Related papers: Causal Optimal Coupling for Gaussian Input-Output …
Sequential experimental design to discover interventions that achieve a desired outcome is a key problem in various domains including science, engineering and public policy. When the space of possible interventions is large, making an…
The paper addresses the problem of finding the causal direction between two associated variables. The proposed solution is to build an autoencoder of their joint distribution and to maximize its estimation capacity relative to both the…
Reconstructing dynamics using samples from sparsely time-resolved snapshots is an important problem in both natural sciences and machine learning. Here, we introduce a new deep learning approach for solving regularized unbalanced optimal…
In this paper, we study the Schr\"odinger Bridge Problem (SBP), which is central to entropic optimal transport. For general reference processes and begin--endpoint distributions, we propose a forward-reverse iterative Monte Carlo procedure…
Identifying causal relations among multi-variate time series is one of the most important elements towards understanding the complex mechanisms underlying the dynamic system. It provides critical tools for forecasting, simulations and…
A computational PDE-constrained optimization approach is proposed for optimal trajectory planning under uncertainty by means of an associated Schroedinger Bridge Problem (SBP). The proposed SBP formulation is interpreted as the mean-field…
We continue the study of adapted optimal transport in the discrete-time Gaussian setting. To this end, we introduce a space of filtered Gaussian processes where both the randomness and the flow of information are driven by a Gaussian white…
Score-based generative models have recently attracted significant attention for their ability to generate high-fidelity data by learning maps from simple Gaussian priors to complex data distributions. A natural generalization of this idea…
A Markovian master equation describing the evolution of open quantum systems in the presence of a time-dependent external field is derived within the Bloch-Redfield formalism. It leads to a system--bath interaction which depends on the…
This work deals with the asymptotic distribution of both potentials and couplings of entropic regularized optimal transport for compactly supported probabilities in $\R^d$. We first provide the central limit theorem of the Sinkhorn…
We propose a novel generative model for time series based on Schr{\"o}dinger bridge (SB) approach. This consists in the entropic interpolation via optimal transport between a reference probability measure on path space and a target measure…
After coarse-graining a complex system, the dynamics of its macro-state may exhibit more pronounced causal effects than those of its micro-state. This phenomenon, known as causal emergence, is quantified by the indicator of effective…
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…
For a fixed flow-based generative model under a small inference budget, sample quality can depend strongly on where the sampler spends its few function evaluations. Flow matching and Schr\"odinger bridges define probability paths, yet their…
Transportation on graphs is a fundamental challenge across many domains, where decisions must respect topological and operational constraints. Despite the need for actionable policies, existing graph-transport methods lack this…
In an intelligent transportation system, the effects and relations of traffic flow at different points in a network are valuable features which can be exploited for control system design and traffic forecasting. In this paper, we define the…
Entropic Optimal Transport (EOT), also referred to as the Schr\"odinger problem, seeks to find a random processes with prescribed initial/final marginals and with minimal relative entropy with respect to a reference measure. The relative…
We present a functional calculus treatment of Entropic Optimal Transport (EOT) between Gaussian measures on separable Hilbert spaces, providing a unified framework that handles infinite-dimensional degeneracy. By leveraging the notion of…
This paper is concerned with transition paths within the framework of the overdamped Langevin dynamics model of chemical reactions. We aim to give an efficient description of typical transition paths in the small temperature regime. We…
The Schr\"odinger Bridge (SB) problem has become a fundamental tool in computational optimal transport and generative modeling. To address this problem, ideal methods such as Iterative Proportional Fitting and Iterative Markovian Fitting…