Related papers: Confidence Regions in Wasserstein Distributionally…
Learning algorithms that divide the data into batches are prevalent in many machine-learning applications, typically offering useful trade-offs between computational efficiency and performance. In this paper, we examine the benefits of…
We study distributionally robust optimization (DRO) problems where the ambiguity set is defined using the Wasserstein metric. We show that this class of DRO problems can be reformulated as semi-infinite programs. We give an exchange method…
The Wasserstein distance is a metric on a space of probability measures that has seen a surge of applications in statistics, machine learning, and applied mathematics. However, statistical aspects of Wasserstein distances are bottlenecked…
Distributionally Robust Optimization (DRO) provides a framework for decision-making under distributional uncertainty, yet its effectiveness can be compromised by outliers in the training data. This paper introduces a principled approach to…
Suppose we are given two metric spaces and a family of continuous transformations from one to the other. Given a probability distribution on each of these two spaces - namely the source and the target measures - the Wasserstein alignment…
How should researchers select experimental sites when the deployment population differs from observed data? I formulate the problem of experimental site selection as an optimal transport problem, developing methods to minimize downstream…
This article aims to introduce the paradigm of distributional robustness from the field of convex optimization to tackle optimal design problems under uncertainty. We consider realistic situations where the physical model, and thereby the…
Tukey's halfspace depth can be seen as a stochastic program and as such it is not guarded against optimizer's curse, so that a limited training sample may easily result in a poor out-of-sample performance. We propose a generalized halfspace…
Distribution data refers to a data set where each sample is represented as a probability distribution, a subject area receiving burgeoning interest in the field of statistics. Although several studies have developed…
Robust and distributionally robust optimization are modeling paradigms for decision-making under uncertainty where the uncertain parameters are only known to reside in an uncertainty set or are governed by any probability distribution from…
The problem of learning functions over spaces of probabilities - or distribution regression - is gaining significant interest in the machine learning community. A key challenge behind this problem is to identify a suitable representation…
The problem of modeling the relationship between univariate distributions and one or more explanatory variables has found increasing interest. Traditional functional data methods cannot be applied directly to distributional data because of…
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…
Wasserstein distributionally robust optimization (DRO) has recently achieved empirical success for various applications in operations research and machine learning, owing partly to its regularization effect. Although connection between…
The standard quadratic optimization problem (StQP) consists of minimizing a quadratic form over the standard simplex. Without assuming convexity or concavity of the quadratic form, the StQP is NP-hard. This problem has many interesting…
We propose a distributionally robust logistic regression model with an unfairness penalty that prevents discrimination with respect to sensitive attributes such as gender or ethnicity. This model is equivalent to a tractable convex…
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…
We study the decentralized distributed computation of discrete approximations for the regularized Wasserstein barycenter of a finite set of continuous probability measures distributedly stored over a network. We assume there is a network of…
Wasserstein distributionally robust optimization (\textsf{WDRO}) is a popular model to enhance the robustness of machine learning with ambiguous data. However, the complexity of \textsf{WDRO} can be prohibitive in practice since solving its…
We consider a general online stochastic optimization problem with multiple budget constraints over a horizon of finite time periods. In each time period, a reward function and multiple cost functions are revealed, and the decision maker…