mlsanityData to 14 Oct 2026

Finite Sample Bounds for Learning with Score Matching

arXiv 2605.14168 ↗First posted 13 May 2026cs.LG cs.DS stat.MLcited by 0

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Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 19 of its 29 references that are in the map. First posted on arXiv 13 May 2026.

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References · 19

  1. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  2. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  3. 2022Convergence of score-based generative modeling for general data distributionscited by 181
  4. 2023Diffusion Models are Minimax Optimal Distribution Estimatorscited by 165
  5. 2024Convergence of Diffusion Models Under the Manifold Hypothesis in High-Dimensionscited by 65
  6. 2022Statistical Efficiency of Score Matching: The View from Isoperimetrycited by 64
  7. 2023Wasserstein Convergence Guarantees for a General Class of Score-Based Generative Modelscited by 58
  8. 2017Learning Graphical Models Using Multiplicative Weightscited by 43
  9. 2013Density Estimation in Infinite Dimensional Exponential Familiescited by 42
  10. 2019Efficient Learning of Discrete Graphical Modelscited by 21
  11. 2025Generalization error bound for denoising score matching under relaxed manifold assumptioncited by 20
  12. 2023Provable benefits of score matchingcited by 18
7 more
  1. 2018Sparse Logistic Regression Learns All Discrete Pairwise Graphical Modelscited by 16
  2. 2025Wasserstein Convergence of Score-based Generative Models under Semiconvexity and Discontinuous Gradientscited by 15
  3. 2021A Computationally Efficient Method for Learning Exponential Family Distributionscited by 10
  4. 2020On Learning Continuous Pairwise Markov Random Fieldscited by 9
  5. 2014Computational Implications of Reducing Data to Sufficient Statisticscited by 6
  6. 2021Learning Continuous Exponential Families Beyond Gaussiancited by 6
  7. 2025Implicit score matching meets denoising score matching: improved rates of convergence and log-density Hessian estimationcited by 4

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