相关论文: Geometric Sparse Coding in Wasserstein Space

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…

Hyperspectral images capture vast amounts of high-dimensional spectral information about a scene, making labeling an intensive task that is resistant to out-of-the-box statistical methods. Unsupervised learning of clusters allows for…

We study the problem of the decentralized computation of entropy-regularized semi-discrete Wasserstein barycenters over a network. Building upon recent primal-dual approaches, we propose a sampling gradient quantization scheme that allows…

We present new algorithms to compute the mean of a set of empirical probability measures under the optimal transport metric. This mean, known as the Wasserstein barycenter, is the measure that minimizes the sum of its Wasserstein distances…

The increasing availability of granular and big data on various objects of interest has made it necessary to develop methods for condensing this information into a representative and intelligible map. Financial regulation is a field that…

We study the decentralized distributed computation of discrete approximations for the regularized Wasserstein barycenter of a finite set of continuous probability measures distributedly stored over a network. We assume there is a network of…

Distributed systems require fusing heterogeneous local probability distributions into a global summary over sparse and unreliable communication networks. Traditional consensus algorithms, which average distributions in Euclidean space,…

In this work clustering schemes for uncertain and structured data are considered relying on the notion of Wasserstein barycenters, accompanied by appropriate clustering indices based on the intrinsic geometry of the Wasserstein space where…

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…

Paraphrase generation is an important and challenging natural language processing (NLP) task. In this work, we propose a deep generative model to generate paraphrase with diversity. Our model is based on an encoder-decoder architecture. An…

Clustering is an important exploratory data analysis technique to group objects based on their similarity. The widely used $K$-means clustering method relies on some notion of distance to partition data into a fewer number of groups. In the…

Wasserstein barycenters have become popular due to their ability to represent the average of probability measures in a geometrically meaningful way. In this paper, we present an algorithm to approximate the Wasserstein-2 barycenters of…

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…

This paper describes a hierarchical learning strategy for generating sparse representations of multivariate datasets. The hierarchy arises from approximation spaces considered at successively finer scales. A detailed analysis of stability,…

The proliferation of large data sets and Bayesian inference techniques motivates demand for better data sparsification. Coresets provide a principled way of summarizing a large dataset via a smaller one that is guaranteed to match the…

Wasserstein barycenters provide a geometric notion of the weighted average of probability measures based on optimal transport. In this paper, we present a scalable algorithm to compute Wasserstein-2 barycenters given sample access to the…

In this thesis, we consider the Wasserstein barycenter problem of discrete probability measures from computational and statistical sides. The statistical focus is estimating the sample size of measures necessary to calculate an…

Variational problems that involve Wasserstein distances have been recently proposed to summarize and learn from probability measures. Despite being conceptually simple, such problems are computationally challenging because they involve…

Many decision problems in science, engineering and economics are affected by uncertain parameters whose distribution is only indirectly observable through samples. The goal of data-driven decision-making is to learn a decision from finitely…

We propose regularization strategies for learning discriminative models that are robust to in-class variations of the input data. We use the Wasserstein-2 geometry to capture semantically meaningful neighborhoods in the space of images, and…