This project implements Bayesian Quadrature on top of GPytorch.

Bayesian Quadrature (BQ) is a probabilistic method to approximate an integral in the form of

or

.

BQ can be useful when is expensive to compute, prohibited to perform Monte Carlo estimation.

The main idea is to use Gaussian Process (GP) as a surrogate function for the true and the linearity of GP. Since integral is just a linear operator, we can obtain a new GP after apply it over a GP. Let's say

After observing , the integral follows a multivariate normal distribution:

Discussion on limitations of BQ:

• is restricted to a certain family (normal, uniform) to have closed-formed solutions for
• BQ is applied in low-dimensional spaces rather than high-dimensional settings.

Python >= 3.6
Pytorch ==1.3
GPytorch == 0.3.6