Related papers: Fitting A Mixture Distribution to Data: Tutorial
An often-cited fact regarding mixing or mixture distributions is that their density functions are able to approximate the density function of any unknown distribution to arbitrary degrees of accuracy, provided that the mixing or mixture…
We obtain an approximate Gaussian distribution from a Poisson distribution after doing a change of variable. A new chi-square function is obtained which can be used for parameter estimations and goodness-of-fit testing when adjusting curves…
Probabilistic clustering models (or equivalently, mixture models) are basic building blocks in countless statistical models and involve latent random variables over discrete spaces. For these models, posterior inference methods can be…
We present a Bayesian mixture model for estimating the joint distribution of mixed ordinal, nominal, and continuous data conditional on a set of fixed variables. The model uses multivariate normal and categorical mixture kernels for the…
This paper presents a high-level description of the R software package mixdistreg to fit mixture of experts distributional regression models. The proposed framework is implemented in R using the deepregression software template, which is…
Cluster analysis is one of the essential tasks in data mining and knowledge discovery. Each type of data poses unique challenges in achieving relatively efficient partitioning of the data into homogeneous groups. While the algorithms for…
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…
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…
The question of polynomial learnability of probability distributions, particularly Gaussian mixture distributions, has recently received significant attention in theoretical computer science and machine learning. However, despite major…
The definition and the properties of a Gaussian point distribution, in contrast to the well-known properties of a Gaussian random field are discussed. Constraints for the number density and the two-point correlation function arise. A simple…
A weighted likelihood approach for robust fitting of a mixture of multivariate Gaussian components is developed in this work. Two approaches have been proposed that are driven by a suitable modification of the standard EM and CEM…
Machine learning systems operate under the assumption that training and test data are sampled from a fixed probability distribution. However, this assumptions is rarely verified in practice, as the conditions upon which data was acquired…
While Bayesian inference provides a principled framework for reasoning under uncertainty, its widespread adoption is limited by the intractability of exact posterior computation, necessitating the use of approximate inference. However,…
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…
Clustering is the process of finding underlying group structures in data. Although mixture model-based clustering is firmly established in the multivariate case, there is a relative paucity of work on matrix variate distributions and none…
We propose a two-component mixture of a noninformative (diffuse) and an informative prior distribution, weighted through the data in such a way to prefer the first component if a prior-data conflict arises. The data-driven approach for…
Generalized linear model with $L_1$ and $L_2$ regularization is a widely used technique for solving classification, class probability estimation and regression problems. With the numbers of both features and examples growing rapidly in the…
We bring together topological data analysis, applied category theory, and machine learning to study multiparameter hierarchical clustering. We begin by introducing a procedure for flattening multiparameter hierarchical clusterings. We…
The paper introduces a methodology for visualizing on a dimension reduced subspace the classification structure and the geometric characteristics induced by an estimated Gaussian mixture model for discriminant analysis. In particular, we…
The Poisson distribution arises naturally when dealing with data involving counts, and it has found many applications in inverse problems and imaging. In this work, we develop an approximate Bayesian inference technique based on expectation…