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We consider stochastic programs where the distribution of the uncertain parameters is only observable through a finite training dataset. Using the Wasserstein metric, we construct a ball in the space of (multivariate and non-discrete)…
Inverse problems in physical or biological sciences often involve recovering an unknown parameter that is random. The sought-after quantity is a probability distribution of the unknown parameter, that produces data that aligns with…
We introduce a general framework for analyzing data modeled as parameterized families of networks. Building on a Gromov-Wasserstein variant of optimal transport, we define a family of parameterized Gromov-Wasserstein distances for comparing…
Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions. A key challenge, especially in high-dimensional settings, is to determine the mixture order and estimate the…
Finite mixture models have long been used across a variety of fields in engineering and sciences. Recently there has been a great deal of interest in quantifying the convergence behavior of the \emph{mixing measure}, a fundamental object…
This paper focuses on a similarity measure, known as the Wasserstein distance, with which to compare images. The Wasserstein distance results from a partial differential equation (PDE) formulation of Monge's optimal transport problem. We…
Flow matching has recently emerged as a flexible and efficient framework for generative modelling by learning deterministic transport dynamics between probability measures. In this work, we extend flow matching to the space of probability…
Wild animals are commonly fitted with trackers that record their position through time, and statistical models for tracking data broadly fall into two categories: models focused on small-scale movement decisions, and models for large-scale…
Systems consisting of spheres rolling on elastic membranes have been used to introduce a core conceptual idea of General Relativity (GR): how curvature guides the movement of matter. However, such schemes cannot accurately represent…
Learning algorithms for implicit generative models can optimize a variety of criteria that measure how the data distribution differs from the implicit model distribution, including the Wasserstein distance, the Energy distance, and the…
Mutual information maximization has emerged as a powerful learning objective for unsupervised representation learning obtaining state-of-the-art performance in applications such as object recognition, speech recognition, and reinforcement…
We address the problem of efficiently computing Wasserstein distances for multiple pairs of distributions drawn from a meta-distribution. To this end, we propose a fast estimation method based on regressing Wasserstein distance on sliced…
In modern production facilities industrial robots and humans are supposed to interact sharing a common working area. In order to avoid collisions, the distances between objects need to be measured conservatively which can be done by a…
Several problems in modeling and control of stochastically-driven dynamical systems can be cast as regularized semi-definite programs. We examine two such representative problems and show that they can be formulated in a similar manner. The…
This paper studies iterative schemes for measure transfer and approximation problems, which are defined through a slicing-and-matching procedure. Similar to the sliced Wasserstein distance, these schemes benefit from the availability of…
We derive quantitative bounds on the rate of convergence in $L^1$ Wasserstein distance of general M-estimators, with an almost sharp (up to a logarithmic term) behavior in the number of observations. We focus on situations where the…
Learning from Interactive Demonstrations has revolutionized the way non-expert humans teach robots. It is enough to kinesthetically move the robot around to teach pick-and-place, dressing, or cleaning policies. However, the main challenge…
Generalizing robot trajectories from human demonstrations to new contexts remains a key challenge in Learning from Demonstration (LfD), particularly when only single-context demonstrations are available. We present a novel Gaussian Mixture…
Distance metric learning is an important component for many tasks, such as statistical classification and content-based image retrieval. Existing approaches for learning distance metrics from pairwise constraints typically suffer from two…
The quantization problem aims to find the best possible approximation of probability measures on ${\mathbb{R}}^d$ using finite, discrete measures. The Wasserstein distance is a typical choice to measure the quality of the approximation.…