# Regularized Zero-Variance Control Variates

arXiv: https://arxiv.org/abs/1811.05073 · HTML: https://mlsanity.com/paper/1811.05073/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Nov 2018.

## Built on by (most cited first, 11 of 11)

- [Sliced-Wasserstein Estimation with Spherical Harmonics as Control Variates](https://mlsanity.com/paper/2402.01493/) (2024)
- [Meta-learning Control Variates: Variance Reduction with Limited Data](https://mlsanity.com/paper/2303.04756/) (2023)
- [Regression for the Mean: Auto-Evaluation and Inference with Few Labels through Post-hoc Regression](https://mlsanity.com/paper/2411.12665/) (2024)
- [Theoretical guarantees for neural control variates in MCMC](https://mlsanity.com/paper/2304.01111/) (2023)
- [When can Regression-Adjusted Control Variates Help? Rare Events, Sobolev Embedding and Minimax Optimality](https://mlsanity.com/paper/2305.16527/) (2023)
- [The Polynomial Stein Discrepancy for Assessing Moment Convergence](https://mlsanity.com/paper/2412.05135/) (2024)
- [Conditional neural control variates for variance reduction in Bayesian inverse problems](https://mlsanity.com/paper/2602.21357/) (2026)
- [Training neural control variates using correlated configurations](https://mlsanity.com/paper/2505.07719/) (2025)
- [Pathwise Gradient Variance Reduction with Control Variates in Variational Inference](https://mlsanity.com/paper/2410.05753/) (2024)
- [It's all In the (Exponential) Family: An Equivalence between Maximum Likelihood Estimation and Control Variates for Sketching Algorithms](https://mlsanity.com/paper/2601.22378/) (2026)
- [Risk-Calibrated Proposal Transport for Finite-Particle Diffusion Steering](https://mlsanity.com/paper/2610.04171/) (2026)

## Abstract (arXiv)

Zero-variance control variates (ZV-CV) are a post-processing method to reduce the variance of Monte Carlo estimators of expectations using the derivatives of the log target. Once the derivatives are available, the only additional computational effort lies in solving a linear regression problem. Significant variance reductions have been achieved with this method in low dimensional examples, but the number of covariates in the regression rapidly increases with the dimension of the target. In this paper, we present compelling empirical evidence that the use of penalized regression techniques in the selection of high-dimensional control variates provides performance gains over the classical least squares method. Another type of regularization based on using subsets of derivatives, or a priori regularization as we refer to it in this paper, is also proposed to reduce computational and storage requirements. Several examples showing the utility and limitations of regularized ZV-CV for Bayesian inference are given. The methods proposed in this paper are accessible through the R package ZVCV.