Centered Partition Processes: Informative Priors for Clustering (with Discussion)

Paganin, Sally; Herring, Amy H.; Olshan, Andrew F.; Dunson, David B.

doi:10.1214/20-ba1197

Cited by 9 publications

(3 citation statements)

References 52 publications

(48 reference statements)

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“…Other proposals [112–114] aim to mitigate the rich-get-richer property of the DP to prefer highly imbalanced clusters; however, exchangeability often no longer holds. Subjective priors can also be specified which further enrich the parameter space by centring around prior information on the clustering structure [115,116]. In general, a BNP prior can be placed directly on the mixing measure H, which induces a prior on both the sequence of weights and the random partition.…”

Section: Bayesian Cluster Analysismentioning

confidence: 99%

Bayesian cluster analysis

Wade

2023

Phil. Trans. R. Soc. A.

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Bayesian cluster analysis offers substantial benefits over algorithmic approaches by providing not only point estimates but also uncertainty in the clustering structure and patterns within each cluster. An overview of Bayesian cluster analysis is provided, including both model-based and loss-based approaches, along with a discussion on the importance of the kernel or loss selected and prior specification. Advantages are demonstrated in an application to cluster cells and discover latent cell types in single-cell RNA sequencing data to study embryonic cellular development. Lastly, we focus on the ongoing debate between finite and infinite mixtures in a model-based approach and robustness to model misspecification. While much of the debate and asymptotic theory focuses on the marginal posterior of the number of clusters, we empirically show that quite a different behaviour is obtained when estimating the full clustering structure. This article is part of the theme issue ‘Bayesian inference: challenges, perspectives, and prospects’.

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Section: Bayesian Cluster Analysismentioning

confidence: 99%

Bayesian cluster analysis

Wade

2023

Phil. Trans. R. Soc. A.

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“…In a second moment, to elicit a value for η 0 , we would reason by calibration, in the spirit of Paganin et al (2021). Consider the prior expectation f (η 0 , ρ 0 ) := E π(ρ)…”

Section: Elicitation Of the Hyper-parametersmentioning

confidence: 99%

Informative Priors for the Consensus Ranking in the Bayesian Mallows Model

Crispino

Antoniano-Villalobos

2023

Bayesian Anal.

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The aim of this work is to study the problem of prior elicitation for the consensus ranking in the Mallows model with Spearman's distance, a popular distance-based model for rankings or permutation data. Previous Bayesian inference for such a model has been limited to the use of the uniform prior over the space of permutations. We present a novel strategy to elicit informative prior beliefs on the location parameter of the model, discussing the interpretation of hyper-parameters and the implication of prior choices for the posterior analysis.

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“…, ξ G ) and each column of Λ j . We remark that if certain prior knowledge about the variable groups is available for the data, then it is also possible to employ informative priors such as those in Paganin et al (2021) for the s j 's. For the Dirichlet parameters α, defining α 0 = K k=1 α k and η = (α 1 /α 0 , .…”

Section: Bayesian Inferencementioning

confidence: 99%

Dimension-Grouped Mixed Membership Models for Multivariate Categorical Data

Gu,

Erosheva,

et al. 2021

Preprint

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Mixed Membership Models (MMMs) are a popular family of latent structure models for complex multivariate data. Instead of forcing each subject to belong to a single cluster, MMMs incorporate a vector of subject-specific weights characterizing partial membership across clusters. With this flexibility come challenges in uniquely identifying, estimating, and interpreting the parameters. In this article, we propose a new class of Dimension-Grouped MMMs (Gro-M 3 s) for multivariate categorical data, which improve parsimony and interpretability. In Gro-M 3 s, observed variables are partitioned into groups such that the latent membership is constant for variables within a group but can differ across groups. Traditional latent class models are obtained when all variables are in one group, while traditional MMMs are obtained when each variable is in its own group. The new model corresponds to a novel decomposition of probability tensors. Theoretically, we derive transparent identifiability conditions for both the unknown grouping structure and model parameters in general settings. Methodologically, we propose a Bayesian approach for Dirichlet Gro-M 3 s to inferring the variable grouping structure and estimating model parameters. Simulation results demonstrate good computational performance and empirically confirm the identifiability results. We illustrate the new methodology through an application to a functional disability dataset.

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Centered Partition Processes: Informative Priors for Clustering (with Discussion)

Cited by 9 publications

References 52 publications

Bayesian cluster analysis

Bayesian cluster analysis

Informative Priors for the Consensus Ranking in the Bayesian Mallows Model

Dimension-Grouped Mixed Membership Models for Multivariate Categorical Data

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