NeuroPMD: Neural Fields for Density Estimation on Product Manifolds
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912795812954112 |
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| author | Consagra, William Gu, Zhiling Zhang, Zhengwu |
| author_facet | Consagra, William Gu, Zhiling Zhang, Zhengwu |
| contents | We propose a novel deep neural network methodology for density estimation on product Riemannian manifold domains. In our approach, the network directly parameterizes the unknown density function and is trained using a penalized maximum likelihood framework, with a penalty term formed using manifold differential operators. The network architecture and estimation algorithm are carefully designed to handle the challenges of high-dimensional product manifold domains, effectively mitigating the curse of dimensionality that limits traditional kernel and basis expansion estimators, as well as overcoming the convergence issues encountered by non-specialized neural network methods. Extensive simulations and a real-world application to brain structural connectivity data highlight the clear advantages of our method over the competing alternatives. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_02994 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | NeuroPMD: Neural Fields for Density Estimation on Product Manifolds Consagra, William Gu, Zhiling Zhang, Zhengwu Machine Learning We propose a novel deep neural network methodology for density estimation on product Riemannian manifold domains. In our approach, the network directly parameterizes the unknown density function and is trained using a penalized maximum likelihood framework, with a penalty term formed using manifold differential operators. The network architecture and estimation algorithm are carefully designed to handle the challenges of high-dimensional product manifold domains, effectively mitigating the curse of dimensionality that limits traditional kernel and basis expansion estimators, as well as overcoming the convergence issues encountered by non-specialized neural network methods. Extensive simulations and a real-world application to brain structural connectivity data highlight the clear advantages of our method over the competing alternatives. |
| title | NeuroPMD: Neural Fields for Density Estimation on Product Manifolds |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2501.02994 |