Tree pyramidal adaptive importance sampling

Abstract

This paper introduces Tree-Pyramidal Adaptive Importance Sampling (TP-AIS), a novel iterated sampling method that outperforms state-of-the-art approaches like deterministic mixture population Monte Carlo (DM-PMC), mixture population Monte Carlo (M-PMC) and layered adaptive importance sampling (LAIS). TP-AIS iteratively builds a proposal distribution parameterized by a tree pyramid, where each tree leaf spans a subspace that represents its importance density. After each new sample operation, a set of tree leaves are subdivided for improving the approximation of the proposal distribution to the target density. Unlike the rest of the methods in the literature, TP-AIS is parameter free and requires no tuning to achieve its best performance. We evaluate TP-AIS with different complexity randomized target probability density functions (PDF) and also analyze its application to different dimensions. The results are compared to state-of-the-art iterative importance sampling approaches and other baseline MCMC approaches using Normalized Effective Sample Size (N-ESS), Jensen-Shannon Divergence, and time complexity.

arXiv comment20 pages + 13 pages of additional result plots and evaluation details

References in corpus (6)

• Effective Sample Size for Importance Sampling based on discrepancy measures
• Generalized Multiple Importance Sampling
• Layered Adaptive Importance Sampling
• Improving Population Monte Carlo: Alternative Weighting and Resampling Schemes
• Experimental Analysis of a Generalized Stratified Sampling Algorithm for Hypercubes
• Improving Grid Based Bayesian Methods

Cited by in corpus (3)

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