  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.
