Related papers: Learning Continuous Wasserstein Barycenter Space f…

Despite remarkable advances made in all-in-one image restoration (AIR) for handling different types of degradations simultaneously, existing methods remain vulnerable to out-of-distribution degradations and images, limiting their real-world…

Wasserstein dictionary learning is an unsupervised approach to learning a collection of probability distributions that generate observed distributions as Wasserstein barycentric combinations. Existing methods for Wasserstein dictionary…

In many applications in statistics and machine learning, the availability of data samples from multiple possibly heterogeneous sources has become increasingly prevalent. On the other hand, in distributionally robust optimization, we seek…

Wasserstein Barycenter is a principled approach to represent the weighted mean of a given set of probability distributions, utilizing the geometry induced by optimal transport. In this work, we present a novel scalable algorithm to…

This paper advances the theory and practice of Domain Generalization (DG) in machine learning. We consider the typical DG setting where the hypothesis is composed of a representation mapping followed by a labeling function. Within this…

The Wasserstein barycenter is a geometric construct which captures the notion of centrality among probability distributions, and which has found many applications in machine learning. However, most algorithms for finding even an approximate…

Efficiently aggregating data from different sources is a challenging problem, particularly when samples from each source are distributed differently. These differences can be inherent to the inference task or present for other reasons:…

Learning generative models is challenging for a network edge node with limited data and computing power. Since tasks in similar environments share model similarity, it is plausible to leverage pre-trained generative models from the cloud or…

Given a collection of probability measures, a practitioner sometimes needs to find an "average" distribution which adequately aggregates reference distributions. A theoretically appealing notion of such an average is the Wasserstein…

We consider the problem of computing a Wasserstein barycenter for a set of discrete probability distributions with finite supports, which finds many applications in areas such as statistics, machine learning and image processing. When the…

Blind all-in-one image restoration models aim to recover a high-quality image from an input degraded with unknown distortions. However, these models require all the possible degradation types to be defined during the training stage while…

Wasserstein barycenter, built on the theory of optimal transport, provides a powerful framework to aggregate probability distributions, and it has increasingly attracted great attention within the machine learning community. However, it…

We study the problem of model aggregation within the Wasserstein space for probability measures on the real line. Given a fixed finite collection of candidate probability models, we consider the associated class of Wasserstein barycenters…

Despite the significant progress made by all-in-one models in universal image restoration, existing methods suffer from a generalization bottleneck in real-world scenarios, as they are mostly trained on small-scale synthetic datasets with…

Blind image restoration (IR) is a common yet challenging problem in computer vision. Classical model-based methods and recent deep learning (DL)-based methods represent two different methodologies for this problem, each with their own…

Divide-and-conquer based methods for Bayesian inference provide a general approach for tractable posterior inference when the sample size is large. These methods divide the data into smaller subsets, sample from the posterior distribution…

Universal image restoration aims to recover clean images from arbitrary real-world degradations using a single inference model. Despite significant progress, existing all-in-one restoration networks do not scale to multiple degradations. As…

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…

Image reconstruction based on indirect, noisy, or incomplete data remains an important yet challenging task. While methods such as compressive sensing have demonstrated high-resolution image recovery in various settings, there remain issues…

We introduce and study a novel model-selection strategy for Bayesian learning, based on optimal transport, along with its associated predictive posterior law: the Wasserstein population barycenter of the posterior law over models. We first…