Related papers: A primer on optimal transport for causal inference…

In the current book I suggest an off-road path to the subject of optimal transport. I tried to avoid prior knowledge of analysis, PDE theory and functional analysis, as much as possible. Thus I concentrate on discrete and semi-discrete…

The basic optimal transportation problem consists in finding the most effective way of moving masses from one location to another, while minimizing the transportation cost. Such concept has been found to be useful to understand various…

Accurate trajectory prediction has long been a major challenge for autonomous driving (AD). Traditional data-driven models predominantly rely on statistical correlations, often overlooking the causal relationships that govern traffic…

The martingale part in the semimartingale decomposition of a Brownian motion with respect to an enlargement of its filtration, is an anticipative mapping of the given Brownian motion. In analogy to optimal transport theory, we define causal…

We propose a nonlinear difference-in-differences method to estimate multivariate counterfactual distributions in classical treatment and control study designs with observational data. Our approach sheds a new light on existing approaches…

Recently, Optimal Transport has been proposed as a probabilistic framework in Machine Learning for comparing and manipulating probability distributions. This is rooted in its rich history and theory, and has offered new solutions to…

In the absence of randomized controlled and natural experiments, it is necessary to balance the distributions of (observable) covariates of the treated and control groups in order to obtain an unbiased estimate of a causal effect of…

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:…

In this paper, we link two existing approaches to derive counterfactuals: adaptations based on a causal graph, and optimal transport. We extend "Knothe's rearrangement" and "triangular transport" to probabilistic graphical models, and use…

This paper is about the general disconnect that we see, both in practice and in literature, between the disciplines of travel demand modeling and causal inference. In this paper, we assert that travel demand modeling should be one of the…

Causality is a subject of philosophical debate and a central scientific issue with a long history. In the statistical domain, the study of cause and effect based on the notion of `fairness' in comparisons dates back several hundred years,…

In this work, we investigate an optimization problem over adapted couplings between pairs of real valued random variables, possibly describing random times. We relate those couplings to a specific class of causal transport plans between…

Statistical science (as opposed to mathematical statistics) involves far more than probability theory, for it requires realistic causal models of data generators - even for purely descriptive goals. Statistical decision theory requires more…

We consider the optimal mass transportation problem in $\RR^d$ with measurably parameterized marginals, for general cost functions and under conditions ensuring the existence of a unique optimal transport map. We prove a joint measurability…

We provide a unifying interpretation of various optimal transport problems as a minimisation of a linear functional over the set of all Choquet representations of a given pair of probability measures ordered with respect to a certain convex…

Many problems ask a question that can be formulated as a causal question: "what would have happened if...?" For example, "would the person have had surgery if he or she had been Black?" To address this kind of questions, calculating an…

Drawing from the theory of optimal transport we propose a rigorous notion of a causal relation for Borel probability measures on a given spacetime. To prepare the ground, we explore the borderland between causality, topology and measure…

To study discrimination in automated decision-making systems, scholars have proposed several definitions of fairness, each expressing a different fair ideal. These definitions require practitioners to make complex decisions regarding which…

To determine causal relationships between two variables, approaches based on Functional Causal Models (FCMs) have been proposed by properly restricting model classes; however, the performance is sensitive to the model assumptions, which…

We address the open question of counterfactual identification for high-dimensional multivariate outcomes from observational data. Pearl (2000) argues that counterfactuals must be identifiable (i.e., recoverable from the observed data…