Related papers: Fast Optimal Transport Averaging of Neuroimaging D…
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…
Optimal transport (OT) provides effective tools for comparing and mapping probability measures. We propose to leverage the flexibility of neural networks to learn an approximate optimal transport map. More precisely, we present a new and…
Brain pathologies often manifest as partial or complete loss of tissue. The goal of many neuroimaging studies is to capture the location and amount of tissue changes with respect to a clinical variable of interest, such as disease…
The primary motivation and application in this article come from brain imaging studies on cognitive impairment in elderly subjects with brain disorders. We propose a regularized Haar wavelet-based approach for the analysis of…
Analysis of brain connectivity is important for understanding how information is processed by the brain. We propose a novel Bayesian vector autoregression (VAR) hierarchical model for analyzing brain connectivity in a resting-state fMRI…
We focus in this paper on high-dimensional regression problems where each regressor can be associated to a location in a physical space, or more generally a generic geometric space. Such problems often employ sparse priors, which promote…
Magnetic resonance imaging (MRI) data is heterogeneous due to differences in device manufacturers, scanning protocols, and inter-subject variability. A conventional way to mitigate MR image heterogeneity is to apply preprocessing…
Brain surface analysis is essential to neuroscience, however, the complex geometry of the brain cortex hinders computational methods for this task. The difficulty arises from a discrepancy between 3D imaging data, which is represented in…
We consider the optimization problem of minimizing a functional defined over a family of probability distributions, where the objective functional is assumed to possess a variational form. Such a distributional optimization problem arises…
Aggregating multi-subject functional magnetic resonance imaging (fMRI) data is indispensable for generating valid and general inferences from patterns distributed across human brains. The disparities in anatomical structures and functional…
Distributed stochastic optimization has drawn great attention recently due to its effectiveness in solving large-scale machine learning problems. Though numerous algorithms have been proposed and successfully applied to general practical…
We present a novel method for efficiently computing optimal transport maps and Wasserstein barycenters in high-dimensional spaces. Our approach uses conditional normalizing flows to approximate the input distributions as invertible…
This article introduces a generalization of the discrete optimal transport, with applications to color image manipulations. This new formulation includes a relaxation of the mass conservation constraint and a regularization term. These two…
Suppose we are given two metric spaces and a family of continuous transformations from one to the other. Given a probability distribution on each of these two spaces - namely the source and the target measures - the Wasserstein alignment…
Mental and cognitive representations are believed to reside on low-dimensional, non-linear manifolds embedded within high-dimensional brain activity. Uncovering these manifolds is key to understanding individual differences in brain…
We present a novel framework based on optimal transport for the challenging problem of comparing graphs. Specifically, we exploit the probabilistic distribution of smooth graph signals defined with respect to the graph topology. This allows…
Many tasks in machine learning and signal processing can be solved by minimizing a convex function of a measure. This includes sparse spikes deconvolution or training a neural network with a single hidden layer. For these problems, we study…
We propose a novel neural algorithm for the fundamental problem of computing the entropic optimal transport (EOT) plan between continuous probability distributions which are accessible by samples. Our algorithm is based on the saddle point…
It was recently shown that under smoothness conditions, the squared Wasserstein distance between two distributions could be efficiently computed with appealing statistical error upper bounds. However, rather than the distance itself, the…
The Histogram of Oriented Gradient is a widely used image feature, which describes local image directionality based on numerical differentiation. Due to its ill-posed nature, small noise may lead to large errors. Conventional HOG may fail…