Related papers: Proximity penalty priors for Bayesian mixture mode…
Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions. A key challenge, especially in high-dimensional settings, is to determine the mixture order and estimate the…
Mixture models are commonly used in applications with heterogeneity and overdispersion in the population, as they allow the identification of subpopulations. In the Bayesian framework, this entails the specification of suitable prior…
Discrete mixture models are routinely used for density estimation and clustering. While conducting inferences on the cluster-specific parameters, current frequentist and Bayesian methods often encounter problems when clusters are placed too…
Objective prior distributions represent an important tool that allows one to have the advantages of using the Bayesian framework even when information about the parameters of a model is not available. The usual objective approaches work off…
Employing nonparametric methods for density estimation has become routine in Bayesian statistical practice. Models based on discrete nonparametric priors such as Dirichlet Process Mixture (DPM) models are very attractive choices due to…
We introduce a Bayesian model for inferring mixtures of subspaces of different dimensions. The key challenge in such a mixture model is specification of prior distributions over subspaces of different dimensions. We address this challenge…
Mixture models and topic models generate each observation from a single cluster, but standard variational posteriors for each observation assign positive probability to all possible clusters. This requires dense storage and runtime costs…
This article establishes general conditions for posterior consistency of Bayesian finite mixture models with a prior on the number of components. That is, we provide sufficient conditions under which the posterior concentrates on…
In binary-transaction data-mining, traditional frequent itemset mining often produces results which are not straightforward to interpret. To overcome this problem, probability models are often used to produce more compact and conclusive…
A common problem in natural sciences is the comparison of competing models in the light of observed data. Bayesian model comparison provides a statistically sound framework for this comparison based on the evidence each model provides for…
In designed experiments and surveys, known laws or design feat ures provide checks on the most relevant aspects of a model and identify the target parameters. In contrast, in most observational studies in the health and social sciences, the…
In statistical applications, it is common to encounter parameters supported on a varying or unknown dimensional space. Examples include the fused lasso regression, the matrix recovery under an unknown low rank, etc. Despite the ease of…
We propose a Bayesian approach using improper priors for hierarchical linear mixed models with flexible random effects and residual error distributions. The error distribution is modelled using scale mixtures of normals, which can capture…
Robust statistical data modelling under potential model mis-specification often requires leaving the parametric world for the nonparametric. In the latter, parameters are infinite dimensional objects such as functions, probability…
In this paper, we present a novel approach to fitting mixture models based on estimating first the posterior distribution of the auxiliary variables that assign each observation to a group in the mixture. The posterior distributions of the…
In Bayesian statistics, the choice of prior distribution is often debatable, especially if prior knowledge is limited or data are scarce. In imprecise probability, sets of priors are used to accurately model and reflect prior knowledge.…
In recent years, large-scale Bayesian learning draws a great deal of attention. However, in big-data era, the amount of data we face is growing much faster than our ability to deal with it. Fortunately, it is observed that large-scale…
We study posterior contraction behaviors for parameters of interest in the context of Bayesian mixture modeling, where the number of mixing components is unknown while the model itself may or may not be correctly specified. Two…
Dirichlet process mixture models (DPMM) play a central role in Bayesian nonparametrics, with applications throughout statistics and machine learning. DPMMs are generally used in clustering problems where the number of clusters is not known…
We study Bayesian estimation of mixture models and argue in favor of fitting the marginal posterior distribution over component assignments directly, rather than Gibbs sampling from the joint posterior on components and parameters as is…