Related papers: Recent Advances in Optimal Transport for Machine L…
The robustness of distributed optimization is an emerging field of study, motivated by various applications of distributed optimization including distributed machine learning, distributed sensing, and swarm robotics. With the rapid…
We study the problem of estimating, in the sense of optimal transport metrics, a measure which is assumed supported on a manifold embedded in a Hilbert space. By establishing a precise connection between optimal transport metrics, optimal…
Optimal Mass Transport (OMT) is a well studied problem with a variety of applications in a diverse set of fields ranging from Physics to Computer Vision and in particular Statistics and Data Science. Since the original formulation of Monge…
Modeling traffic distribution and extracting optimal flows in multilayer networks is of utmost importance to design efficient multi-modal network infrastructures. Recent results based on optimal transport theory provide powerful and…
Intelligent transportation systems have recently emerged to address the growing interest for safer, more efficient, and sustainable transportation solutions. In this direction, this paper presents distributed algorithms for control and…
The ability to measure similarity between documents enables intelligent summarization and analysis of large corpora. Past distances between documents suffer from either an inability to incorporate semantic similarities between words or from…
We propose dynamical optimal transport (OT) problems constrained in a parameterized probability subset. In application problems such as deep learning, the probability distribution is often generated by a parameterized mapping function. In…
Efficient motion planning algorithms are of central importance for deploying robots in the real world. Unfortunately, these algorithms often drastically reduce the dimensionality of the problem for the sake of feasibility, thereby foregoing…
We present an optimal mass transport framework on the space of Gaussian mixture models, which are widely used in statistical inference. Our method leads to a natural way to compare, interpolate and average Gaussian mixture models.…
Neural network-based optimal transport (OT) is a recent and fruitful direction in the generative modeling community. It finds its applications in various fields such as domain translation, image super-resolution, computational biology and…
This paper addresses the limitations of standard uncertainty models, e.g., robust (norm-bounded) and stochastic (one fixed distribution, e.g., Gaussian), and proposes to model uncertainty via Optimal Transport (OT) ambiguity sets. These…
Imbalanced data pose challenges for deep learning based classification models. One of the most widely-used approaches for tackling imbalanced data is re-weighting, where training samples are associated with different weights in the loss…
Recent studies have proposed different methods to improve multilingual word representations in contextualized settings including techniques that align between source and target embedding spaces. For contextualized embeddings, alignment…
We present several algorithms designed to learn a pattern of correspondence between two data sets in situations where it is desirable to match elements that exhibit a relationship belonging to a known parametric model. In the motivating…
Traffic prediction plays an essential role in intelligent transportation system. Accurate traffic prediction can assist route planing, guide vehicle dispatching, and mitigate traffic congestion. This problem is challenging due to the…
Selecting prototypical examples from a source distribution to represent a target data distribution is a fundamental problem in machine learning. Existing subset selection methods often rely on implicit importance scores, which can be skewed…
Motivated by robust dynamic resource allocation in operations research, we study the \textit{Online Learning to Transport} (OLT) problem where the decision variable is a probability measure, an infinite-dimensional object. We draw…
A novel algorithm is proposed to solve the sample-based optimal transport problem. An adversarial formulation of the push-forward condition uses a test function built as a convolution between an adaptive kernel and an evolving probability…
Optimization networks are a new methodology for holistically solving interrelated problems that have been developed with combinatorial optimization problems in mind. In this contribution we revisit the core principles of optimization…
Optimal transport (OT) is a widely used technique in machine learning, graphics, and vision that aligns two distributions or datasets using their relative geometry. In symmetry-rich settings, however, OT alignments based solely on pairwise…