Related papers: A Distributed Framework for the Construction of Tr…
We consider inference (filtering) problems over probabilistic graphical models with aggregate data generated by a large population of individuals. We propose a new efficient belief propagation type algorithm over tree-structured graphs with…
Multivariate spatial fields are of interest in many applications, including climate model emulation. Not only can the marginal spatial fields be subject to nonstationarity, but the dependence structure among the marginal fields and between…
We investigate in this work a versatile convex framework for multiple image segmentation, relying on the regularized optimal mass transport theory. In this setting, several transport cost functions are considered and used to match…
This paper focuses on multi-block optimization problems over transport polytopes, which underlie various applications including strongly correlated quantum physics and machine learning. Conventional block coordinate descent-type methods for…
We present a new transport-based approach to efficiently perform sequential Bayesian inference of static model parameters. The strategy is based on the extraction of conditional distribution from the joint distribution of parameters and…
Regularization has become a primary tool for developing reliable estimators of the covariance matrix in high-dimensional settings. To curb the curse of dimensionality, numerous methods assume that the population covariance (or inverse…
Lattice field theories are fundamental testbeds for computational physics; yet, sampling their Boltzmann distributions remains challenging due to multimodality and long-range correlations. While normalizing flows offer a promising…
Distribution estimation for noisy data via density deconvolution is a notoriously difficult problem for typical noise distributions like Gaussian. We develop a density deconvolution estimator based on quadratic programming (QP) that can…
Optimal transport is a powerful framework for the efficient allocation of resources between sources and targets. However, traditional models often struggle to scale effectively in the presence of large and heterogeneous populations. In this…
Monge map refers to the optimal transport map between two probability distributions and provides a principled approach to transform one distribution to another. Neural network based optimal transport map solver has gained great attention in…
Optimal Transport is a theory that allows to define geometrical notions of distance between probability distributions and to find correspondences, relationships, between sets of points. Many machine learning applications are derived from…
We study the estimation problem of distribution-on-distribution regression, where both predictors and responses are probability measures. Existing approaches typically rely on a global optimal transport map or tangent-space linearization,…
With the growing attention towards developing the multimodal transport system to enhance urban mobility, there is an increasing need to construct new, rebuild or expand existing infrastructure to facilitate existing and accommodate newly…
We extract a core principle underlying seemingly different fundamental distributed settings, showing sparsity awareness may induce faster algorithms for problems in these settings. To leverage this, we establish a new framework by…
We investigate certain optimization problems for Shannon information measures, namely, minimization of joint and conditional entropies $H(X,Y)$, $H(X|Y)$, $H(Y|X)$, and maximization of mutual information $I(X;Y)$, over convex regions. When…
Most existing motion planning algorithms assume that a map (of some quality) is fully determined prior to generating a motion plan. In many emerging applications of robotics, e.g., fast-moving agile aerial robots with constrained embedded…
The objective in statistical Optimal Transport (OT) is to consistently estimate the optimal transport plan/map solely using samples from the given source and target marginal distributions. This work takes the novel approach of posing…
In many real world problems, optimization decisions have to be made with limited information. The decision maker may have no a priori or posteriori data about the often nonconvex objective function except from on a limited number of points…
Optimal transport is the problem of designing a joint distribution for two random variables with fixed marginals. In virtually the entire literature on this topic, the objective is to minimize expected cost. This paper is the first to study…
Optimal transport has found widespread applications in signal processing and machine learning. Among its many equivalent formulations, optimal transport seeks to reconstruct a random variable/vector with a prescribed distribution at the…