-v84-yu18b, title = {Graphical Models for Non-Negative Data Using Generalized Score Matching}, author = {Shiqing Yu and Mathias Drton and Ali Shojaie}, booktitle = {Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics}, pages = {1781--1790}, year = {2018}, editor = {Amos Storkey and Fernando Perez-Cruz}, volume = {84}, series = {Proceedings of Machine Learning Research}, month = {09--11 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v84/yu18b/yu18b.pdf}, url = { http://proceedings.mlr.press/v84/yu18b.html }, 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 closed-form estimates for exponential families of continuous distributions over $\mathbb{R}^m$. Hyvärinen (2007) extended the approach to distributions supported on the non-negative orthant $\mathbb{R}_+^m$. In this paper, we give a generalized form of score matching for non-negative data that improves estimation efficiency. We also generalize the regularized score matching method of Lin et al. (2016) for non-negative Gaussian graphical models, with improved theoretical guarantees.} }
Endnote
%0 Conference Paper %T Graphical Models for Non-Negative Data Using Generalized Score Matching %A Shiqing Yu %A Mathias Drton %A Ali Shojaie %B Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2018 %E Amos Storkey %E Fernando Perez-Cruz %F pmlr-v84-yu18b %I PMLR %P 1781--1790 %U http://proceedings.mlr.press/v84/yu18b.html %V 84 %X 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 closed-form estimates for exponential families of continuous distributions over $\mathbb{R}^m$. Hyvärinen (2007) extended the approach to distributions supported on the non-negative orthant $\mathbb{R}_+^m$. In this paper, we give a generalized form of score matching for non-negative data that improves estimation efficiency. We also generalize the regularized score matching method of Lin et al. (2016) for non-negative Gaussian graphical models, with improved theoretical guarantees.
APA
Yu, S., Drton, M. & Shojaie, A.. (2018). Graphical Models for Non-Negative Data Using Generalized Score Matching. Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 84:1781-1790 Available from http://proceedings.mlr.press/v84/yu18b.html .

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