Tree-Wasserstein Barycenter for Large-Scale Multilevel Clustering and Scalable Bayes

Probabilistic Multilevel Clustering via Composite Transportation Distance

We propose a novel probabilistic approach to multilevel clustering problems based on composite transportation distance, which is a variant of transportation distance where the underlying metric is Kullback-Leibler divergence. Our method involves solving a joint optimization problem over spaces of probability measures to simultaneously discover grouping structures within groups and among groups. By exploiting the connection of our method to the problem of finding composite transportation barycenters, we develop fast and efficient optimization algorithms even for potentially large-scale multilev…

Bayesian Learning with Wasserstein Barycenters

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 show how this estimator, termed Bayesian Wasserstein barycenter (BWB), arises naturally in a general, parameter-free Bayesian model-selection framework, when the considered Bayesian risk is the Wasserstein distance. Examples are given, illustrating how the BWB extends some classic parametric and non-parametric selection strategies. Furthermore, we also provi…

基于Wasserstein重心高斯过程的贝叶斯优化

Wasserstein Barycenter Gaussian Process based Bayesian Optimization

针对标准高斯过程贝叶斯优化中超参数拟合存在缺陷的问题，提出通过预设多组超参数拟合并用Wasserstein重心组合的WBGP-BO方法，在棘手测试问题上仍能收敛到最优解。

On Efficient Multilevel Clustering via Wasserstein Distances

We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data. Our method involves a joint optimization formulation over several spaces of discrete probability measures, which are endowed with Wasserstein distance metrics. We propose several variants of this problem, which admit fast optimization algorithms, by exploiting the connection to the problem of finding Wasserstein barycenters. Consistency properties are establishe…

具有组级上下文的贝叶斯非参数多层聚类

Bayesian Nonparametric Multilevel Clustering with Group-Level Contexts

我们提出了一个贝叶斯非参数框架的多级聚类，利用组级上下文信息，同时发现低维结构的组内容和分区组成集群。使用Dirichlet过程作为构建块，我们的模型构建了一个产品基本测量与嵌套结构，以适应内容和上下文的观察在多个层次。该模型具有的属性，链接嵌套狄利克雷过程（nDP）和狄利克雷过程混合模型（dirichlet）在一个有趣的方式：整合出所有的内容的结果，在上下文中，而整合出特定于组的上下文的结果，在nDP混合物的内容变量。我们提供了一个Polya-urn视图的模型和一个有效的折叠吉布斯推理过程。在真实世界数据集上的大量实验表明，通过我们的模型在文本和图像域中利用上下文信息的优势。

Multilevel Clustering via Wasserstein Means

We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data. Our method involves a joint optimization formulation over several spaces of discrete probability measures, which are endowed with Wasserstein distance metrics. We propose a number of variants of this problem, which admit fast optimization algorithms, by exploiting the connection to the problem of finding Wasserstein barycenters. Consistency properties are establ…