EUROPT 2024
Abstract Submission

328. Gradient flows and kernelization in the Hellinger-Kantorovich (a.k.a. Wasserstein-Fisher-Rao) space

Invited abstract in session FD-7: Optimal Transport for Machine Learning and Inverse Problems, stream Optimization for Inverse Problems and Machine Learning.

Friday, 14:10 - 15:50
Room: M:I

Authors (first author is the speaker)

1. Jia-Jie Zhu
Weierstrass Institute for Applied Analysis and Stochastics, Berlin

Abstract

Motivated by applications of the optimal transport theory in optimization and machine learning, we present a principled investigation of gradient flow dissipation geometry, emphasizing the Hellinger (Fisher-Rao) type gradient flows and the connections with the Wasserstein space. The talk will introduce new advances in two directions: 1) the kernelization of Hellinger type distance and gradient flows, revealing precise connections with Stein flows, kernel discrepancies, and nonparametric regression; 2) new convergence results of the Hellinger-Kantorovich, a.k.a. Wasserstein-Fisher-Rao, gradient flows.

Joint work with Alexander Mielke.

Keywords

Status: accepted


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