Faster Adaptive Importance Sampling in Low Dimensions

Abstract

Adaptive importance sampling using kernel density estimation techniques was introduced by West. This technique adapts the importance sampling function to the underlying integrand, thus yielding small-variance estimates. One drawback of this approach is that evaluation of the kernel mixture density is slow. We present a linear tensor spline representation of the adaptive importance function using variable bandwidth kernels that retains the small variance properties of West's approach but executes more quickly.