Related papers: Designing Ambiguity Sets for Distributionally Robu…

Uncertainty sets are at the heart of robust optimization (RO) because they play a key role in determining the RO models' tractability, robustness, and conservativeness. Different types of uncertainty sets have been proposed that model…

This paper focuses on solving a data-driven distributionally robust optimization problem over a network of agents. The agents aim to minimize the worst-case expected cost computed over a Wasserstein ambiguity set that is centered at the…

Causal discovery from observational data is an important tool in many branches of science. Under certain assumptions it allows scientists to explain phenomena, predict, and make decisions. In the large sample limit, sound and complete…

Decision making under uncertainty is challenging as the data-generating process (DGP) is often unknown. Bayesian inference proceeds by estimating the DGP through posterior beliefs on the model's parameters. However, minimising the expected…

Conditional Optimal Transport (COT) problem aims to find a transport map between conditional source and target distributions while minimizing the transport cost. Recently, these transport maps have been utilized in conditional generative…

Estimating the structure of directed acyclic graphs (DAGs, also known as Bayesian networks) is a challenging problem since the search space of DAGs is combinatorial and scales superexponentially with the number of nodes. Existing approaches…

Building on a recent framework for distributionally robust optimization, we consider estimation of the inverse covariance matrix for multivariate data. We provide a novel notion of a Wasserstein ambiguity set specifically tailored to this…

Transport systems on networks are crucial in various applications, but face a significant risk of being adversely affected by unforeseen circumstances such as disasters. The application of entropy-regularized optimal transport (OT) on graph…

This paper proposes distributed algorithms to solve robust convex optimization (RCO) when the constraints are affected by nonlinear uncertainty. We adopt a scenario approach by randomly sampling the uncertainty set. To facilitate the…

This paper deals with an optimization problem over a network of agents, where the cost function is the sum of the individual objectives of the agents and the constraint set is the intersection of local constraints. Most existing methods…

In robust optimization, we would like to find a solution that is immunized against all scenarios that are modeled in an uncertainty set. Which scenarios to include in such a set is therefore of central importance for the tractability of the…

The goal of regression and classification methods in supervised learning is to minimize the empirical risk, that is, the expectation of some loss function quantifying the prediction error under the empirical distribution. When facing scarce…

Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…

Topology Optimization seeks to find the best design that satisfies a set of constraints while maximizing system performance. Traditional iterative optimization methods like SIMP can be computationally expensive and get stuck in local…

Robust optimization methods have shown practical advantages in a wide range of decision-making applications under uncertainty. Recently, their efficacy has been extended to multi-period settings. Current approaches model uncertainty either…

Conformal predictive systems are sets of predictive distributions with theoretical out-of-sample calibration guarantees. The calibration guarantees are typically that the set of predictions contains a forecast distribution whose prediction…

We introduce a two-stage probabilistic framework for statistical downscaling using unpaired data. Statistical downscaling seeks a probabilistic map to transform low-resolution data from a biased coarse-grained numerical scheme to…

We address the problem of generating simulated, yet realistic, time-series data from a causal model with the same observational and interventional distributions as a given real dataset (probabilistic causal digital twin). While non-causal…

Following [21, 23], the present work investigates a new relative entropy-regularized algorithm for solving the optimal transport on a graph problem within the randomized shortest paths formalism. More precisely, a unit flow is injected into…

This work addresses the problem of learning directed acyclic graphs (DAGs) from nodal observations generated by a linear structural equation model. DAG learning is a central task in signal processing, machine learning, and causal inference,…