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 - 15:50Room: 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
- Optimization for learning and data analysis
- Data driven optimization
- Optimization under uncertainty and applications
Status: accepted
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