Related papers: On The Identifiability of Mixture Models from Grou…
This paper addresses the problem of full model estimation for non-parametric finite mixture models. It presents an approach for selecting the number of components and the subset of discriminative variables (i.e., the subset of variables…
We consider the estimation of the mixing distribution of a normal distribution where both the shift and scale are unobserved random variables. We argue that in general, the model is not identifiable. We give an elegant non-constructive…
The use of a finite mixture of normal distributions in model-based clustering allows to capture non-Gaussian data clusters. However, identifying the clusters from the normal components is challenging and in general either achieved by…
We present new results for consistency of maximum likelihood estimators with a focus on multivariate mixed models. Our theory builds on the idea of using subsets of the full data to establish consistency of estimators based on the full…
The Gaussian mixture model is widely used in unsupervised learning, owing to its simplicity and interpretability. However, a fundamental limitation of the classical Gaussian mixture model is that it forces each observation to belong to…
In model-based clustering using finite mixture models, it is a significant challenge to determine the number of clusters (cluster size). It used to be equal to the number of mixture components (mixture size); however, this may not be valid…
In this paper, we develop a finite mixture of convolutional distributions, a statistical model to analyze continuous data distributed approximately on a mixture of low-dimensional affine subspaces. The observations are assumed independent…
Singularities of a statistical model are the elements of the model's parameter space which make the corresponding Fisher information matrix degenerate. These are the points for which estimation techniques such as the maximum likelihood…
Mixture models have been around for over 150 years, as an intuitively simple and practical tool for enriching the collection of probability distributions available for modelling data. In this chapter we describe the basic ideas of the…
This paper studies identifiability and convergence behaviors for parameters of multiple types in finite mixtures, and the effects of model fitting with extra mixing components. First, we present a general theory for strong identifiability,…
We propose a novel estimator for the number of components (denoted by $M$) in a K-variate non-parametric finite mixture model, where the analyst has repeated observations of $K\geq2$ variables that are independent given a finitely supported…
Mixture models are widely used in modeling heterogeneous data populations. A standard approach of mixture modeling assumes that the mixture component takes a parametric kernel form. In many applications, making parametric assumptions on the…
We present a new subspace-based method to construct probabilistic models for high-dimensional data and highlight its use in anomaly detection. The approach is based on a statistical estimation of probability density using densities of…
Finite mixture models have long been used across a variety of fields in engineering and sciences. Recently there has been a great deal of interest in quantifying the convergence behavior of the \emph{mixing measure}, a fundamental object…
In finite mixture models, apart from underlying mixing measure, true kernel density function of each subpopulation in the data is, in many scenarios, unknown. Perhaps the most popular approach is to choose some kernel functions that we…
A natural Bayesian approach for mixture models with an unknown number of components is to take the usual finite mixture model with Dirichlet weights, and put a prior on the number of components---that is, to use a mixture of finite mixtures…
The Dirichlet process mixture model and more general mixtures based on discrete random probability measures have been shown to be flexible and accurate models for density estimation and clustering. The goal of this paper is to illustrate…
Mixed membership models are an extension of finite mixture models, where each observation can partially belong to more than one mixture component. A probabilistic framework for mixed membership models of high-dimensional continuous data is…
A Bernoulli Mixture Model (BMM) is a finite mixture of random binary vectors with independent dimensions. The problem of clustering BMM data arises in a variety of real-world applications, ranging from population genetics to activity…
This paper is concerned with the formulation of $N$-mixture models for estimating the abundance and probability of detection of a species from binary response, count and time-to-detection data. A modelling framework, which encompasses…