19 papers
Improved Stochastic Optimization of LogSumExp
Egor Gladin, Alexey Kroshnin, Jia-Jie Zhu +1
The LogSumExp function, dual to the Kullback-Leibler (KL) divergence, plays a central role in many important optimization problems, including entropy-regularized optimal transport…
Evolution of Gaussians in the Hellinger-Kantorovich-Boltzmann gradient flow
Matthias Liero, Alexander Mielke, Oliver Tse +1
This study leverages the basic insight that the gradient-flow equation associated with the relative Boltzmann entropy, in relation to a Gaussian reference measure within the Hellin…
Hellinger-Kantorovich Gradient Flows: Global Exponential Decay of Entropy Functionals
Alexander Mielke, Jia-Jie Zhu
We investigate a family of gradient flows of positive and probability measures, focusing on the Hellinger-Kantorovich (HK) geometry, which unifies transport mechanism of Otto-Wasse…
Inclusive KL Gradient Flows: Otto-Wasserstein, Fisher-Rao-Gaussian, and Local-Estimator Dynamics
Jia-Jie Zhu
Otto's Wasserstein gradient flow of the inclusive (forward) Kullback--Leibler (KL) divergence offers a principled framework for analyzing statistical inference algorithms, yet algo…
Kernel Approximation of Fisher-Rao Gradient Flows
Jia-Jie Zhu, Alexander Mielke
The purpose of this paper is to answer a few open questions in the interface of kernel methods and PDE gradient flows. Motivated by recent advances in machine learning, particularl…
Interaction-Force Transport Gradient Flows
Egor Gladin, Pavel Dvurechensky, Alexander Mielke +1
This paper presents a new gradient flow dissipation geometry over non-negative and probability measures. This is motivated by a principled construction that combines the unbalanced…