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Interactions are ubiquitous in our world, spanning from social interactions between human individuals to physical interactions between robots and objects to mechanistic interactions among different components of an intelligent system. Despite their prevale ...
Semi-discrete optimal transport problems, which evaluate the Wasserstein distance between a discrete and a generic (possibly non-discrete) probability measure, are believed to be computationally hard. Even though such problems are ubiquitous in statistics, ...
Mechanism design theory examines the design of allocation mechanisms or incentive systems involving multiple rational but self-interested agents and plays a central role in many societally important problems in economics. In mechanism design problems, agen ...
The maximal achievable advantage of a (computationally unbounded) distinguisher to determine whether a source Z is distributed according to distribution P0 or P1, when given access to one sample of Z, is characterized by the statistical distance ...
Many decision problems in science, engineering, and economics are affected by uncertainty, which is typically modeled by a random variable governed by an unknown probability distribution. For many practical applications, the probability distribution is onl ...
Stochastic optimization is a popular modeling paradigm for decision-making under uncertainty and has a wide spectrum of applications in management science, economics and engineering. However, the stochastic optimization models one faces in practice are int ...
We study stochastic programs where the decision-maker cannot observe the distribution of the exogenous uncertainties but has access to a finite set of independent samples from this distribution. In this setting, the goal is to find a procedure that transfo ...
Stochastic programming and distributionally robust optimization seek deterministic decisions that optimize a risk measure, possibly in view of the most adverse distribution in an ambiguity set. We investigate under which circumstances such deterministic de ...
Wasserstein distances are metrics on probability distributions inspired by the problem of optimal mass transportation. Roughly speaking, they measure the minimal effort required to reconfigure the probability mass of one distribution in order to recover th ...
We present a non-perturbative calculation of the 1-point probability distribution function (PDF) for the spherically-averaged matter density field. The PDF is represented as a path integral and is evaluated using the saddle-point method. It factorizes into ...
