Nonparametric Estimation of Joint Entropy via Partitioned Sample-Spacing
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912737537294336 |
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| author | Ho, Jungwoo Park, Sangun Oh, Soyeong |
| author_facet | Ho, Jungwoo Park, Sangun Oh, Soyeong |
| contents | We propose a nonparametric estimator of multivariate joint entropy based on partitioned sample spacing (PSS). The method extends univariate spacing ideas to $\mathbb{R}^{d}$ by partitioning into localized cells and aggregating within-cell statistics, with strong consistency guarantees under mild conditions. In benchmarks across diverse distributions, PSS consistently outperforms $k$-nearest neighbor estimators and achieves accuracy competitive with recent normalizing flow-based methods, while requiring no training or auxiliary density modeling. The estimator scales favorably in moderately high dimensions ($d = 10$--$40$) and shows particular robustness to correlated or skewed distributions. These properties position PSS as a practical and reliable alternative to both $k$NN and NF-based entropy estimators, with broad utility in information-theoretic machine learning tasks such as total-correlation estimation, representation learning, and feature selection. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_13602 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonparametric Estimation of Joint Entropy via Partitioned Sample-Spacing Ho, Jungwoo Park, Sangun Oh, Soyeong Statistics Theory Machine Learning We propose a nonparametric estimator of multivariate joint entropy based on partitioned sample spacing (PSS). The method extends univariate spacing ideas to $\mathbb{R}^{d}$ by partitioning into localized cells and aggregating within-cell statistics, with strong consistency guarantees under mild conditions. In benchmarks across diverse distributions, PSS consistently outperforms $k$-nearest neighbor estimators and achieves accuracy competitive with recent normalizing flow-based methods, while requiring no training or auxiliary density modeling. The estimator scales favorably in moderately high dimensions ($d = 10$--$40$) and shows particular robustness to correlated or skewed distributions. These properties position PSS as a practical and reliable alternative to both $k$NN and NF-based entropy estimators, with broad utility in information-theoretic machine learning tasks such as total-correlation estimation, representation learning, and feature selection. |
| title | Nonparametric Estimation of Joint Entropy via Partitioned Sample-Spacing |
| topic | Statistics Theory Machine Learning |
| url | https://arxiv.org/abs/2511.13602 |