Related papers: Distributionally Robust Prescriptive Analytics wit…

Given a collection of probability measures, a practitioner sometimes needs to find an "average" distribution which adequately aggregates reference distributions. A theoretically appealing notion of such an average is the Wasserstein…

In data-driven learning and inference tasks, the high cost of acquiring samples from the target distribution often limits performance. A common strategy to mitigate this challenge is to augment the limited target samples with data from a…

Standard rare-event simulation techniques require exact distributional specifications, which limits their effectiveness in the presence of distributional uncertainty. To address this, we develop a novel framework for estimating rare-event…

Robust estimation for modern portfolio selection on a large set of assets becomes more important due to large deviation of empirical inference on big data. We propose a distributionally robust methodology for high-dimensional mean-variance…

Deep neural networks are known to be vulnerable to adversarial attacks (AA). For an image recognition task, this means that a small perturbation of the original can result in the image being misclassified. Design of such attacks as well as…

Existing approaches to depth or disparity estimation output a distribution over a set of pre-defined discrete values. This leads to inaccurate results when the true depth or disparity does not match any of these values. The fact that this…

This paper studies a class of multiagent stochastic optimization problems where the objective is to minimize the expected value of a function which depends on a random variable. The probability distribution of the random variable is unknown…

We study distributionally robust optimization (DRO) problems with uncertainty sets consisting of high-dimensional random vectors that are close in the multivariate Wasserstein distance to a reference random vector. We give conditions when…

Distribution forecast can quantify forecast uncertainty and provide various forecast scenarios with their corresponding estimated probabilities. Accurate distribution forecast is crucial for planning - for example when making production…

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…

Studied here are Wasserstein generative adversarial networks (WGANs) with GroupSort neural networks as their discriminators. It is shown that the error bound of the approximation for the target distribution depends on the width and depth…

While statistical modeling of distributional data has gained increased attention, the case of multivariate distributions has been somewhat neglected despite its relevance in various applications. This is because the Wasserstein distance,…

In this paper we propose tight upper and lower bounds for the Wasserstein distance between any two {{univariate continuous distributions}} with probability densities $p_1$ and $p_2$ having nested supports. These explicit bounds are…

This paper investigates the robust optimal control of sampled-data stochastic systems with multiplicative noise and distributional ambiguity. We consider a class of discrete-time optimal control problems where the controller \emph{jointly}…

Model Updating is frequently used in Structural Health Monitoring to determine structures' operating conditions and whether maintenance is required. Data collected by sensors are used to update the values of some initially unknown…

We present a data-driven approach for distributionally robust chance constrained optimization problems (DRCCPs). We consider the case where the decision maker has access to a finite number of samples or realizations of the uncertainty. The…

Distributionally robust optimization has emerged as an attractive way to train robust machine learning models, capturing data uncertainty and distribution shifts. Recent statistical analyses have proved that generalization guarantees of…

In this paper, by proposing two new kinds of distributional uncertainty sets, we explore robustness of distortion risk measures against distributional uncertainty. To be precise, we first consider a distributional uncertainty set which is…

We study the robust quickest change detection under unknown pre- and post-change distributions. To deal with uncertainties in the data-generating distributions, we formulate two data-driven ambiguity sets based on the Wasserstein distance,…

Consider a setting with multiple units (e.g., individuals, cohorts, geographic locations) and outcomes (e.g., treatments, times, items), where the goal is to learn a multivariate distribution for each unit-outcome entry, such as the…