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This paper addresses the problem of the communication of optimally compressed information for mobile robot path-planning. In this context, mobile robots compress their current local maps to assist another robot in reaching a target in an…
We study the complexity of approximating the multimarginal optimal transport (MOT) distance, a generalization of the classical optimal transport distance, considered here between $m$ discrete probability distributions supported each on $n$…
This paper concerns the application of techniques from optimal transport (OT) to mean field control, in which the probability measures of interest in OT correspond to empirical distributions associated with a large collection of controlled…
A framework is proposed that addresses both conditional density estimation and latent variable discovery. The objective function maximizes explanation of variability in the data, achieved through the optimal transport barycenter generalized…
We address the problem of identifying the dynamical law governing the evolution of a population of indistinguishable particles, when only aggregate distributions at successive times are observed. Assuming a Markovian evolution on a discrete…
Robust Bayesian inference is the calculation of posterior probability bounds given perturbations in a probabilistic model. This paper focuses on perturbations that can be expressed locally in Bayesian networks through convex sets of…
In this work, we face the issue of achieving an efficient dynamic mapping in vehicular networking scenarios, i.e., to obtain an accurate estimate of the positions and trajectories of connected vehicles in a certain area. State of the art…
Creating accurate spatial representations that take into account uncertainty is critical for autonomous robots to safely navigate in unstructured environments. Although recent LIDAR based mapping techniques can produce robust occupancy…
We consider optimal transport problems where the cost for transporting a given probability measure $\mu_0$ to another one $\mu_1$ consists of two parts: the first one measures the transportation from $\mu_0$ to an intermediate (pivot)…
We introduce a new theoretical framework to analyze deep learning optimization with connection to its generalization error. Existing frameworks such as mean field theory and neural tangent kernel theory for neural network optimization…
This work explores multi-modal inference in a high-dimensional simplified model, analytically quantifying the performance gain of multi-modal inference over that of analyzing modalities in isolation. We present the Bayes-optimal performance…
In this work we study a constrained monotone inclusion involving the normal cone to a closed vector subspace and a priori information on primal solutions. We model this information by imposing that solutions belongs to the fixed point set…
We consider the convolution operator for a measure supported on complex curves. The measure which we consider here is an analogue of the affine arclength measure for real curves. By modifying a combinatorial argument called the band…
When machine learning models are deployed on a test distribution different from the training distribution, they can perform poorly, but overestimate their performance. In this work, we aim to better estimate a model's performance under…
Modal shift in public transport as a consequence of a disruption on a line has in some cases unforeseen consequences such as an increase in congestion in the rest of the network. How information is provided to users and their behavior plays…
This article studies the \emph{robust covariance matrix estimation} of a data collection $X = (x_1,\ldots,x_n)$ with $x_i = \sqrt \tau_i z_i + m$, where $z_i \in \mathbb R^p$ is a \textit{concentrated vector} (e.g., an elliptical random…
In the study of natural and artificial complex systems, responses that are not completely determined by the considered decision variables are commonly modelled probabilistically, resulting in response distributions varying across decision…
The performance of a machine learning model degrades when it is applied to data from a similar but different domain than the data it has initially been trained on. To mitigate this domain shift problem, domain adaptation (DA) techniques…
We study a problem of best-effort adaptation motivated by several applications and considerations, which consists of determining an accurate predictor for a target domain, for which a moderate amount of labeled samples are available, while…
We present a neural framework for learning conditional optimal transport (OT) maps between probability distributions. Our approach introduces a conditioning mechanism capable of processing both categorical and continuous conditioning…