相关论文: Data-driven regularization of Wasserstein barycent…

This paper presents a new approach to the classical problem of quantifying posterior contraction rates (PCRs) in Bayesian statistics. Our approach relies on Wasserstein distance, and it leads to two main contributions which improve on the…

This paper presents a computational framework for the concise encoding of an ensemble of persistence diagrams, in the form of weighted Wasserstein barycenters [100], [102] of a dictionary of atom diagrams. We introduce a multi-scale…

Communication is one of the bottlenecks of distributed optimisation and learning. To overcome this bottleneck, we propose a novel quantization method that transforms a vector into a sample of components' indices drawn from a categorical…

We study nonparametric density estimation problems where error is measured in the Wasserstein distance, a metric on probability distributions popular in many areas of statistics and machine learning. We give the first minimax-optimal rates…

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…

As the demand to integrate Artificial Intelligence into high-stakes environments continues to grow, explaining the reasoning behind neural-network predictions has shifted from a theoretical curiosity to a strict operational requirement. Our…

Inverse problems in physical or biological sciences often involve recovering an unknown parameter that is random. The sought-after quantity is a probability distribution of the unknown parameter, that produces data that aligns with…

This paper presents a new method for conditional probability density simulation. The method is design to work with unstructured data set when data are not characterized by the same covariates yet share common information. Specific examples…

The fairness of clustering algorithms has gained widespread attention across various areas, including machine learning, In this paper, we study fair $k$-means clustering in Euclidean space. Given a dataset comprising several groups, the…

This paper is focused on the study of entropic regularization in optimal transport as a smoothing method for Wasserstein estimators, through the prism of the classical tradeoff between approximation and estimation errors in statistics.…

We consider the fusion of two aerodynamic data sets originating from differing fidelity physical or computer experiments. We specifically address the fusion of: 1) noisy and in-complete fields from wind tunnel measurements and 2)…

A data-driven MPC scheme is proposed to safely control constrained stochastic linear systems using distributionally robust optimization. Distributionally robust constraints based on the Wasserstein metric are imposed to bound the state…

Federated reinforcement learning typically aggregates value functions or policies by parameter averaging, which emphasizes expected return and can obscure statistical multimodality and tail behavior that matter in safety-critical settings.…

The optimal transportation problem defines a geometry of probability measures which leads to a definition for weighted averages (barycenters) of measures, finding application in the machine learning and computer vision communities as a…

Many time series can be modeled as a sequence of segments representing high-level discrete states, such as running and walking in a human activity application. Flexible models should describe the system state and observations in stationary…

We develop a data-driven algorithm for automatically selecting the regularisation parameter in Bayesian inversion under random tree Besov priors. One of the key challenges in Bayesian inversion is the construction of priors that are both…

Change point detection for time series analysis is a difficult and important problem in applied statistics, for which a variety of approaches have been developed in the past several decades. Here, the Wasserstein metric is employed as a…

In this work we consider regularized Wasserstein barycenters (average in Wasserstein distance) in Fourier basis. We prove that random Fourier parameters of the barycenter converge to some Gaussian random vector by distribution. The…

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,…

Wasserstein distributionally robust optimization (DRO) has gained prominence in operations research and machine learning as a powerful method for achieving solutions with favorable out-of-sample performance. Two compelling explanations for…