2022/05/26 by Yifei Wang, Wang, Yifei, Peng Chen +5
Biochemistry, Genetics and Molecular Biology · Engineering · Medicine · #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Optical Imaging and Spectroscopy Techniques #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques #Spectroscopy Techniques in Biomedical and Chemical Research
paper · pdf · doi:10.48550/arxiv.2205.13098
openalex publication_date 2022/05/26 · openalex created_date 2022/06/13 · openalex updated_date 2026/07/28
The computation of Wasserstein gradient direction is essential for posterior sampling problems and scientific computing. The approximation of the Wasserstein gradient with finite samples requires solving a variational problem. We study the variational problem in the family of two-layer networks with squared-ReLU activations, towards which we derive a semi-definite programming (SDP) relaxation. This SDP can be viewed as an approximation of the Wasserstein gradient in a broader function family including two-layer networks. By solving the convex SDP, we obtain the optimal approximation of the Wasserstein gradient direction in this class of functions. Numerical experiments including PDE-constrained Bayesian inference and parameter estimation in COVID-19 modeling demonstrate the effectiveness of the proposed method.