arXiv Machine Learning By Jia-Jie Zhu

Inclusive KL Gradient Flows: Otto-Wasserstein, Fisher-Rao-Gaussian, and Local-Estimator Dynamics

Read the original on arXiv Machine Learning →

arXiv:2411. 00214v2 Announce Type: replace-cross Abstract: Otto's Wasserstein gradient flow of the inclusive (forward) Kullback--Leibler (KL) divergence offers a principled framework for analyzing statistical inference algorithms, yet algorithms targeting the exclusive (reverse) KL divergence are rarely studied with such tools.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

arXiv Machine Learning
Sep 17

Preservation of Log-Concavity and Convergence of Wasserstein-Fisher-Rao Gradient Flows

The paper investigates Wasserstein-Fisher-Rao (WFR) gradient flows for sampling from probability distributions known only up to a normalisation constant. It demonstrates that for strongly log-concave targets satisfying certain curvature conditions, WFR flows preserve strong log-concavity—unlike pure Wasserstein flows, which only do so in the Gaussian case. Leveraging this property, the authors derive explicit non-asymptotic convergence rates for the symmetrised Kullback-Leibler divergence, showing an additive decomposition into Wasserstein and Fisher‑Rao contributions and eliminating the need for a warm start.

By Francesca Romana Crucinio, Sahani Pathiraja
arXiv Machine Learning
Aug 13

Fine-Tuning Generative Models for Extreme Events via CVaR-Penalized Wasserstein Gradient Flows

arXiv:2608. 11544v1 Announce Type: cross Abstract: We propose CVaR-penalized Generative Particle Algorithm (CVaR-GPA), a robust, tail-agnostic algorithm for fine-tuning generative models to learn heavy-tailed distributions and capture extreme events, requiring no prior knowledge or estimation of the target's tail characteristics.

By Thejani Gamage, Hyemin Gu, Zhizhen Zhang, Ziyu Chen, Markos Katsoulakis, Luc Rey-Bellet
arXiv Machine Learning
Jul 7

A Gradient Flow Perspective on Minimum MMD Estimation

arXiv:2607. 03871v1 Announce Type: new Abstract: Minimum maximum mean discrepancy (MMD) estimation has emerged as a robust and likelihood-free alternative to maximum likelihood estimation for parameter estimation.

By Sophia Seulkee Kang, Louis Sharrock, Xiaoyuan Cheng, Fran\c{c}ois-Xavier Briol, Zonghao Chen