# Generalized Score Matching for General Domains

arXiv: https://arxiv.org/abs/2009.11428 · HTML: https://mlsanity.com/paper/2009.11428/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Sep 2020.

## Built on by (most cited first, 13 of 13)

- [Reflected Diffusion Models](https://mlsanity.com/paper/2304.04740/) (2023)
- [Robust and Scalable Bayesian Online Changepoint Detection](https://mlsanity.com/paper/2302.04759/) (2023)
- [Robust and Conjugate Gaussian Process Regression](https://mlsanity.com/paper/2311.00463/) (2023)
- [Score Matching With Missing Data](https://mlsanity.com/paper/2506.00557/) (2025)
- [SMURF-THP: Score Matching-based UnceRtainty quantiFication for Transformer Hawkes Process](https://mlsanity.com/paper/2310.16336/) (2023)
- [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)
- [High-Dimensional Differential Parameter Inference in Exponential Family using Time Score Matching](https://mlsanity.com/paper/2410.10637/) (2024)
- [Learned Bayesian Cram'er-Rao Bound for Unknown Measurement Models Using Score Neural Networks](https://mlsanity.com/paper/2502.00724/) (2025)
- [Approximate Stein Classes for Truncated Density Estimation](https://mlsanity.com/paper/2306.00602/) (2023)
- [Score Matching-based Pseudolikelihood Estimation of Neural Marked Spatio-Temporal Point Process with Uncertainty Quantification](https://mlsanity.com/paper/2310.16310/) (2023)
- [Interaction Models and Generalized Score Matching for Compositional Data](https://mlsanity.com/paper/2109.04671/) (2021)
- [Should the Boundary Term Be Learned in Reflected Diffusion? Conormal Trace and Reflection Masking](https://mlsanity.com/paper/2608.03469/) (2026)

## Abstract (arXiv)

Estimation of density functions supported on general domains arises when the data is naturally restricted to a proper subset of the real space. This problem is complicated by typically intractable normalizing constants. Score matching provides a powerful tool for estimating densities with such intractable normalizing constants, but as originally proposed is limited to densities on ℝm and ℝ_+m. In this paper, we offer a natural generalization of score matching that accommodates densities supported on a very general class of domains. We apply the framework to truncated graphical and pairwise interaction models, and provide theoretical guarantees for the resulting estimators. We also generalize a recently proposed method from bounded to unbounded domains, and empirically demonstrate the advantages of our method.