Related papers: Gromov-Wasserstein Barycenters: The Analysis Probl…
Inspired by the Kantorovich formulation of optimal transport distance between probability measures on a metric space, Gromov-Wasserstein (GW) distances comprise a family of metrics on the space of isomorphism classes of metric measure…
The learning of Gaussian Mixture Models (also referred to simply as GMMs) plays an important role in machine learning. Known for their expressiveness and interpretability, Gaussian mixture models have a wide range of applications, from…
The Gromov-Wasserstein distances were proposed a few years ago to compare distributions which do not lie in the same space. In particular, they offer an interesting alternative to the Wasserstein distances for comparing probability measures…
Computing the unregularized Wasserstein barycenter for measure-valued data is a challenging optimization task. Recent algorithms have been tailored to either discrete measures as point clouds or continuous measures discretized on regular…
We propose min Generalized Sliced Gromov--Wasserstein (min-GSGW), a sliced formulation for the Gromov--Wasserstein (GW) problem using expressive generalized slicers. The key idea is to learn coupled nonlinear slicers that assign compatible…
We generalize the Brouwer-Zimmermann algorithm, which is the most efficient general algorithm for computing the minimum distance of a random linear code, to the case of generalized Hamming weights. We also adapt this algorithm to compute…
The Gromov-Wasserstein (GW) distance enables comparing metric measure spaces based solely on their internal structure, making it invariant to isomorphic transformations. This property is particularly useful for comparing datasets that…
Aligning data from different domains is a fundamental problem in machine learning with broad applications across very different areas, most notably aligning experimental readouts in single-cell multiomics. Mathematically, this problem can…
The Wasserstein barycenter problem is to compute the average of $m$ given probability measures, which has been widely studied in many different areas; however, real-world data sets are often noisy and huge, which impedes its applications in…
In this paper, we introduce a generalization of the Wasserstein barycenter, to a case where the initial probability measures live on different subspaces of R^d. We study the existence and uniqueness of this barycenter, we show how it is…
The assignment problem, a cornerstone of operations research, seeks an optimal one-to-one mapping between agents and tasks to minimize total cost. This work traces its evolution from classical formulations and algorithms to modern optimal…
The standard Bayesian technique for searching pulsar timing data for gravitational wave (GW) bursts with memory (BWMs) using Markov Chain Monte Carlo (MCMC) sampling is very computationally expensive to perform. In this paper, we explain…
We study rates of convergence for estimation of the Gromov-Wasserstein (GW) distance. For two marginals supported on compact subsets of $\R^{d_x}$ and $\R^{d_y}$, respectively, with $\min \{ d_x,d_y \} > 4$, prior work established the rate…
The Gromov--Wasserstein (GW) distance and its fused extension (FGW) are powerful tools for comparing heterogeneous data. Their computation is, however, challenging since both distances are based on non-convex, quadratic optimal transport…
In this paper, we focus on computational aspects of the Wasserstein barycenter problem. We propose two algorithms to compute Wasserstein barycenters of $m$ discrete measures of size $n$ with accuracy $\e$. The first algorithm, based on…
Computing Wasserstein barycenters is a fundamental geometric problem with widespread applications in machine learning, statistics, and computer graphics. However, it is unknown whether Wasserstein barycenters can be computed in polynomial…
Wasserstein barycenters provide a geometrically meaningful way to aggregate probability distributions, built on the theory of optimal transport. They are difficult to compute in practice, however, leading previous work to restrict their…
We study the fixed-support Wasserstein barycenter problem (FS-WBP), which consists in computing the Wasserstein barycenter of $m$ discrete probability measures supported on a finite metric space of size $n$. We show first that the…
Inspired by recent advances in distributed algorithms for approximating Wasserstein barycenters, we propose a novel distributed algorithm for this problem. The main novelty is that we consider time-varying computational networks, which are…
The sliced Wasserstein barycenter (SWB) is a widely acknowledged method for efficiently generalizing the averaging operation within probability measure spaces. However, achieving marginal fairness SWB, ensuring approximately equal distances…