2020/04/04 by Casey Chu, Chu, Casey, Kentaro Minami +3 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Generative Adversarial Networks and Image Synthesis #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Model Reduction and Neural Networks #cs.LG #stat.ML
paper · pdf · doi:10.48550/arxiv.2004.01822
ICLR 2020, Workshop on Integration of Deep Neural Models and Differential Equations
arxiv created 2020/04/04 · openalex publication_date 2020/04/04 · arxiv updated 2020/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We formalize an equivalence between two popular methods for Bayesian inference: Stein variational gradient descent (SVGD) and black-box variational inference (BBVI). In particular, we show that BBVI corresponds precisely to SVGD when the kernel is the neural tangent kernel. Furthermore, we interpret SVGD and BBVI as kernel gradient flows; we do this by leveraging the recent perspective that views SVGD as a gradient flow in the space of probability distributions and showing that BBVI naturally motivates a Riemannian structure on that space. We observe that kernel gradient flow also describes dynamics found in the training of generative adversarial networks (GANs). This work thereby unifies several existing techniques in variational inference and generative modeling and identifies the kernel as a fundamental object governing the behavior of these algorithms, motivating deeper analysis of its properties.