MCMC Computations for Bayesian Mixture Models Using Repulsive Point Processes

Beraha, Mario; Argiento, Raffaele; Møller, Jesper; Guglielmi, Alessandra

doi:10.1080/10618600.2021.2000424

Cited by 15 publications

(18 citation statements)

References 39 publications

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“…In order to favour components that are well separated, the independence assumption on the atoms can be relaxed through the use of repulsive priors [ 124 – 126 ], determinantal point processes [ 127 ] or non-local priors [ 128 ]. In particular, this form of prior regularization helps to improve interpretation and encourages more meaningful clustering structures, however, it also results in more complicated posterior computations.…”

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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“…Unfortunately, the methods proposed tend to add considerable additional computational complexity to an already computationally challenging problem. However, recent results [32] in the context of mixture models suggest that this approach may be worth exploring in future work on channel data inference.…”

Section: B Strauss-saleh-valenzuela Modelmentioning

confidence: 99%

Bayesian Inference for Stochastic Multipath Radio Channel Models

Hirsch

Bharti

Pedersen

et al. 2023

IEEE Trans. Antennas Propagat.

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Stochastic radio channel models based on underlying point processes of multipath components have been studied intensively since the seminal papers of Turin and Saleh-Valenzuela. Despite of this, inference regarding parameters of these models has remained a major challenge. Current methods typically have a somewhat ad hoc flavor involving a multitude of steps requiring user specification of tuning parameters. In this paper, we propose to instead adopt the principled framework of Bayesian inference to conduct inference for the Saleh-Valenzuela model. The posterior distribution is not analytically tractable and we therefore compute approximations of the posterior using Markov chain Monte Carlo (MCMC) methods specific to point processes. To demonstrate the flexibility of our approach, we additionally propose a new multipath model and apply our inference method to it. The resulting inference methodology is computationally demanding and our successful implementation relies critically on our novel multipath component updates within the MCMC sampler. We demonstrate the usefulness of our approach on simulated and real radio channel data.

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“…In particular, it is possible to define such a process by specifying a density with respect to a Poisson point process. For instance, Quinlan et al (2020); Xie & Xu (2019); Beraha et al (2022) assume a pairwise interaction process whose density, with respect to a suitably defined Poisson process, is…”

Section: Bayesian Clustering Via Latent Mixturesmentioning

confidence: 99%

“…We consider a model for simultaneous dimensionality reduction and clustering as above, but assume a repulsive point process as the prior for the component-specific location parameters of the mixture for the latent scores. Repulsive mixtures (Beraha et al, 2022) offer a practical solution to the lack of robustness of mixture models with i.i.d. component parameters.…”

Section: Introductionmentioning

confidence: 99%

Bayesian clustering of high-dimensional data via latent repulsive mixtures

Ghilotti¹,

Beraha²,

Guglielmi³

2023

Preprint

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Model-based clustering of moderate or large dimensional data is notoriously difficult. We propose a model for simultaneous dimensionality reduction and clustering by assuming a mixture model for a set of latent scores, which are then linked to the observations via a Gaussian latent factor model. This approach was recently investigated by Chandra et al. (2020). The authors use a factor-analytic representation and assume a mixture model for the latent factors. However, performance can deteriorate in the presence of model misspecification. Assuming a repulsive point process prior for the component-specific means of the mixture for the latent scores is shown to yield a more robust model that outperforms the standard mixture model for the latent factors in several simulated scenarios. To favor well-separated clusters of data, the repulsive point process must be anisotropic, and its density should be tractable for efficient posterior inference. We address these issues by proposing a general construction for anisotropic determinantal point processes.

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MCMC Computations for Bayesian Mixture Models Using Repulsive Point Processes

Cited by 15 publications

References 39 publications

Bayesian cluster analysis

Bayesian cluster analysis

Bayesian Inference for Stochastic Multipath Radio Channel Models

Bayesian clustering of high-dimensional data via latent repulsive mixtures

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