Robust Multiple Importance Sampling with Tsallis <i>φ</i>-Divergences

Abstract

Multiple Importance Sampling (MIS) combines the probability density functions (pdf) of several sampling techniques. The combination weights depend on the proportion of samples used for the particular techniques. Weights can be found by optimization of the variance, but this approach is costly and numerically unstable. We show in this paper that MIS can be represented as a divergence problem between the integrand and the pdf, which leads to simpler computations and more robust solutions. The proposed idea is validated with 1D numerical examples and with the illumination problem of computer graphics.

Keywords

• multiple importance sampling
• Monte Carlo integration
• φ-divergence
• f-divergence
• Tsallis divergence
• Kullback–Leibler divergence