Gradient flows have been a popular tool in the analysis of PDEs. Recently, various gradient flows have been studied in machine learning literature. This article is an introduction to the concept of gradient flows in the 2-Wasserstein space.
Langevin Monte Carlo is a class of Markov Chain Monte Carlo algorithms that generate samples from a probability distribution of interest by simulating the Langevin Equation. This post explores the basics of Langevin Monte Carlo.
The 1-Wasserstein distance is a popular integral probability metric. In this post, the dual form of the 1-Wasserstein distance is derived from its primal form.