Generative model for optimal density estimation on unknown manifold
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913910294052864 |
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| author | Stéphanovitch, Arthur |
| author_facet | Stéphanovitch, Arthur |
| contents | We propose a generative model that achieves minimax-optimal convergence rates for estimating probability distributions supported on unknown low-dimensional manifolds. Building on Fefferman's solution to the geometric Whitney problem, our estimator is itself supported on a submanifold that matches the regularity of the data's support. This geometric adaptation enables the estimator to be simultaneously minimax-optimal for all \( γ\)-Hölder Integral Probability Metrics (IPMs) with \( γ\geq 1 \). We validate our approach through experiments on synthetic and real datasets, demonstrating competitive or superior performance compared to Wasserstein GAN and score-based generative models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_19587 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generative model for optimal density estimation on unknown manifold Stéphanovitch, Arthur Statistics Theory We propose a generative model that achieves minimax-optimal convergence rates for estimating probability distributions supported on unknown low-dimensional manifolds. Building on Fefferman's solution to the geometric Whitney problem, our estimator is itself supported on a submanifold that matches the regularity of the data's support. This geometric adaptation enables the estimator to be simultaneously minimax-optimal for all \( γ\)-Hölder Integral Probability Metrics (IPMs) with \( γ\geq 1 \). We validate our approach through experiments on synthetic and real datasets, demonstrating competitive or superior performance compared to Wasserstein GAN and score-based generative models. |
| title | Generative model for optimal density estimation on unknown manifold |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2506.19587 |