Related papers: Coherent distributions: Hilbert space approach and…
In this paper, the distribution dependent stochastic differential equation in a separable Hilbert space with a Dini continuous drift is investigated. The existence and uniqueness of weak and strong solutions are obtained. Moreover, some…
We study the problem of computing the tightest upper and lower bounds on the probability that the sum of $n$ dependent Bernoulli random variables exceeds an integer $k$. Under knowledge of all pairs of bivariate distributions denoted by a…
In this paper we address the complexity of solving linear programming problems with a set of differential equations that converge to a fixed point that represents the optimal solution. Assuming a probabilistic model, where the inputs are…
It is well known that the entropy $H(X)$ of a discrete random variable $X$ is always greater than or equal to the entropy $H(f(X))$ of a function $f$ of $X$, with equality if and only if $f$ is one-to-one. In this paper, we give tight…
While useful probability bounds for $n$ pairwise independent Bernoulli random variables adding up to at least an integer $k$ have been proposed in the literature, none of these bounds are tight in general. In this paper, we provide several…
Hausel and Rodriguez-Villegas recently observed that work of G\"ottsche, combined with a classical result of Erd\H{o}s and Lehner on integer partitions, implies that the limiting Betti distribution for the Hilbert schemes…
We focus on the distribution regression problem: regressing to a real-valued response from a probability distribution. Although there exist a large number of similarity measures between distributions, very little is known about their…
In this paper, we propose a new distribution with unitary support which can be characterized as a ratio of the type $W=X_1/(X_1+X_2)$, where $(X_1, X_2)^\top$ follows a bivariate extreme distribution with Fr\'echet margins, that is, $X_1$…
We study control of constrained linear systems with only partial statistical information about the uncertainty affecting the system dynamics and the sensor measurements. Specifically, given a finite collection of disturbance realizations…
We study the sharp bounds of $\mathbb{E}[X_1\cdots X_d]$ when the univariate marginal distributions are known, but the dependence structure between them is unspecified. Maximizing products over non-negative variables is straightforward via…
We imagine an experiment on an unknown quantum mechanical system in which the system is prepared in various ways and a range of measurements are performed. For each measurement M and preparation rho the experimenter can determine, given…
A/B testing refers to the task of determining the best option among two alternatives that yield random outcomes. We provide distribution-dependent lower bounds for the performance of A/B testing that improve over the results currently…
We focus on the distribution regression problem: regressing to vector-valued outputs from probability measures. Many important machine learning and statistical tasks fit into this framework, including multi-instance learning and point…
We investigate convergence properties of discrete-time semigroup quantum dynamics, including asymptotic stability, probability and speed of convergence to pure states and subspaces. These properties are of interest in both the analysis of…
This paper expands the notion of robust moment problems to incorporate distributional ambiguity using Wasserstein distance as the ambiguity measure. The classical Chebyshev-Cantelli (zeroth partial moment) inequalities, Scarf and Lo (first…
We address the challenge of sequential data-driven decision-making under context distributional uncertainty. This problem arises in numerous real-world scenarios where the learner optimizes black-box objective functions in the presence of…
Previous results indicate that while chaos can lead to substantial entropy production, thereby maximizing dynamical entanglement, this still falls short of maximality. Random Matrix Theory (RMT) modeling of composite quantum systems,…
Let X be a locally compact Abelian group. We consider linear forms of independent random variables with values in X. In doing so, one of the coefficients of the linear forms is a random variable with a Bernoulli distribution. For some…
We consider a system of weak* closed sets of finite-dimensional distributions. We show that a corresponding system of random variables can be defined on a probability space with a probability measure determined up to some set of measures,…
We consider an elliptic problem with unknowns on the boundary of the domain of the elliptic equation and suppose that the right-hand side of this equation is square integrable and that the boundary data are arbitrary (specifically,…