Kullback-Leibler Consistency of $p$-dimensional P\'olya Tree Posteriors and Differential Entropy Estimation

Fernando Corrêa; Rafael Bassi Stern; Julio Michael Stern

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arXiv · 2504.02950

Kullback-Leibler Consistency of $p$-dimensional P\'olya Tree Posteriors and Differential Entropy Estimation

Fernando Corrêa·Rafael Bassi Stern·Julio Michael Stern

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Abstract

We exploit the multiplicative structure of P\'olya Tree priors to establish novel consistency results on $p$-dimensional trees, conditions to obtain Kullback-Leibler minimax contraction rates for univariate density estimation and a representation theorem of entropy functionals of P\'olya Tree posteriors. These results motivate a novel differential entropy estimator that is consistent under mild conditions on large dimensions.

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Fernando Corrêa, Rafael Bassi Stern, Julio Michael Stern. 2025-04-03. Kullback-Leibler Consistency of $p$-dimensional P\'olya Tree Posteriors and Differential Entropy Estimation. https://arxiv.org/abs/2504.02950

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