We present a mathematical analysis of a non-convex energy landscape for Robust Subspace Recovery. Under a deterministic condition, the only stationary point in a large neighborhood of an underlying subspace is the subspace itself. The same deterministic condition implies that a geodesic gradient descent method can exactly recover the underlying …
Integration against an intractable probability measure is among the fundamental challenges of Bayesian inference. A useful approach to this problem seeks a deterministic coupling of the measure of interest with a tractable “reference” measure (e.g., a standard Gaussian). This coupling is induced by a transport map, and enables direct simulation …
In statistical learning theory, generalization error is used to quantify the degree to which a supervised machine learning algorithm may overfit to training data. We overview some recent work [Xu and Raginsky (2017)] that bounds generalization error of empirical risk minimization based on the mutual information I(S;W) between the algorithm …
Willem’s Abstract: Atmospheric light detection and ranging (lidar) provides a unique capability to resolve atmospheric vertical structures of clouds and aerosols with very high sensitivity at high altitude and temporal resolutions. A variety of lidar instruments exist which focus on the measurement of the optical properties of the atmosphere in …
With the availability of huge amounts of unlabeled data, unsupervised learning methods are gaining increasing popularity and importance. We focus on ”unsupervised ensemble learning”, where one obtains the predictions of multiple classifiers over a set of unlabeled instances. The classifiers may be human experts as in crowdsourcing, or prediction algorithms …
High-dimensional high-order arrays, or tensors, arise in many modern scientific applications including genomics, brain imaging, and social science. In this talk, we consider two specific problems in tensor data analysis: low-rank tensor completion and tensor SVD. We first propose a framework for low-rank tensor completion via a novel tensor measurement …