Density Estimation on Rectifiable Sets
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866908383455477760 |
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| author | Kendrick, Jack |
| author_facet | Kendrick, Jack |
| contents | Kernel density estimation is a popular method for estimating unseen probability distributions. However, the convergence of these classical estimators to the true density slows down in high dimensions. Moreover, they do not define meaningful probability distributions when the intrinsic dimension of data is much smaller than its ambient dimension. We build on previous work on density estimation on manifolds to show that a modified kernel density estimator converges to the true density on $d-$rectifiable sets. As a special case, we consider algebraic varieties and semi-algebraic sets and prove a convergence rate in this setting. We conclude the paper with a numerical experiment illustrating the convergence of this estimator on sparse data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_23023 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Density Estimation on Rectifiable Sets Kendrick, Jack Statistics Theory Classical Analysis and ODEs 62G05, 62G07 Kernel density estimation is a popular method for estimating unseen probability distributions. However, the convergence of these classical estimators to the true density slows down in high dimensions. Moreover, they do not define meaningful probability distributions when the intrinsic dimension of data is much smaller than its ambient dimension. We build on previous work on density estimation on manifolds to show that a modified kernel density estimator converges to the true density on $d-$rectifiable sets. As a special case, we consider algebraic varieties and semi-algebraic sets and prove a convergence rate in this setting. We conclude the paper with a numerical experiment illustrating the convergence of this estimator on sparse data. |
| title | Density Estimation on Rectifiable Sets |
| topic | Statistics Theory Classical Analysis and ODEs 62G05, 62G07 |
| url | https://arxiv.org/abs/2505.23023 |