相关论文: Conditional simulation via entropic optimal transp…
Many causal parameters depend on a moment of the joint distribution of potential outcomes. Such parameters are especially relevant in policy evaluation settings, where noncompliance is common and accommodated through the model of Imbens &…
In many statistical settings, two types of data are available: coupled data, which preserve the joint structure among variables but are limited in size due to cost or privacy constraints, and marginal data, which are available at larger…
Entropically regularized optimal transport between probability measures supported on compact subsets of Euclidean space admits a representation as an information projection under moment inequality constraints. Exploiting this structure, I…
We propose a generative multivariate posterior sampler via flow matching. It offers a simple training objective, and does not require access to likelihood evaluation. The method learns a dynamic, block-triangular velocity field in the joint…
Optimal transport (OT) serves as a natural framework for comparing probability measures, with applications in statistics, machine learning, and applied mathematics. Alas, statistical estimation and exact computation of the OT distances…
Transporting causal information across populations is a critical challenge in clinical decision-making. Causal modeling provides criteria for identifiability and transportability, but these require knowledge of the causal graph, which…
The Optimal Transport (OT) problem investigates a transport map that connects two distributions while minimizing a given cost function. Finding such a transport map has diverse applications in machine learning, such as generative modeling…
In many inverse problems, model parameters cannot be precisely determined from observational data. Bayesian inference provides a mechanism for capturing the resulting parameter uncertainty, but typically at a high computational cost. This…
We address optimal control problems on the space of measures for an objective containing a smooth functional and an optimal transport regularization. That is, the quadratic Monge-Kantorovich distance between a given prior measure and the…
We study stochastic gradient descent for solving conditional stochastic optimization problems, in which an objective to be minimized is given by a parametric nested expectation with an outer expectation taken with respect to one random…
When faced with a small sample from a large universe of possible outcomes, scientists often turn to the venerable Good--Turing estimator. Despite its pedigree, however, this estimator comes with considerable drawbacks, such as the need to…
In this note we prove that in a metric measure space $(X, d, m)$ verifying the measure contraction property with parameters $K \in \mathbb{R}$ and $1< N< \infty$, any optimal transference plan between two marginal measures is induced by an…
We study the regularity properties of the minimisers of entropic optimal transport providing a natural analogue of the $\varepsilon$-regularity theory of quadratic optimal transport in the entropic setting. More precisely, we show that if…
Nonparametric Bayesian models are used routinely as flexible and powerful models of complex data. Many times, a statistician may have additional informative beliefs about data distribution of interest, e.g., its mean or subset components,…
In compact settings, the convergence rate of the empirical optimal transport cost to its population value is well understood for a wide class of spaces and cost functions. In unbounded settings, however, hitherto available results require…
This paper develops a set of empirically tractable and flexible sieve estimators for semi-nonparametric multidimensional matching models with transferable utility, focusing on worker-job matching. We generalize the parametric…
The Gromov--Wasserstein problem is a non-convex optimization problem over the polytope of transportation plans between two probability measures supported on two spaces, each equipped with a cost function evaluating similarities between…
In machine learning and computer vision, optimal transport has had significant success in learning generative models and defining metric distances between structured and stochastic data objects, that can be cast as probability measures. The…
Given samples from two joint distributions, we consider the problem of Optimal Transportation (OT) between them when conditioned on a common variable. We focus on the general setting where the conditioned variable may be continuous, and the…
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…