Earth Mover's Distance and Equivalent Metrics

Speaker: 
William Leeb - Yale University
Date: 
Mar 26 2014 - 3:00pm
Event type: 
IDeAS
Room: 
110 Fine Hall
Abstract: 

Earth Mover's Distance (EMD) is a robust and interpretable metric for comparing probability distributions. Unlike conventional distances, EMD exploits the geometry of the space on which the distributions are defined. However, it is not easy to compute directly. In this talk, I will present metrics equivalent to EMD that can be computed fast. I will explain how these metrics emerge from the theory of Hölder spaces and their duals. I will also show that in any space equipped with a diffusion semigroup of the kind widely used in machine learning, there is a natural metric with respect to which the classical characterizations of Hölder spaces and their duals generalize. If time permits, I will discuss an analogous theory on spaces equipped with hierarchical partition trees.