NeuroPMD: Neural Fields for Density Estimation on Product Manifolds

• URL: http://arxiv.org/abs/2501.02994v1
• Date: Mon, 06 Jan 2025 13:13:13 GMT
• Title: NeuroPMD: Neural Fields for Density Estimation on Product Manifolds
• Authors: William Consagra, Zhiling Gu, Zhengwu Zhang,
• Abstract summary: In our approach, the network directly parameterizes the unknown density function and is trained using a penalized maximum likelihood framework. The network architecture and estimation algorithm are carefully designed to handle the challenges of high-dimensional product manifold domains.
• Score: 4.096453902709292
• License:
• Abstract: 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.

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