Finite Sample Bounds for Learning with Score Matching
Summary
This paper provides the first non-asymptotic sample complexity bounds for learning exponential families of polynomials with score matching, showing polynomial dependence on model dimension.
View Cached Full Text
Cached at: 05/15/26, 06:27 AM
# Finite Sample Bounds for Learning with Score Matching Source: [https://arxiv.org/abs/2605.14168](https://arxiv.org/abs/2605.14168) [View PDF](https://arxiv.org/pdf/2605.14168) > Abstract:Learning of continuous exponential family distributions with unbounded support remains an important area of research for both theory and applications in high\-dimensional statistics\. In recent years, score matching has become a widely used method for learning exponential families with continuous variables due to its computational ease when compared against maximum likelihood estimation\. However, theoretical understanding of the statistical properties of score matching is still lacking\. In this work, we provide a non\-asymptotic sample complexity analysis for learning the structure of exponential families of polynomials with score matching\. The derived sample bounds show a polynomial dependence on the model dimension\. These bounds are the first of its kind, as all prior work has shown only asymptotic bounds on the sample complexity\. ## Submission history From: Devin Smedira \[[view email](https://arxiv.org/show-email/961e51ad/2605.14168)\] **\[v1\]**Wed, 13 May 2026 22:48:18 UTC \(31 KB\)
Similar Articles
From Privacy to Generalization: Linear Max-Information Bounds for DP-SGD
This paper proves a finite-sample bound on the approximate max-information of DP-SGD that is at most linear in dataset size, yielding PAC-Bayes generalization bounds for models trained with differential privacy.
Score-Based Causal Discovery of Latent Variable Causal Models
This paper introduces score-based methods for causal discovery in the presence of latent variables, offering theoretical guarantees of consistency and score equivalence, and unifies several constraint-based approaches.
Zeroth-Order Non-Log-Concave Sampling with Variance Reduction and Applications to Inverse Problems
Proposes a variance-reduced zeroth-order Langevin sampling method for non-log-concave distributions, establishing the first non-asymptotic convergence guarantees, and applies it to inverse problems with score-based generative priors.
Sharp First-Order Lower Bounds for Higher-Order Smooth Nonconvex Optimization
This paper proves sharp dimension-free first-order lower bounds for finding epsilon-stationary points in higher-order smooth nonconvex optimization, resolving open problems for Hessian-Lipschitz and third-order smooth cases.
A Unified Measure-Theoretic View of Diffusion, Score-Based, and Flow Matching Generative Models
This arXiv preprint proposes a unified measure-theoretic framework for understanding diffusion, score-based, and flow matching generative models. It establishes connections between these methods via continuity/Fokker-Planck equations and analyzes their sampling schemes and theoretical guarantees.