This repository presents python3 code for the paper entitled ``Scalable Control Variates for Monte Carlo Methods via Stochastic Optimization" by Shijing Si, Chris Oates, Andrew B. Duncan, Lawrence Carin, and François-Xavier Briol (https://arxiv.org/abs/2006.07487). Specifically, we provide the code for polynomial, kernel and neural networks control variates.

python3.5+

scipy==1.5.2

numpy==1.19.2

torch==1.6.0

sklearn==0.23.2

In order to make it easy for people to use it, we provide an example in the demonstration--polynomial_integrand_experiments.ipynb file, where the integrand is polynomials of the form $\Sum_{i=1}^{m}\Sum_{j=1}^{n}A_{i,j}x_{i}^{j}$; and the probability measure is normal distribution with zero mean and standard deviation $\sigma$.

For all these control variates, you need to instantiate the class first, SteinSecondOrderQuadPolyCV (Second order polynomial Control Variates), SteinFirstOrderQuadPolyCV (First order controil variates), SteinFirstOrderNeuralNets (Neural Networks), and GaussianControlVariate (Kernel Control Variates). For the kernel control variates, we need to import OatesGram to evaluate the Gram matrix of the kernel. Then you need to feed the samples ($X$), and evaluations $f(X)$, and score function evaluations at $X$ to the train() method of these classes to train the control variates.

The performance may vary significantly with different configuration of hyper-parameters. So please tune the hyper-parameters to get good results.