Wednesday, March 22, 2017 - 4:30pm
Building and Room Number
I will introduce principal differences analysis (PDA), a method for analyzing differences between high-dimensional distributions which operates by finding the projection that maximizes the statistical divergence between the resulting univariate populations. Unlike standard two-sample tests, PDA not only returns a p-value, but also quantifies how much each variable contributes to the overall difference between the populations. Furthermore, this approach retains high statistical power (even at low sample-sizes) when the underlying differences are only over a sparse subset of the features. Relying on the Cramer-Wold device, PDA requires no assumptions about the form of the underlying distributions, nor the nature of their inter-class differences. While our broader framework can utilize any choice of metric between distributions, we provide algorithms for PDA using the Wasserstein distance. Finally, I will highlight some existing theory and open questions relating the geometry of nonparametric distributions to projections thereof in the context of finite-sample estimation.