# Graphical Models for Non-Negative Data Using Generalized Score Matching

arXiv: https://arxiv.org/abs/1802.06340 · HTML: https://mlsanity.com/paper/1802.06340/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Feb 2018.

## Built on by (most cited first, 6 of 6)

- [Robust and Scalable Bayesian Online Changepoint Detection](https://mlsanity.com/paper/2302.04759/) (2023)
- [Score Matching With Missing Data](https://mlsanity.com/paper/2506.00557/) (2025)
- [Standardisation-function Kernel Stein Discrepancy: A Unifying View on Kernel Stein Discrepancy Tests for Goodness-of-fit](https://mlsanity.com/paper/2106.12105/) (2021)
- [Score Matching for Truncated Density Estimation on a Manifold](https://mlsanity.com/paper/2206.14668/) (2022)
- [Denoising Score Matching with Random Fourier Features](https://mlsanity.com/paper/2101.05239/) (2021)
- [Interaction Models and Generalized Score Matching for Compositional Data](https://mlsanity.com/paper/2109.04671/) (2021)

## Abstract (arXiv)

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 Hyv"arinen (2005) avoids direct calculation of the normalizing constant and yields closed-form estimates for exponential families of continuous distributions over ℝm. Hyv"arinen (2007) extended the approach to distributions supported on the non-negative orthant 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.