Ensemble Control Variates

2025-08-31

AI Summary

In medium- to high-dimensional Bayesian inference, zero-variance control variates (ZVCV) suffer from excessive computational cost due to over-parameterization in conventional regularized regression frameworks. Method: We propose a novel Stein-type control variate method based on ensemble learning—replacing explicit regularization with an ordinary least squares (OLS) ensemble and model averaging strategy that directly aggregates multiple basis-function estimators. This approach achieves stable and efficient variance reduction without requiring explicit regularization. Contribution/Results: Theoretical analysis and empirical evaluation demonstrate that the proposed ensemble ZVCV matches the statistical efficiency of state-of-the-art regularized ZVCV methods while significantly accelerating computation—particularly in medium- to high-dimensional settings. By shifting the design paradigm for Stein control variates from regularization-centric to ensemble-centric modeling, our work provides a scalable, accurate, and computationally efficient tool for large-scale Bayesian inference.

Technology Category

• Machine Learning: Ensemble Methods
• Reasoning under Uncertainty: Stochastic Optimization
• Computer Vision: Learning & Optimization for CV

Application Category

• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Control variates have become an increasingly popular variance-reduction technique in Bayesian inference. Many broadly applicable control variates are based on the Langevin-Stein operator, which leverages gradient information from any gradient-based sampler to produce variance-reduced estimators of expectations. These control variates typically require optimising over a function $u(θ)$ within a user-defined functional class $G$, such as the space of $Q$th-order polynomials or a reproducing kernel Hilbert space. We propose using averaging-based ensemble learning to construct Stein-based control variates. While the proposed framework is broadly applicable, we focus on ensembles constructed from zero-variance control variates (ZVCV), a popular parametric approach based on solving a linear approximation problem that can easily be over-parameterised in medium-to-high dimensional settings. A common remedy is to use regularised ZVCV via penalised regression, but these methods can be prohibitively slow. We introduce ensemble ZVCV methods based on ensembles of OLS estimators and evaluate the proposed methods against established methods in the literature in a simulation study. Our results show that ensemble ZVCV methods are competitive with regularised ZVCV methods in terms of statistical efficiency, but are substantially faster. This work opens a new direction for constructing broadly applicable control variate techniques via ensemble learning.

Problem

• Proposes ensemble learning for Stein control variates
• Addresses over-parameterization in zero-variance control variates
• Improves computational speed while maintaining statistical efficiency

Innovation

• Ensemble learning for Stein-based control variates
• Averaging-based ensembles from zero-variance control variates
• Faster ensemble ZVCV methods using OLS estimators