Related papers: Ensemble Riemannian Data Assimilation over the Was…

We study the problem of distributional matrix completion: Given a sparsely observed matrix of empirical distributions, we seek to impute the true distributions associated with both observed and unobserved matrix entries. This is a…

This paper proposes an extension to the classical 3D variational data assimilation approach by explicitly incorporating as a prior information, the transform-domain sparsity observed in a large class of geophysical signals. In particular,…

In this article we study a variational problem providing a way to extend for all times minimizing geodesics connecting two given probability measures, in the Wasserstein space. This is simply obtained by allowing for negative coefficients…

The Wasserstein distance is an attractive tool for data analysis but statistical inference is hindered by the lack of distributional limits. To overcome this obstacle, for probability measures supported on finitely many points, we derive…

In this paper we tackle the problem of comparing distributions of random variables and defining a mean pattern between a sample of random events. Using barycenters of measures in the Wasserstein space, we propose an iterative version as an…

Understanding proper distance measures between distributions is at the core of several learning tasks such as generative models, domain adaptation, clustering, etc. In this work, we focus on mixture distributions that arise naturally in…

We introduce a theoretical framework for performing statistical tasks---including, but not limited to, averaging and principal component analysis---on the space of (possibly asymmetric) matrices with arbitrary entries and sizes. This is…

Bayesian methods are developed for the multivariate nonparametric regression problem where the domain is taken to be a compact Riemannian manifold. In terms of the latter, the underlying geometry of the manifold induces certain symmetries…

We introduce a new paradigm, $\textit{measure synchronization}$, for synchronizing graphs with measure-valued edges. We formulate this problem as maximization of the cycle-consistency in the space of probability measures over relative…

We consider the problem of density estimation on Riemannian manifolds. Density estimation on manifolds has many applications in fluid-mechanics, optics and plasma physics and it appears often when dealing with angular variables (such as…

Data assimilation addresses the general problem of how to combine model-based predictions with partial and noisy observations of the process in an optimal manner. This survey focuses on sequential data assimilation techniques using…

Gaussian processes (GPs) are a well-known nonparametric Bayesian inference technique, but they suffer from scalability problems for large sample sizes, and their performance can degrade for non-stationary or spatially heterogeneous data. In…

This tutorial provides a broad introduction to Bayesian data assimilation that will be useful to practitioners, in interpreting algorithms and results, and for theoretical studies developing novel schemes with an understanding of the rich…

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…

The Wasserstein distance has emerged as a key metric to quantify distances between probability distributions, with applications in various fields, including machine learning, control theory, decision theory, and biological systems.…

Analyzing spatially varying effects is pivotal in geographic analysis. However, accurately capturing and interpreting this variability is challenging due to the increasing complexity and non-linearity of geospatial data. Recent advancements…

The adapted Wasserstein distance is a metric for quantifying distributional uncertainty and assessing the sensitivity of stochastic optimization problems on time series data. A computationally efficient alternative to it, is provided by the…

This chapter describes a novel approach for the treatment of model error in geophysical data assimilation. In this method, model error is treated as a deterministic process fully correlated in time. This allows for the derivation of the…

Word embeddings are high dimensional vector representations of words that capture their semantic similarity in the vector space. There exist several algorithms for learning such embeddings both for a single language as well as for several…

We commonly refer to state-estimation theory in geosciences as data assimilation. This term encompasses the entire sequence of operations that, starting from the observations of a system, and from additional statistical and dynamical…