Relabelling in Bayesian mixture models by pivotal units

  title={Relabelling in Bayesian mixture models by pivotal units},
  author={Leonardo Egidi and Roberta Pappad{\`a} and Francesco Pauli and Nicola Torelli},
  journal={Statistics and Computing},
Label switching is a well-known and fundamental problem in Bayesian estimation of finite mixture models. It arises when exploring complex posterior distributions by Markov Chain Monte Carlo (MCMC) algorithms, because the likelihood of the model is invariant to the relabelling of mixture components. If the MCMC sampler randomly switches labels, then it is unsuitable for exploring the posterior distributions for component-related parameters. In this paper, a new procedure based on the post-MCMC… 
pivmet: Pivotal Methods for Bayesian Relabelling and k-Means Clustering
The R package pivmet presented in this paper includes different methods for extracting pivotal units from a dataset, and provides functions to perform consensus clustering based on pivotal units, which may allow to improve classical techniques.
Anchored Bayesian Gaussian mixture models
This work proposes a model in which a small number of observations are assumed to arise from some of the labeled component densities, allowing inference on the component features without post-processing and produces interpretable results, often similar to those resulting from relabeling algorithms.
Developments in Bayesian Hierarchical Models and Prior Specification withApplication to Analysis of Soccer Data
A new class of prior distributions which might depend on the data and specified as a mixture between a noninformative and an informative prior is proposed, well suited for robustness tasks, especially in case of informative prior misspecification.
Minimum Hellinger distance estimation for a semiparametric location-shifted mixture model
ABSTRACT In this article, we propose a minimum Hellinger distance estimation (MHDE) for a semiparametric two-component mixture model where the two components are unknown location-shifted symmetric
Assessment of uncertainty in bid arrival times: A Bayesian mixture model
A Bayesian approach to model uncertainty in the bid arrival time by focusing on the time of the first bid in secondary (retail) market online business-to-business auctions is proposed, based on a Bayesian finite mixture of beta distributions.
Maxima Units Search (MUS) algorithm: methodology and applications
An algorithm for extracting identity submatrices of small rank and pivotal units from large and sparse matrices is proposed and possible applications in different contexts are explored.
Random effects clustering in multilevel modeling: choosing a proper partition
A novel criterion for estimating a latent partition of the observed groups based on the output of a hierarchical model is presented. It is based on a loss function combining the Gini income
K-means seeding via MUS algorithm
A modified version of K-means is proposed, based on a suitable choice of the initial centers, that takes advantage of the information contained in a co-association matrix to define a pivot-based initialization step.
Analysis of Greenhouse Gas Emissions in European Based on Hybrid Models
  • Hua Yang, Jie Zhang, Feng Jiang
  • Economics
    2018 Ninth International Conference on Intelligent Control and Information Processing (ICICIP)
  • 2018
The emission of greenhouse gas (GG) is a prime cause of global warming. But the emission reduction may lower economic growth rate. Since different countries have different industrial structure, the


Label Switching in Bayesian Mixture Models: Deterministic Relabeling Strategies
This paper uses latent allocations for the design of the MCMC strategy to derive an easy and efficient solution to the label switching problem, and compares the strategy with other relabeling algorithms on univariate and multivariate data examples and demonstrates improvements over alternative strategies.
Markov Chain Monte Carlo Methods and the Label Switching Problem in Bayesian Mixture Modeling
The solutions to the label switching problem of Markov chain Monte Carlo methods, such as artificial identifiability constraints, relabelling algorithms and label invariant loss functions are reviewed.
label.switching: An R Package for Dealing with the Label Switching Problem in MCMC Outputs
The \pkg{label.switching} package is introduced, which contains one probabilistic and seven deterministic relabelling algorithms in order to post-process a given MCMC sample, provided by the user.
Dealing with label switching in mixture models
It is demonstrated that this fails in general to solve the ‘label switching’ problem, and an alternative class of approaches, relabelling algorithms, which arise from attempting to minimize the posterior expected loss under a class of loss functions are described.
Probabilistic relabelling strategies for the label switching problem in Bayesian mixture models
It is demonstrated that the idea of probabilistic relabelling can be expressed in a rigorous framework based on the EM algorithm and introduced and compared to existing deterministic relabelled algorithms.
Difficulties in Drawing Inferences With Finite-Mixture Models
The authors' simulations show that MCMC performs much better than ML if the label-switching problem is adequately addressed, and that asymmetric prior information performs as well as or better than the other proposed methods.
Markov chain Monte Carlo Estimation of Classical and Dynamic Switching and Mixture Models
Joint Bayesian estimation of all latent variables, model parameters, and parameters that determine the probability law of the latent process is carried out by a new MCMC method called permutation sampling.
Computational and Inferential Difficulties with Mixture Posterior Distributions
This article proposes alternatives for Bayesian inference for permutation invariant posteriors, including a clustering device and alternative appropriate loss functions and shows that exploration of these modes can be imposed using tempered transitions.
An online Bayesian mixture labelling method by minimizing deviance of classification probabilities to reference labels
This article proposes a new simple labelling method by minimizing the deviance of the class probabilities to a fixed reference labels that can be implemented by an online algorithm, which can reduce the storage requirements and save much computation time.
An Artificial Allocations Based Solution to the Label Switching Problem in Bayesian Analysis of Mixtures of Distributions
Label switching is a well-known problem occurring in MCMC outputs in Bayesian mixture modeling. In this article we propose a formal solution to this problem by considering the space of the artificial