A0910
Title: NeuroPMD: Neural fields for density estimation on product manifolds
Authors: William Consagra - University of South Carolina (United States) [presenting]
Zhiling Gu - Yale (United States)
Zhengwu Zhang - UNC Chapel Hill (United States)
Abstract: A novel deep neural network methodology is proposed for density estimation on product Riemannian manifold domains. In the 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 the method over the competing alternatives.
