Testing for equality of two high-dimensional distributions is a challenging problem, and this becomes even more challenging when the sample size is small. Over the last few decades, several graph-based two-sample tests have been proposed in the literature, ...
We consider two statistical problems at the intersection of functional and non-Euclidean data analysis: the determination of a Fréchet mean in the Wasserstein space of multivariate distributions; and the optimal registration of deformed random measures and ...
We study some linear and nonlinear shot noise models where the jumps are drawn from a compound Poisson process with jump sizes following an Erlang-m distribution. We show that the associated Master equation can be written as a spatial mth order partial dif ...
We present new techniques to analyze natural local search algorithms for several variants of the max-sum diversification problem which, in its most basic form, is as follows: given an n-point set X subset of R-d and an integer k, select k points in X so th ...
Percolation, in its most general interpretation, refers to the “flow” of something (a physical agent, data or information) in a network, possibly accompanied by some nonlinear dynamical processes on the network nodes (sometimes denoted reaction–diffusion s ...
Consider a random process s that is a solution of the stochastic differential equation Ls = w with L a homogeneous operator and w a multidimensional Levy white noise. In this paper, we study the asymptotic effect of zooming in or zooming out of the process ...
We present a general theory of Group equivariant Convolutional Neural Networks (G-CNNs) on homogeneous spaces such as Euclidean space and the sphere. Feature maps in these networks represent fields on a homogeneous base space, and layers are equivariant ma ...
3D objects, modeled using Computer Aided Geometric Design (CAGD) tools, are traditionally represented using a boundary representation (B-rep), and typically use spline functions to parameterize these boundary surfaces. However, recent development in physic ...
Governments choose to issue risky or riskless debt depending on the nature of the stochastic process of output. We use Brownian motion and Poisson shocks a modeling method in the literature on corporate default known as Levy processes to approximate a deco ...
