B1979
Title: Finite sample guarantees of projection pursuit
Authors: Satyaki Mukherjee - Technical University of Munich (Germany) [presenting]
Abstract: Using projection pursuit, we consider the general dimensionality reduction problem of locating in a high-dimensional data cloud, a k-dimensional non-Gaussian subspace of interesting features. Consider a search for mutually orthogonal unit directions which maximise the 2-Wasserstein distance of the empirical distribution of data-projections along these directions from a standard Gaussian. Under a generative model, where there is a underlying (unknown) low-dimensional non-Gaussian subspace, we prove rigorous statistical guarantees on the accuracy of approximating this unknown subspace by the directions found by our projection pursuit approach. We also discuss ongoing research into the algorithmic side of projection pursuit. We discuss the various challenges differentiating the algorithmic problem from the statistical one.
