Related papers: Sliced Distribution Matching based on Cumulative D…
Real-life data are often non-IID due to complex distributions and interactions, and the sensitivity to the distribution of samples can differ among learning models. Accordingly, a key question for any supervised or unsupervised model is…
Distance correlation has become an increasingly popular tool for detecting the nonlinear dependence between a pair of potentially high-dimensional random vectors. Most existing works have explored its asymptotic distributions under the null…
Kernel embeddings of distributions and the Maximum Mean Discrepancy (MMD), the resulting distance between distributions, are useful tools for fully nonparametric two-sample testing and learning on distributions. However, it is rarely that…
Distance distributions are a key building block in stochastic geometry modelling of wireless networks and in many other fields in mathematics and science. In this paper, we propose a novel framework for analytically computing the closed…
We compute a number of distance-dependent universal scaling functions characterizing the distance statistics of large maps of genus one. In particular, we obtain explicitly the probability distribution for the length of the shortest…
This work briefly explores the possibility of approximating spatial distance (alternatively, similarity) between data points using the Isolation Forest method envisioned for outlier detection. The logic is similar to that of isolation: the…
We consider conservative cross-diffusion systems for two species where individual motion rates depend linearly on the local density of the other species. We develop duality estimates and obtain stability and approximation results. We first…
This work builds a unified framework for the study of quadratic form distance measures as they are used in assessing the goodness of fit of models. Many important procedures have this structure, but the theory for these methods is dispersed…
The quantale of distance distributions is of fundamental importance for understanding probabilistic metric spaces as enriched categories. Motivated by the categorical interpretation of partial metric spaces, we are led to investigate the…
We derive distributional limits for empirical transport distances between probability measures supported on countable sets. Our approach is based on sensitivity analysis of optimal values of infinite dimensional mathematical programs and a…
We present a theory for slicing probabilistic imperative programs -- containing random assignments, and ``observe'' statements (for conditioning) -- represented as probabilistic control-flow graphs (pCFGs) whose nodes modify probability…
This report presents a new, algorithmic approach to the distributions of the distance between two points distributed uniformly at random in various polygons, based on the extended Kinematic Measure (KM) from integral geometry. We first…
Optimal transport with quadratic cost provides a geometric framework for steering an ensemble, modeled by a probability law, with minimal effort. Yet ambient-space formulations become unwieldy in high dimensions, and sensing or actuation in…
This paper presents a distributed stochastic model predictive control (SMPC) approach for large-scale linear systems with private and common uncertainties in a plug-and-play framework. Using the so-called scenario approach, the centralized…
We conduct a KL-divergence based procedure for testing elliptical distributions. The procedure simultaneously takes into account the two defining properties of an elliptically distributed random vector: independence between length and…
In this paper, we consider robust control using randomized algorithms. We extend the existing order statistics distribution theory to the general case in which the distribution of population is not assumed to be continuous and the order…
In this paper we discuss a class of AutoEncoder based generative models based on one dimensional sliced approach. The idea is based on the reduction of the discrimination between samples to one-dimensional case. Our experiments show that…
Modern randomization methods in clinical trials are invariably adaptive, meaning that the assignment of the next subject to a treatment group uses the accumulated information in the trial. Some of the recent adaptive randomization methods…
In this article we present very intuitive, easy to follow, yet mathematically rigorous, approach to the so called data fitting process. Rather than minimizing the distance between measured and simulated data points, we prefer to find such…
The design of a metric between probability distributions is a longstanding problem motivated by numerous applications in Machine Learning. Focusing on continuous probability distributions on the Euclidean space $\mathbb{R}^d$, we introduce…