mlsanityData to 7 Oct 2026

Nonparametric Score Estimators

arXiv 2005.10099 ↗First posted 20 May 2020stat.ML cs.LGcited by 22

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Abstract (arXiv)

Estimating the score, i.e., the gradient of log density function, from a set of samples generated by an unknown distribution is a fundamental task in inference and learning of probabilistic models that involve flexible yet intractable densities. Kernel estimators based on Stein's methods or score matching have shown promise, however their theoretical properties and relationships have not been fully-understood. We provide a unifying view of these estimators under the framework of regularized nonparametric regression. It allows us to analyse existing estimators and construct new ones with desirable properties by choosing different hypothesis spaces and regularizers. A unified convergence analysis is provided for such estimators. Finally, we propose score estimators based on iterative regularization that enjoy computational benefits from curl-free kernels and fast convergence.

Key facts. Cited by 22 papers in the map (data through 7 Oct 2026). First posted on arXiv 20 May 2020.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 3; 2022: 3; 2023: 2; 2024: 5; 2025: 5; 2026: 4.

22 papers.

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  1. 2021Estimating High Order Gradients of the Data Distribution by Denoisingcited by 63
  2. 2024Optimal score estimation via empirical Bayes smoothingcited by 60
  3. 2023Nonparametric Generative Modeling with Conditional Sliced-Wasserstein Flowscited by 15
  4. 2024Linear Causal Representation Learning from Unknown Multi-node Interventionscited by 14
  5. 2023Differentiable Neural Networks with RePU Activation: with Applications to Score Estimation and Isotonic Regressioncited by 8
  6. 2022Algorithmic Differentiation for Automated Modeling of Machine Learned Force Fieldscited by 7
  7. 2024A Skewness-Based Criterion for Addressing Heteroscedastic Noise in Causal Discoverycited by 7
  8. 2024Bridging the Sim-to-Real Gap with Bayesian Inferencecited by 6
  9. 2025Distinguishing Cause from Effect with Causal Velocity Modelscited by 6
  10. 2022MARS: Meta-Learning as Score Matching in the Function Spacecited by 5
  11. 2021Active Slices for Sliced Stein Discrepancycited by 3
  12. 2021AutoTransfer: Subject Transfer Learning with Censored Representations on Biosignals Datacited by 3
10 more
  1. 2024Nonparametric Automatic Differentiation Variational Inference with Spline Approximationcited by 3
  2. 2026Aligning Few-Step Generative Models by Amortizing Sample-based Variational Inferencecited by 3
  3. 2022A Kernelised Stein Statistic for Assessing Implicit Generative Modelscited by 1
  4. 2025Nonlinear Multiple Response Regression and Learning of Latent Spacescited by 1
  5. 2025Constraint-Aware Flow Matching via Randomized Explorationcited by 1
  6. 2025Nonparametric learning of heterogeneous graphical model on network-linked datacited by 0
  7. 2025Simulation Priors for Data-Efficient Deep Learningcited by 0
  8. 2026Variance-Reduced Diffusion Sampling via Target Score Identitycited by 0
  9. 2026Multi-Source Transfer Learning of Sparse Single-Index Modelscited by 0
  10. 2026Non-parametric recovery of causal diffusion mechanisms from steady-state observationscited by 0