# Score Matching for Truncated Density Estimation on a Manifold

arXiv: https://arxiv.org/abs/2206.14668 · HTML: https://mlsanity.com/paper/2206.14668/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 31 references that are in the map.
- First posted on arXiv 29 Jun 2022.

## Builds on (most cited first, 6 of 6)

- [A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluation](https://mlsanity.com/paper/1602.03253/) (2016)
- [A Kernel Test of Goodness of Fit](https://mlsanity.com/paper/1602.02964/) (2016)
- [Estimation of High-Dimensional Graphical Models Using Regularized Score Matching](https://mlsanity.com/paper/1507.00433/) (2015)
- [Estimating Density Models with Truncation Boundaries using Score Matching](https://mlsanity.com/paper/1910.03834/) (2019)
- [Generalized Score Matching for General Domains](https://mlsanity.com/paper/2009.11428/) (2020)
- [Graphical Models for Non-Negative Data Using Generalized Score Matching](https://mlsanity.com/paper/1802.06340/) (2018)

## Built on by (most cited first, 2 of 2)

- [High-Dimensional Differential Parameter Inference in Exponential Family using Time Score Matching](https://mlsanity.com/paper/2410.10637/) (2024)
- [Approximate Stein Classes for Truncated Density Estimation](https://mlsanity.com/paper/2306.00602/) (2023)

## Abstract (arXiv)

When observations are truncated, we are limited to an incomplete picture of our dataset. Recent methods propose to use score matching for truncated density estimation, where the access to the intractable normalising constant is not required. We present a novel extension of truncated score matching to a Riemannian manifold with boundary. Applications are presented for the von Mises-Fisher and Kent distributions on a two dimensional sphere in ℝ3, as well as a real-world application of extreme storm observations in the USA. In simulated data experiments, our score matching estimator is able to approximate the true parameter values with a low estimation error and shows improvements over a naive maximum likelihood estimator.