Related papers: Mixtures and products in two graphical models

Probabilistic mixture models have been widely used for different machine learning and pattern recognition tasks such as clustering, dimensionality reduction, and classification. In this paper, we focus on trying to solve the most common…

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…

We propose a multivariate probability distribution that models a linear correlation between binary and continuous variables. The proposed distribution is a natural extension of the previously developed multivariate binary distribution. As…

In this article, we introduce mixture representations for likelihood ratio ordered distributions. Essentially, the ratio of two probability densities, or mass functions, is monotone if and only if one can be expressed as a mixture of…

This article concerns a class of generalized linear mixed models for clustered data, where the random effects are mapped uniquely onto the grouping structure and are independent between groups. We derive necessary and sufficient conditions…

We review Boltzmann machines and energy-based models. A Boltzmann machine defines a probability distribution over binary-valued patterns. One can learn parameters of a Boltzmann machine via gradient based approaches in a way that log…

We study mixed models with a single grouping factor, where inference about unknown parameters requires optimizing a marginal likelihood defined by an intractable integral. Low-dimensional numerical integration techniques are regularly used…

We define a message-passing algorithm for computing magnetizations in Restricted Boltzmann machines, which are Ising models on bipartite graphs introduced as neural network models for probability distributions over spin configurations. To…

In this article, we introduce finite mixture models (FMMs) renowned for capturing population heterogeneity. Our focus lies in establishing stochastic comparisons between two arithmetic (finite) mixture models, employing the vector…

Many econometric models can be analyzed as finite mixtures. We focus on two-component mixtures and we show that they are nonparametrically point identified by a combination of an exclusion restriction and tail restrictions. Our…

We consider a two-component mixture model with one known component. We develop methods for estimating the mixing proportion and the unknown distribution nonparametrically, given i.i.d.~data from the mixture model, using ideas from shape…

We introduce a lattice Boltzmann for simulating an immiscible binary fluid mixture. Our collision rules are derived from a macroscopic thermodynamic description of the fluid in a way motivated by the Cahn-Hilliard approach to…

We present some product representations for random variables with the Linnik, Mittag-Leffler and Weibull distributions and establish the relationship between the mixing distributions in these representations. The main result is the…

Bayesian nonparametric mixture models are common for modeling complex data. While these models are well-suited for density estimation, recent results proved posterior inconsistency of the number of clusters when the true number of…

The linearized collision operator of the Boltzmann equation can in a natural way be written as a sum of a positive multiplication operator, the collision frequency, and an integral operator. Compactness of the integral operator for…

In theory, the probabilistic linkage method provides two distinct advantages over non-probabilistic methods, including minimal rates of linkage error and accurate measures of these rates for data users. However, implementations can fall…

We study the mixing properties of permutations obtained as a product of two uniformly random permutations of fixed cycle types. For instance, we give an exact formula for the probability that elements $1,2,...,k$ are in distinct cycles of…

Probabilistic finite mixture models are widely used for unsupervised clustering. These models can often be improved by adapting them to the topology of the data. For instance, in order to classify spatially adjacent data points similarly,…

Restricted Boltzmann machines (RBMs) are endowed with the universal power of modeling (binary) joint distributions. Meanwhile, as a result of their confining network structure, training RBMs confronts less difficulties (compared with more…

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…