2021/10/21 by Clément Bonet, Nicolas Courty, Bonet, Clément +5 · 1 citation
Computer Science · Engineering · Medicine · #3D Shape Modeling and Analysis #Advanced Image Processing Techniques #Advanced Neuroimaging Techniques and Applications #FOS: Computer and information sciences #FOS: Mathematics #Generative Adversarial Networks and Image Synthesis #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2110.10972
openalex publication_date 2021/10/21 · openalex created_date 2021/10/25 · openalex updated_date 2026/07/28
Minimizing functionals in the space of probability distributions can be done\nwith Wasserstein gradient flows. To solve them numerically, a possible approach\nis to rely on the Jordan-Kinderlehrer-Otto (JKO) scheme which is analogous to\nthe proximal scheme in Euclidean spaces. However, it requires solving a nested\noptimization problem at each iteration, and is known for its computational\nchallenges, especially in high dimension. To alleviate it, very recent works\npropose to approximate the JKO scheme leveraging Brenier's theorem, and using\ngradients of Input Convex Neural Networks to parameterize the density\n(JKO-ICNN). However, this method comes with a high computational cost and\nstability issues. Instead, this work proposes to use gradient flows in the\nspace of probability measures endowed with the sliced-Wasserstein (SW)\ndistance. We argue that this method is more flexible than JKO-ICNN, since SW\nenjoys a closed-form differentiable approximation. Thus, the density at each\nstep can be parameterized by any generative model which alleviates the\ncomputational burden and makes it tractable in higher dimensions.\n