Skip to content
AI Atlas
PaperActive

Generalized Score Matching for Parameter Estimation on Convex Domains

arxiv.org/abs/2609.11521

Explore graph
quality89

Updated 2 h ago · first seen 11 Sept 2026

paper_01M294FP85HVY83VTQ0KB3PAH2

Published
11 Sept 2026
T1 · 2 h ago
arXiv
2609.11521
T1 · 2 h ago
Category
cs.LG
T1 · 2 h ago

As of

Rewind the record: see this entity's attributes exactly as AI Atlas knew them on a given day.

Claim history · Abstract

1 claims · 1 propertiesShow all properties

Abstractabstract1

Claim history for Abstract
ValueValid from → toStatusSourceConfidenceExtractor
Maximum likelihood (ML) estimation is a principled and statistically efficient approach for learning probabilistic models. However, for unnormalized models, ML estimation requires evaluating the partition function and differentiating through it, which may not always be tractable. Score matching provides a practically viable alternative that circumvents this obstacle by fitting the score in a way that eliminates dependence on the normalizing constant. We derive the generalized score matching objective on a convex subset of $\mathbb{R}^{d}$ constructively starting from Minimum Probability Flow (MPF) learning, and show how classical score matching as well as domain-adapted variants for non-negative data arise naturally within the proposed framework. We show that the resulting objective is a {\it proper local scoring rule} of second-order, which provides the theoretical guarantee that the true density is recovered when the objective is minimized. Furthermore, for a model belonging to the exponential family, we establish convexity of the objective together with consistency of the finite-sample estimator under standard regularity conditions. Our derivation sheds new light on the scope and applicability of generalized score matching in various problem settings. We compare generalized score matching-based estimators on constrained domains, where the partition function is analytically intractable. We provide experimental results on parameter estimation for model densities belonging to the exponential family defined over convex subsets of $\mathbb{R}^{d}$, and a generative modeling use-case to demonstrate broader applicability of the proposed generalized score matching framework. → currentcurrentarXiv (Atom API + RSS)T1highdeterministic

Claims are temporal and append-only: a new observation closes the previous claim (valid_to) instead of overwriting it. Conflicting claims from different sources are kept side by side and flagged — never averaged. Methodology →