mlsanityData to 7 Oct 2026

Theoretical guarantees for neural control variates in MCMC

arXiv 2304.01111 ↗First posted 3 Apr 2023math.ST cs.LG math.PRcited by 4

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Abstract (arXiv)

In this paper, we propose a variance reduction approach for Markov chains based on additive control variates and the minimization of an appropriate estimate for the asymptotic variance. We focus on the particular case when control variates are represented as deep neural networks. We derive the optimal convergence rate of the asymptotic variance under various ergodicity assumptions on the underlying Markov chain. The proposed approach relies upon recent results on the stochastic errors of variance reduction algorithms and function approximation theory.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 13 of its 38 references that are in the map. First posted on arXiv 3 Apr 2023.

Builds on

13 of 38 references.

References · 13

  1. 2017Solving high-dimensional partial differential equations using deep learningcited by 549
  2. 2017Nonparametric regression using deep neural networks with ReLU activation functioncited by 431
  3. 2021On the approximation of functions by tanh neural networkscited by 81
  4. 2014Control functionals for Monte Carlo integrationcited by 59
  5. 2022Simultaneous approximation of a smooth function and its derivatives by deep neural networks with piecewise-polynomial activationscited by 29
  6. 2020Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditionscited by 25
  7. 2020Approximating smooth functions by deep neural networks with sigmoid activation functioncited by 18
  8. 2019PowerNet: Efficient Representations of Polynomials and Smooth Functions by Deep Neural Networks with Rectified Power Unitscited by 12
  9. 2018Regularized Zero-Variance Control Variatescited by 10
  10. 2020Scalable Control Variates for Monte Carlo Methods via Stochastic Optimizationcited by 10
  11. 2023Meta-learning Control Variates: Variance Reduction with Limited Datacited by 6
  12. 2017Empirical Variance Minimization with Applications in Variance Reduction and Optimal Controlcited by 3
1 more
  1. 2019Variance reduction for Markov chains with application to MCMCcited by 2

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Cited by year

Citing papers per year: 2023: 2; 2024: 1; 2025: 1.

4 papers.

  1. 2023When can Regression-Adjusted Control Variates Help? Rare Events, Sobolev Embedding and Minimax Optimalitycited by 4
  2. 2023Bayesian Numerical Integration with Neural Networkscited by 3
  3. 2024Prediction-Enhanced Monte Carlo: A Machine Learning View on Control Variatecited by 2
  4. 2025Training neural control variates using correlated configurationscited by 1