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Gromov-Wasserstein (GW) is a powerful tool to compare probability measures whose supports are in different metric spaces. GW suffers however from a computational drawback since it requires to solve a complex non-convex quadratic program. We…
Conditional distribution is a fundamental quantity for describing the relationship between a response and a predictor. We propose a Wasserstein generative approach to learning a conditional distribution. The proposed approach uses a…
This brief note aims to introduce the recent paradigm of distributional robustness in the field of shape and topology optimization. Acknowledging that the probability law of uncertain physical data is rarely known beyond a rough…
Predicting the behavior of AI-driven agents is particularly challenging without a preexisting model. In our paper, we address this by treating AI agents as nonlinear dynamical systems and adopting a probabilistic perspective to predict…
Generating samples given a specific label requires estimating conditional distributions. We derive a tractable upper bound of the Wasserstein distance between conditional distributions to lay the theoretical groundwork to learn conditional…
This work presents the first systematic development of Stein's method for matrix distributions. We establish the basic essential ingredients of Stein's method for matrix normal approximation: we derive a generator-based Stein identity from…
We use adversarial network architectures together with the Wasserstein distance to generate or refine simulated detector data. The data reflect two-dimensional projections of spatially distributed signal patterns with a broad spectrum of…
Distributionally robust optimization (DRO)-based robust adaptive beamforming (RAB) enables enhanced robustness against model uncertainties, such as steering vector mismatches and interference-plus-noise covariance matrix estimation errors.…
A recurring obstacle in the study of Wasserstein gradient flow is the lack of convexity of the square Wasserstein metric. In this paper, we develop a class of transport metrics that have better convexity properties and use these metrics to…
Flow Matching has recently gained attention in generative modeling as a simple and flexible alternative to diffusion models. While existing statistical guarantees adapt tools from the analysis of diffusion models, we take a different…
Stein's method has been widely used for probability approximations. However, in the multi-dimensional setting, most of the results are for multivariate normal approximation or for test functions with bounded second- or higher-order…
We develop a finite-dimensional approximation of the Frobenius-Perron operator using the finite volume method applied to the continuity equation for the evolution of probability. A Courant-Friedrichs-Lewy condition ensures that the…
Squared Wasserstein distance is a frequently used tool to measure discrepancy between probability distributions. This distance is typically computed between empirical measures of size $n$ from two underlying random samples. Unfortunately,…
Feedback particle filter (FPF) is a numerical algorithm to approximate the solution of the nonlinear filtering problem in continuous-time settings. In any numerical implementation of the FPF algorithm, the main challenge is to numerically…
We study the scenario approach for solving chance-constrained optimization in time-coupled dynamic environments. Scenario generation methods approximate the true feasible region from scenarios generated independently and identically from…
Covariate shift arises when covariate distributions differ between source and target populations while the conditional distribution of the response remains invariant, and it underlies problems in missing data and causal inference. We…
Optimal experimental design (OED) aims to choose the observations in an experiment to be as informative as possible, according to certain statistical criteria. In the linear case (when the observations depend linearly on the unknown…
We study distribution-on-distribution regression problems in which a response distribution depends on multiple distributional predictors. Such settings arise naturally in applications where the outcome distribution is driven by several…
We study a variant of the dynamical optimal transport problem in which the energy to be minimised is modulated by the covariance matrix of the distribution. Such transport metrics arise naturally in mean-field limits of certain ensemble…
Free-energy-based adaptive biasing methods, such as Metadynamics, the Adaptive Biasing Force (ABF) and their variants, are enhanced sampling algorithms widely used in molecular simulations. Although their efficiency has been empirically…