# From here to infinity: sparse finite versus Dirichlet process mixtures in model-based clustering

@article{FrhwirthSchnatter2019FromHT, title={From here to infinity: sparse finite versus Dirichlet process mixtures in model-based clustering}, author={Sylvia Fr{\"u}hwirth-Schnatter and Gertraud Malsiner‐Walli}, journal={Advances in Data Analysis and Classification}, year={2019}, volume={13}, pages={33 - 64} }

In model-based clustering mixture models are used to group data points into clusters. A useful concept introduced for Gaussian mixtures by Malsiner Walli et al. (Stat Comput 26:303–324, 2016) are sparse finite mixtures, where the prior distribution on the weight distribution of a mixture with K components is chosen in such a way that a priori the number of clusters in the data is random and is allowed to be smaller than K with high probability. The number of clusters is then inferred a…

## 48 Citations

### A Bayesian sparse finite mixture model for clustering data from a heterogeneous population

- Computer Science
- 2020

A Bayesian approach for clustering data using a sparse finite mixture model (SFMM) and a split-merge strategy is inserted within the algorithm in order to increase the mixing of the Markov chain in relation to the number of clusters.

### Infinite Mixtures of Multivariate Normal-Inverse Gaussian Distributions for Clustering of Skewed Data

- Computer Science, MathematicsJournal of Classification
- 2022

An infinite mixture model framework, also known as Dirichlet process mixture model, is proposed for the mixtures of MNIG distributions and the number of components is inferred along with the parameter estimates in a Bayesian framework thus alleviating the need for model selection criteria.

### Clustering multivariate data using factor analytic Bayesian mixtures with an unknown number of components

- Computer ScienceStat. Comput.
- 2020

This work considers a set of eight parameterizations, giving rise to parsimonious representations of the covariance matrix per cluster, which are compared to similar models estimated using the expectation–maximization algorithm on simulated and real datasets.

### Generalized Mixtures of Finite Mixtures and Telescoping Sampling

- Computer Science, MathematicsBayesian Analysis
- 2021

The novel telescoping sampler is proposed which allows Bayesian inference for mixtures with arbitrary component distributions without the need to resort to RJMCMC methods and is demonstrated on several data sets.

### Infinite Mixtures of Infinite Factor Analysers

- Computer Science
- 2017

The IMIFA model obviates the need for model selection criteria, reduces the computational burden associated with the search of the model space, improves clustering performance by allowing cluster-specific numbers of factors, and quantifies uncertainty in the numbers of clusters and cluster- specific factors.

### Gibbs sampling for mixtures in order of appearance: the ordered allocation sampler

- Computer Science, Mathematics
- 2021

This work derives a sampler that is straightforward to implement for mixing distributions with tractable size-biased ordered weights and mitigates the label-switching problem in infinite mixtures.

### Variance matrix priors for Dirichlet process mixture models with Gaussian kernels

- Computer Science
- 2022

The results show that the choice of prior is critical for deriving reliable posterior inferences in problems of higher dimensionality, and the use of the DPMM in clustering is also applicable to density estimation.

### IS INFINITY THAT FAR? A BAYESIAN NONPARAMETRIC PERSPECTIVE OF FINITE MIXTURE MODELS

- Mathematics, Computer Science
- 2022

A new class of priors is introduced: the Normalized Independent Point Process, which is based on an auxiliary variable MCMC, which allows handling the otherwise intractable posterior distribution and overcomes the challenges associated with the Reversible Jump algorithm.

### Escaping the curse of dimensionality in Bayesian model based clustering

- Computer Science
- 2020

A Bayesian oracle for clustering is defined, with the oracle clustering posterior based on the true values of low-dimensional latent variables, and a class of LAtent Mixtures for Bayesian (Lamb) clustering that have equivalent behavior to this oracle as dimension grows are defined.

### Dynamic mixtures of finite mixtures and telescoping sampling

- Computer Science
- 2020

A novel sampling scheme is proposed for MFMs called the telescoping sampler which allows Bayesian inference for mixtures with arbitrary component distributions and the ease of its application using different component distributions is demonstrated on real data sets.

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