Kullback-Leibler Consistency of $p$-dimensional Pólya Tree Posteriors and Differential Entropy Estimation
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912802218704896 |
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| author | Corrêa, Fernando Stern, Rafael Bassi Stern, Julio Michael |
| author_facet | Corrêa, Fernando Stern, Rafael Bassi Stern, Julio Michael |
| contents | We exploit the multiplicative structure of Pólya 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 Pólya Tree posteriors. These results motivate a novel differential entropy estimator that is consistent under mild conditions on large dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_02950 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Kullback-Leibler Consistency of $p$-dimensional Pólya Tree Posteriors and Differential Entropy Estimation Corrêa, Fernando Stern, Rafael Bassi Stern, Julio Michael Statistics Theory We exploit the multiplicative structure of Pólya 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 Pólya Tree posteriors. These results motivate a novel differential entropy estimator that is consistent under mild conditions on large dimensions. |
| title | Kullback-Leibler Consistency of $p$-dimensional Pólya Tree Posteriors and Differential Entropy Estimation |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2504.02950 |