Related papers: Causal Optimal Coupling for Gaussian Input-Output …
Computational optimal transport (OT) has recently emerged as a powerful framework with applications in various fields. In this paper we focus on a relaxation of the original OT problem, the entropic OT problem, which allows to implement…
An exact expression of the bridge-mediated donor-acceptor effective coupling, is derived. For systems represented by a tight-binding Hamiltonian with nearest-neighbor interactions, we show that the effective coupling, is equal to the…
Estimating causal interactions in complex dynamical systems is an important problem encountered in many fields of current science. While a theoretical solution for detecting the causal interactions has been previously formulated in the…
Inferring the coupling structure of complex systems from time series data in general by means of statistical and information-theoretic techniques is a challenging problem in applied science. The reliability of statistical inferences…
We propose a new method of discovering causal relationships in temporal data based on the notion of causal compression. To this end, we adopt the Pearlian graph setting and the directed information as an information theoretic tool for…
We consider a discrete-time linear-quadratic Gaussian control problem in which we minimize a weighted sum of the directed information from the state of the system to the control input and the control cost. The optimal control and sensing…
Causal inference provides an analytical framework to identify and quantify cause-and-effect relationships among a network of interacting agents. This paper offers a novel framework for analyzing cascading failures in power transmission…
We propose constrained causal Bayesian optimization (cCBO), an approach for finding interventions in a known causal graph that optimize a target variable under some constraints. cCBO first reduces the search space by exploiting the graph…
Many modern distributed systems consist of devices that generate more data than what can be transmitted via a communication link in near real time with high-fidelity. We consider the scheduling problem in which a device has access to…
Resampling from a target measure whose density is unknown is a fundamental problem in mathematical statistics and machine learning. A setting that dominates the machine learning literature consists of learning a map from an easy-to-sample…
In this paper, we present a variational treatment of the linear dependence for a non-orthogonal time-dependent basis set in solving the Schr\"odinger equation. The method is based on: i) the definition of a linearly independent working…
Optimal transport is the problem of designing a joint distribution for two random variables with fixed marginals. In virtually the entire literature on this topic, the objective is to minimize expected cost. This paper is the first to study…
The Entropic Optimal Transport (EOT) problem and its dynamic counterpart, the Schr\"odinger bridge (SB) problem, play an important role in modern machine learning, linking generative modeling with optimal transport theory. While recent…
In this paper, we introduce a framework for contextual distributionally robust optimization (DRO) that considers the causal and continuous structure of the underlying distribution by developing interpretable and tractable decision rules…
Sampling conditional distributions is a fundamental task for Bayesian inference and density estimation. Generative models, such as normalizing flows and generative adversarial networks, characterize conditional distributions by learning a…
We formulate and solve a class of finite-time transport and mixing problems in the set-oriented framework. The aim is to obtain optimal discrete-time perturbations in nonlinear dynamical systems to transport a specified initial measure on…
Learning a causal directed acyclic graph from data is a challenging task that involves solving a combinatorial problem for which the solution is not always identifiable. A new line of work reformulates this problem as a continuous…
Traffic dynamics on single or isolated complex networks has been extensively studied in the past decade. Recently, several coupled network models have been developed to describe the interactions between real-world networked systems. In a…
We study the problem of identifying the causal relationship between two discrete random variables from observational data. We recently proposed a novel framework called entropic causality that works in a very general functional model but…
We address the problem of Schr\"odinger potential estimation, which plays a crucial role in modern generative modelling approaches based on Schr\"odinger bridges and stochastic optimal control for SDEs. Given a simple prior diffusion…