Measuring dependence in the Wasserstein distance for Bayesian nonparametric models

Catalano, Marta; Lijoi, Antonio; Prünster, Igor

doi:10.1214/21-aos2065

Cited by 10 publications

(3 citation statements)

References 37 publications

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“…To this end, one needs to build dependent random probability measures (see Quintana et al, 2022 for a recent review) with two key features in mind: (i) mathematical tractability, which corresponds to obtaining manageable representations for the posterior and/or the marginal structure, i.e., the partition distribution or the prediction rule; (ii) the ability to control the amount of dependence, since this is directly linked to the borrowing of information between the two groups: the more the dependence, the more information will be shared across the two groups. This is usually done by expressing the linear correlation between pairwise set-wise evaluations, Cor( P1 (A), P2 (A)) for any Borel set A, and has been recently extended to an arbitrary number of groups by relying on the Wasserstein distance (Catalano et al, 2021a(Catalano et al, , 2021b.…”

Section: Borrowing Of Informationmentioning

confidence: 99%

Bayesian modeling via discrete nonparametric priors

Catalano

Lijoi

Prünster

et al. 2023

Jpn J Stat Data Sci

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The availability of complex-structured data has sparked new research directions in statistics and machine learning. Bayesian nonparametrics is at the forefront of this trend thanks to two crucial features: its coherent probabilistic framework, which naturally leads to principled prediction and uncertainty quantification, and its infinite-dimensionality, which exempts from parametric restrictions and ensures full modeling flexibility. In this paper, we provide a concise overview of Bayesian nonparametrics starting from its foundations and the Dirichlet process, the most popular nonparametric prior. We describe the use of the Dirichlet process in species discovery, density estimation, and clustering problems. Among the many generalizations of the Dirichlet process proposed in the literature, we single out the Pitman–Yor process, and compare it to the Dirichlet process. Their different features are showcased with real-data illustrations. Finally, we consider more complex data structures, which require dependent versions of these models. One of the most effective strategies to achieve this goal is represented by hierarchical constructions. We highlight the role of the dependence structure in the borrowing of information and illustrate its effectiveness on unbalanced datasets.

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Section: Borrowing Of Informationmentioning

confidence: 99%

Bayesian modeling via discrete nonparametric priors

Catalano

Lijoi

Prünster

et al. 2023

Jpn J Stat Data Sci

Self Cite

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“…Typically, copula-based dependence measurements are expressed as a discrepancy of the estimated copula from the independent case. Here, instead, we will consider the Wasserstein distance between a copula and the comonotonicity copula M. This perspective has been also recently considered in [36] in a Bayesian setting.…”

Section: Background On Optimal Transport Wasserstein Distance and Cop...mentioning

confidence: 99%

“…The Wasserstein distance allows for a meaningful comparison between distributions also without density. This property is not shared by the most common distances and divergences, such as the total variation distance, the Hellinger distance, or the Kullback-Leibler divergence (see, e.g., [36]).…”

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confidence: 98%

Wasserstein Dissimilarity for Copula-Based Clustering of Time Series with Spatial Information

Benevento,

Durante

2023

Mathematics

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The clustering of time series with geo-referenced data requires a suitable dissimilarity matrix interpreting the comovements of the time series and taking into account the spatial constraints. In this paper, we propose a new way to compute the dissimilarity matrix, merging both types of information, which leverages on the Wasserstein distance. We then make a quasi-Gaussian assumption that yields more convenient formulas in terms of the joint correlation matrix. The method is illustrated in a case study involving climatological data.

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