Scalable Control Variates for Monte Carlo Methods via Stochastic
Optimization
- URL: http://arxiv.org/abs/2006.07487v2
- Date: Wed, 21 Jul 2021 11:46:11 GMT
- Title: Scalable Control Variates for Monte Carlo Methods via Stochastic
Optimization
- Authors: Shijing Si, Chris. J. Oates, Andrew B. Duncan, Lawrence Carin,
Fran\c{c}ois-Xavier Briol
- Abstract summary: This paper presents a framework that encompasses and generalizes existing approaches that use controls, kernels and neural networks.
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.
- Score: 62.47170258504037
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: 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.
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