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.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2019
- DOI:
- 10.48550/arXiv.1912.08434
- arXiv:
- arXiv:1912.08434
- Bibcode:
- 2019arXiv191208434F
- Keywords:
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- Statistics - Machine Learning;
- Computer Science - Machine Learning;
- Statistics - Computation
- E-Print:
- 20 pages + 13 pages of additional result plots and evaluation details