Related papers: A minimax approach to duality for linear distribut…

We study the dimensional Brunn-Minkowski inequality for even log-concave probability measures $\mu$ on $\mathbb{R}^n$ via an analytic approach based on diffusion operators and gradient estimates. Our main result asserts that for every pair…

We explore the minimax optimality of goodness-of-fit tests on general domains using the kernelized Stein discrepancy (KSD). The KSD framework offers a flexible approach for goodness-of-fit testing, avoiding strong distributional…

We study the problem of independence testing given independent and identically distributed pairs taking values in a $\sigma$-finite, separable measure space. Defining a natural measure of dependence $D(f)$ as the squared $L^2$-distance…

We introduce the post-processing preorder and equivalence relations for general measurements on a possibly infinite-dimensional general probabilistic theory described by an order unit Banach space $E$ with a Banach predual. We define the…

The small amount of measurements in distribution grids makes their monitoring more difficult. Topological observability may not be possible, and thus, pseudo-measurements are needed to perform state estimation, which is required to control…

We consider the problem of estimating functionals of discrete distributions, and focus on tight nonasymptotic analysis of the worst case squared error risk of widely used estimators. We apply concentration inequalities to analyze the random…

We apply duality theory to discretized convex minimization problems to obtain computable guaranteed upper bounds for the distance of given discrete functions and the exact discrete minimizer. Furthermore, we show that the discrete duality…

We study the question of closeness testing for two discrete distributions. More precisely, given samples from two distributions $p$ and $q$ over an $n$-element set, we wish to distinguish whether $p=q$ versus $p$ is at least $\eps$-far from…

The aim of this paper is to address optimality of stochastic control strategies via dynamic programming subject to total variation distance ambiguity on the conditional distribution of the controlled process. We formulate the stochastic…

We study the transportation problem on the unit sphere $S^{n-1}$ for symmetric probability measures and the cost function $c(x,y) = \log \frac{1}{\langle x, y \rangle}$. We calculate the variation of the corresponding Kantorovich functional…

We study the problem of maximizing a spectral risk measure of a given output function which depends on several underlying variables, whose individual distributions are known but whose joint distribution is not. We establish and exploit an…

We give a general unified method that can be used for $L_1$ {\em closeness testing} of a wide range of univariate structured distribution families. More specifically, we design a sample optimal and computationally efficient algorithm for…

We study the problem of transporting one probability measure to another via an autonomous velocity field. We rely on tools from the theory of optimal transport. In one space-dimension, we solve a linear homogeneous functional equation to…

Consider the class of zero-mean functions with fixed $L^{\infty}$ and $L^1$ norms and exactly $N\in \mathbb{N}$ nodal points. Which functions $f$ minimize $W_p(f_+,f_-)$, the Wasserstein distance between the measures whose densities are the…

We analyze a recently proposed class of algorithms for the problem of sampling from probability distributions $\mu^\ast$ in $\mathbb{R}^d$ with a Lebesgue density of the form $\mu^\ast(x) \propto \exp(-f(Kx)-g(x))$, where $K$ is a linear…

This paper considers an ML inspired approach to hypothesis testing known as classifier/classification-accuracy testing ($\mathsf{CAT}$). In $\mathsf{CAT}$, one first trains a classifier by feeding it labeled synthetic samples generated by…

The lack of measurements in distribution grids poses a severe challenge for their monitoring: since there may not be enough sensors to achieve numerical observability, load forecasts (pseudo-measurements) are typically used, and thus an…

This paper studies a discrepancy-sensitive approach to dynamic fractional cascading. We provide an efficient data structure for dominated maxima searching in a dynamic set of points in the plane, which in turn leads to an efficient dynamic…

We consider the problem of comparing probability densities between two groups. A new probabilistic tensor product smoothing spline framework is developed to model the joint density of two variables. Under such a framework, the probability…

We study the optimal transport problem for $d>2$ discrete measures. This is a linear programming problem on $d$-tensors. It gives a way to compute a "distance" between two sets of discrete measures. We introduce an entropic regularization…