Related papers: Finite mixture models do not reliably learn the nu…
We consider the frequency response problem and derive a posteriori error estimates for the discrete error in a reduced finite element model obtained using the component mode synthesis (CMS) method. We provide estimates in a linear quantity…
The study of mixture models constitutes a large domain of research in statistics. In the first part of this work, we present phi-divergences and the existing methods which produce robust estimators. We are more particularly interested in…
Given sufficiently many components, it is often cited that finite mixture models can approximate any other probability density function (pdf) to an arbitrary degree of accuracy. Unfortunately, the nature of this approximation result 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…
The state-of-the art proof of a global inf-sup condition on mixed finite element schemes does not allow for an analysis of truly indefinite, second-order linear elliptic PDEs. This paper, therefore, first analyses a nonconforming finite…
We develop a structural framework for modeling and inferring unobserved heterogeneity in dynamic panel-data models. Unlike methods treating clustering as a descriptive device, we model heterogeneity as arising from a latent clustering…
The normal compositional model (NCM) has been extensively used in hyperspectral unmixing. However, most of the previous research has focused on estimation of endmembers and/or their variability. Also, little work has employed spatial…
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…
Mixture models are often used to identify meaningful subpopulations (i.e., clusters) in observed data such that the subpopulations have a real-world interpretation (e.g., as cell types). However, when used for subpopulation discovery,…
In this paper, we study the classical problem of estimating the proportion of a finite population. First, we consider a fixed sample size method and derive an explicit sample size formula which ensures a mixed criterion of absolute and…
In some situations, EM algorithm shows slow convergence problems. One possible reason is that standard procedures update the parameters simultaneously. In this paper we focus on finite mixture estimation. In this framework, we propose a…
The large-sample properties of likelihood-based statistical inference under mixture models have received much attention from statisticians. Although the consistency of the nonparametric MLE is regarded as a standard conclusion, many…
Future prediction is a fundamental principle of intelligence that helps plan actions and avoid possible dangers. As the future is uncertain to a large extent, modeling the uncertainty and multimodality of the future states is of great…
Forward and inverse models are used throughout different engineering fields to predict and understand the behaviour of systems and to find parameters from a set of observations. These models use root-finding and minimisation techniques…
Dependence modeling of multivariate count data has garnered significant attention in recent years. Multivariate elliptical copulas are typically preferred in statistical literature to analyze dependence between repeated measurements of…
Finite mixture models have been widely used to model and analyze data from a heterogeneous populations. Moreover, data of this kind can be missing or subject to some upper and/or lower detection limits because of the restriction of…
Financial studies require volatility based models which provides useful insights on risks related to investments. Stochastic volatility models are one of the most popular approaches to model volatility in such studies. The asset returns…
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…
Finite mixture modelling is a popular method in the field of clustering and is beneficial largely due to its soft cluster membership probabilities. A common method for fitting finite mixture models is to employ spectral clustering, which…
The most fundamental problem in statistics is the inference of an unknown probability distribution from a finite number of samples. For a specific observed data set, answers to the following questions would be desirable: (1) Estimation:…