Earth Mover's Distance (EMD) characterizes a metric space between discrete probability distributions (i.e., histograms) by evaluating the minimum transportation costs of probability mass. The name is an analogy of the transportation costs of moving a pile of dirt into another one, as enunciated by Gaspard Monge in 1781. In this talk, we focus on learning a ground metric (i.e., the transportation cost values) from a set of reference distance values and corresponding histograms. We consider two distinct formulations under a unifying framework, one for regression, and a second one for classification. An application of interest is the characterization of the space of flavor and fragrance products, which we illustrate within a computational creativity framework. Over the past decades, flavor and fragrance companies have amassed a large amount of data from their own internal creation processes, yet product creation still relies on human expertise and arduous experimentation. By learning a ground metric, our proposed methodology can aid in the process of designing new compositions based on the existing knowledge encoded by hundred of thousands of existing products and ingredients. We illustrate the overall creation process with examples and simulations.

Javier Zazo is a postdoctoral fellow at Harvard University, working on computational machine learning and representation learning. He is part of CRCS and SEAS department. He received his Ph.D. from Universidad Politecnica de Madrid (UPM) working on non-convex optimization, game theory and related applications. Javier received his Telecommunications Engineer degree from UPM and Technische Universitat Darmstadt (TUD), and M.Sc. from the National University of Ireland (NUIM). In 2015 he was a research visitor to University at Buffallo (UB). His current research interests include optimal transport, optimization methods and deep learning.