Related papers: Causal Optimal Coupling for Gaussian Input-Output …
In decision-making problems, the outcome of an intervention often depends on the causal relationships between system components and is highly costly to evaluate. In such settings, causal Bayesian optimization (CBO) can exploit the causal…
The solution of the path structured multimarginal Schr\"{o}dinger bridge problem (MSBP) is the most-likely measure-valued trajectory consistent with a sequence of observed probability measures or distributional snapshots. We leverage recent…
We formulate and solve a regression problem with time-stamped distributional data. Distributions are considered as points in the Wasserstein space of probability measures, metrized by the 2-Wasserstein metric, and may represent images,…
Causal discovery aims to uncover cause-and-effect relationships encoded in causal graphs by leveraging observational, interventional data, or their combination. The majority of existing causal discovery methods are developed assuming…
This paper investigates causal optimal transportation problems, in the framework of two Polish spaces, both endowed with filtrations. Specific concretizations yield primal problems equivalent to several classical problems of stochastic…
This article is aimed at presenting the Schr\"odinger problem and some of its connections with optimal transport. We hope that it can be used as a basic user's guide to Schr\"odinger problem. We also give a survey of the related literature.…
Multi-marginal Optimal Transport (mOT), a generalization of OT, aims at minimizing the integral of a cost function with respect to a distribution with some prescribed marginals. In this paper, we consider an entropic version of mOT with a…
The article presents new entropic continuity bounds for conditional expectations and conditional covariance matrices. These bounds are expressed in terms of the relative entropy between different coupling distributions. Our approach…
Fundamental and necessary principles for achieving efficient portfolio optimization based on asset and diversification dynamics are presented. The Commonality Principle is a necessary and sufficient condition for identifying optimal drivers…
We consider transport over a strongly connected, directed graph. The scheduling amounts to selecting transition probabilities for a discrete-time Markov evolution which is designed to be consistent with certain initial and final marginals.…
The theory of optimal transportation has developed into a powerful and elegant framework for comparing probability distributions, with wide-ranging applications in all areas of science. The fundamental idea of analyzing probabilities by…
Optimal transport (OT) and Schr{\"o}dinger bridge (SB) problems have emerged as powerful frameworks for transferring probability distributions with minimal cost. However, existing approaches typically focus on endpoint matching while…
A new pairwise cost function is proposed for the optimal transport barycenter problem, adopting the form of the minimal action between two points, with a Lagrangian that takes into account an underlying probability distribution. Under this…
Many numerical and learning algorithms rely on the solution of the Monge-Kantorovich problem and Wasserstein distances, which provide appropriate distributional metrics. While the natural approach is to treat the problem as an…
Simulating longitudinal data from specified marginal structural models is a crucial but challenging task for evaluating causal inference methods and informing study design. While data generation typically proceeds in a fully conditional…
Understanding complex systems by inferring trajectories from sparse sample snapshots is a fundamental challenge in a wide range of domains, e.g., single-cell biology, meteorology, and economics. Despite advancements in Bridge and Flow…
Traffic forecasting is an important application of spatiotemporal series prediction. Among different methods, graph neural networks have achieved so far the most promising results, learning relations between graph nodes then becomes a…
We introduce an approach to inferring the causal architecture of stochastic dynamical systems that extends rate distortion theory to use causal shielding---a natural principle of learning. We study two distinct cases of causal inference:…
We propose to learn the time-varying stochastic computational resource usage of software as a graph structured Schr\"odinger bridge problem. In general, learning the computational resource usage from data is challenging because resources…
We consider the problem of stochastic optimal control, where the state-feedback control policies take the form of a probability distribution and where a penalty on the entropy is added. By viewing the cost function as a Kullback- Leibler…