Scalable Control Variates for Monte Carlo Methods via Stochastic Optimization
Control variates are a well-established tool to reduce the variance of Monte Carlo estimators. However, for large-scale problems including high-dimensional and large-sample settings, their advantages can be outweighed by a substantial computational cost. This paper considers control variates based on Stein operators, presenting a framework that encompasses and generalizes existing approaches that use polynomials, kernels and neural networks. A learning strategy based on minimising a variational objective through stochastic optimization is proposed, leading to scalable and effective control variates. Novel theoretical results are presented to provide insight into the variance reduction that can be achieved, and an empirical assessment, including applications to Bayesian inference, is provided in support.
Code (0)
등록된 구현이 없습니다.
Tasks
Bayesian InferenceStochastic OptimizationSimilar Papers 제목 키워드 기반
Sliced-Wasserstein Estimation with Spherical Harmonics as Control Variates
The Sliced-Wasserstein (SW) distance between probability measures is defined as the average of the Wasserstein distances resulting for the associated one-dimensional projections. As a consequence, the SW distance can be …
Stabilizing Estimates of Shapley Values with Control Variates
Shapley values are among the most popular tools for explaining predictions of blackbox machine learning models. However, their high computational cost motivates the use of sampling approximations, inducing a considerable…
When can Regression-Adjusted Control Variates Help? Rare Events, Sobolev Embedding and Minimax Optimality
This paper studies the use of a machine learning-based estimator as a control variate for mitigating the variance of Monte Carlo sampling. Specifically, we seek to uncover the key factors that influence the efficiency of…
regressionNeural Control Variates for Variance Reduction
In statistics and machine learning, approximation of an intractable integration is often achieved by using the unbiased Monte Carlo estimator, but the variances of the estimation are generally high in many applications. …
Reinforcement LearningJoint control variate for faster black-box variational inference
Black-box variational inference performance is sometimes hindered by the use of gradient estimators with high variance. This variance comes from two sources of randomness: Data subsampling and Monte Carlo sampling. While…
Stochastic OptimizationVariational Inference