Related papers: Quantized Gromov-Wasserstein
Wasserstein distances are metrics on probability distributions inspired by the problem of optimal mass transportation. Roughly speaking, they measure the minimal effort required to reconfigure the probability mass of one distribution in…
Wasserstein barycenters provide a principled approach for aggregating probability measures, while preserving the geometry of their ambient space. Existing discrete methods are not scalable as they assume access to the complete set of…
Motivated by the 2D class averaging problem in single-particle cryo-electron microscopy (cryo-EM), we present a k-means algorithm based on a rotationally-invariant Wasserstein metric for images. Unlike existing methods that are based on…
Spatial statistics is a growing discipline providing important analytical techniques in a wide range of disciplines in the natural and social sciences. In the R package GWmodel, we introduce techniques from a particular branch of spatial…
Many variants of the Wasserstein distance have been introduced to reduce its original computational burden. In particular the Sliced-Wasserstein distance (SW), which leverages one-dimensional projections for which a closed-form solution of…
This paper studies iterative schemes for measure transfer and approximation problems, which are defined through a slicing-and-matching procedure. Similar to the sliced Wasserstein distance, these schemes benefit from the availability of…
We study multi-objective optimization over probability distributions in Wasserstein space. Recently, Nguyen et al. (2025) introduced Multiple Wasserstein Gradient Descent (MWGraD) algorithm, which exploits the geometric structure of…
We introduce a method for jointly registering ensembles of partitioned datasets in a way which is both geometrically coherent and partition-aware. Once such a registration has been defined, one can group partition blocks across datasets in…
The sliced Wasserstein (SW) distance has been widely recognized as a statistically effective and computationally efficient metric between two probability measures. A key component of the SW distance is the slicing distribution. There are…
The challenge of approximating functions in infinite-dimensional spaces from finite samples is widely regarded as formidable. We delve into the challenging problem of the numerical approximation of Sobolev-smooth functions defined on…
We study optimization problems whereby the optimization variable is a probability measure. Since the probability space is not a vector space, many classical and powerful methods for optimization (e.g., gradients) are of little help. Thus,…
First-order phase transitions in the early universe can generate stochastic gravitational waves (GWs), offering a unique probe of high-scale particle physics. The Left-Right Symmetric Model (LRSM), which restores parity symmetry at high…
The sliced Wasserstein distance (SW) reduces optimal transport on $\mathbb{R}^d$ to a sum of one-dimensional projections, and thanks to this efficiency, it is widely used in geometry, generative modeling, and registration tasks. Recent work…
Covariate shift arises when covariate distributions differ between source and target populations while the conditional distribution of the response remains invariant, and it underlies problems in missing data and causal inference. We…
Single-cell genomics has significantly advanced our understanding of cellular behavior, catalyzing innovations in treatments and precision medicine. However, single-cell sequencing technologies are inherently destructive and can only…
Modeling observations as random distributions embedded within Wasserstein spaces is becoming increasingly popular across scientific fields, as it captures the variability and geometric structure of the data more effectively. However, the…
In past decades the scientific community has been looking for a reliable first-principles method to predict the electronic structure of solids with high accuracy. Here we present an approach which we call the quasiparticle self-consistent…
Wasserstein gradient flows are continuous time dynamics that define curves of steepest descent to minimize an objective function over the space of probability measures (i.e., the Wasserstein space). This objective is typically a divergence…
Since its introduction as a computable approximation of the Reeb graph, the Mapper graph has become one of the most popular tools from topological data analysis for performing data visualization and inference. However, finding an…
A novel neural architecture was recently developed that enforces an exact upper bound on the Lipschitz constant of the model by constraining the norm of its weights in a minimal way, resulting in higher expressiveness compared to other…