Generalized Score Matching for Parameter Estimation on Convex Domains

• URL: http://arxiv.org/abs/2609.11521v1
• Date: Thu, 10 Sep 2026 13:23:41 GMT
• Title: Generalized Score Matching for Parameter Estimation on Convex Domains
• Abstract summary: We derive the generalized score matching objective on a convex subset of $mathbbRd$.<n>We show how classical score matching as well as domain-adapted variants for non-negative data arise naturally within the proposed framework.<n>Our derivation sheds new light on the scope and applicability of generalized score matching in various problem settings.
• Score: 13.954816561132942
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

Related papers

• Tailoring Strictly Proper Scoring Rules for Downstream Tasks: An Application to Causal Inference [48.78219918881965]
  We propose a principled framework for deriving task-specific strictly proper scoring rules by matching the local curvature of the downstream error metric.<n>We apply this to the Average Treatment Effect (ATE) estimation, deriving a closed-form loss and its corresponding canonical probability mapping.
  arXiv  Detail & Related papers  (2026-06-02T08:41:25Z)
• Score Matching for Estimating Finite Point Processes [11.422667985375469]
  We develop a formal framework for score matching on finite point processes via Janossy measures.<n>We introduce an (autoregressive) weighted score-matching estimator, whose statistical properties we analyze in classical parametric settings.
  arXiv  Detail & Related papers  (2025-12-04T09:46:48Z)
• On diffusion-based generative models and their error bounds: The log-concave case with full convergence estimates [5.13323375365494]
  We provide theoretical guarantees for the convergence behaviour of diffusion-based generative models under strongly log-concave data.<n>Our class of functions used for score estimation is made of Lipschitz continuous functions avoiding any Lipschitzness assumption on the score function.<n>This approach yields the best known convergence rate for our sampling algorithm.
  arXiv  Detail & Related papers  (2023-11-22T18:40:45Z)
• Sample Complexity Bounds for Score-Matching: Causal Discovery and Generative Modeling [82.36856860383291]
  We demonstrate that accurate estimation of the score function is achievable by training a standard deep ReLU neural network. We establish bounds on the error rate of recovering causal relationships using the score-matching-based causal discovery method.
  arXiv  Detail & Related papers  (2023-10-27T13:09:56Z)
• Learning Unnormalized Statistical Models via Compositional Optimization [73.30514599338407]
  Noise-contrastive estimation(NCE) has been proposed by formulating the objective as the logistic loss of the real data and the artificial noise. In this paper, we study it a direct approach for optimizing the negative log-likelihood of unnormalized models.
  arXiv  Detail & Related papers  (2023-06-13T01:18:16Z)
• Predicting Out-of-Domain Generalization with Neighborhood Invariance [59.05399533508682]
  We propose a measure of a classifier's output invariance in a local transformation neighborhood. Our measure is simple to calculate, does not depend on the test point's true label, and can be applied even in out-of-domain (OOD) settings. In experiments on benchmarks in image classification, sentiment analysis, and natural language inference, we demonstrate a strong and robust correlation between our measure and actual OOD generalization.
  arXiv  Detail & Related papers  (2022-07-05T14:55:16Z)
• Optimal variance-reduced stochastic approximation in Banach spaces [114.8734960258221]
  We study the problem of estimating the fixed point of a contractive operator defined on a separable Banach space. We establish non-asymptotic bounds for both the operator defect and the estimation error.
  arXiv  Detail & Related papers  (2022-01-21T02:46:57Z)
• Optimal regularizations for data generation with probabilistic graphical models [0.0]
  Empirically, well-chosen regularization schemes dramatically improve the quality of the inferred models. We consider the particular case of L 2 and L 1 regularizations in the Maximum A Posteriori (MAP) inference of generative pairwise graphical models.
  arXiv  Detail & Related papers  (2021-12-02T14:45:16Z)
• Evaluating State-of-the-Art Classification Models Against Bayes Optimality [106.50867011164584]
  We show that we can compute the exact Bayes error of generative models learned using normalizing flows. We use our approach to conduct a thorough investigation of state-of-the-art classification models.
  arXiv  Detail & Related papers  (2021-06-07T06:21:20Z)
• Nonparametric Score Estimators [49.42469547970041]
  Estimating the score from a set of samples generated by an unknown distribution is a fundamental task in inference and learning of probabilistic models. We provide a unifying view of these estimators under the framework of regularized nonparametric regression. We propose score estimators based on iterative regularization that enjoy computational benefits from curl-free kernels and fast convergence.
  arXiv  Detail & Related papers  (2020-05-20T15:01:03Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.