Title: The More, the Merrier: the Blessing of Dimensionality for Learning Large Gaussian Mixtures
Abstract: I will discuss recent developments in high dimensional geometric statistical inference. The problems will include the reconstruction of polytopes from uniformly random points and the estimation of parameters of Gaussian Mixture Models. The main questions are the stability of the estimation and the design of efficient algorithms. The techniques involve provably correct and stable versions of the method of moments and more general harmonic analysis. The main original result is a somewhat unexpected “blessing of dimensionality”, where we show that the problem of estimating the parameters of a Gaussian Mixture Model is generically easy in high dimension, while it is generically hard in low dimension.
Joint work with J. Anderson, M. Belkin, N. Goyal and J. Voss.