Related papers: Mixtures and products in two graphical models
We describe discrete restricted Boltzmann machines: probabilistic graphical models with bipartite interactions between visible and hidden discrete variables. Examples are binary restricted Boltzmann machines and discrete naive Bayes models.…
We derive relations between theoretical properties of restricted Boltzmann machines (RBMs), popular machine learning models which form the building blocks of deep learning models, and several natural notions from discrete mathematics and…
Learning the parameters of graphical models using the maximum likelihood estimation is generally hard which requires an approximation. Maximum composite likelihood estimations are statistical approximations of the maximum likelihood…
The restricted Boltzmann machine is a network of stochastic units with undirected interactions between pairs of visible and hidden units. This model was popularized as a building block of deep learning architectures and has continued to…
Modern datasets are becoming heterogeneous. To this end, we present in this paper Mixed-Variate Restricted Boltzmann Machines for simultaneously modelling variables of multiple types and modalities, including binary and continuous…
We describe and analyze a broad class of mixture models for real-valued multivariate data in which the probability density of observations within each component of the model is represented as an arbitrary combination of basis functions.…
The restricted Boltzmann machine is a graphical model for binary random variables. Based on a complete bipartite graph separating hidden and observed variables, it is the binary analog to the factor analysis model. We study this graphical…
Conditional restricted Boltzmann machines are undirected stochastic neural networks with a layer of input and output units connected bipartitely to a layer of hidden units. These networks define models of conditional probability…
There are many advantages to use probability method for nonlinear system identification, such as the noises and outliers in the data set do not affect the probability models significantly; the input features can be extracted in probability…
Mixture models are one of the most widely used statistical tools when dealing with data from heterogeneous populations. This paper considers the long-standing debate over finite mixture and infinite mixtures and brings the two modelling…
A restricted Boltzmann machine (RBM) is an undirected graphical model constructed for discrete or continuous random variables, with two layers, one hidden and one visible, and no conditional dependency within a layer. In recent years, RBMs…
Finite mixture models are statistical models which appear in many problems in statistics and machine learning. In such models it is assumed that data are drawn from random probability measures, called mixture components, which are…
Multivariate normal mixtures provide a flexible model for high-dimensional data. They are widely used in statistical genetics, statistical finance, and other disciplines. Due to the unboundedness of the likelihood function, classical…
In some contexts, mixture models can fit certain variables well at the expense of others in ways beyond the analyst's control. For example, when the data include some variables with non-trivial amounts of missing values, the mixture model…
We investigate the representation of hierarchical models in terms of marginals of other hierarchical models with smaller interactions. We focus on binary variables and marginals of pairwise interaction models whose hidden variables are…
Finite mixtures of matrix normal distributions are a powerful tool for classifying three-way data in unsupervised problems. The distribution of each component is assumed to be a matrix variate normal density. The mixture model can be…
In this paper we parameterize non-negative matrices of sum one and rank at most two. More precisely, we give a family of parameterizations using the least possible number of parameters. We also show how these parameterizations relate to a…
We propose a probability distribution for multivariate binary random variables. The probability distribution is expressed as principal minors of the parameter matrix, which is a matrix analogous to the inverse covariance matrix in the…
The goal of this paper is to demonstrate the general modeling and practical simulation of random equations with mixture model parameter random variables. Random equations, understood as stationary (non-dynamical) equations with parameters…
Boltzmann machines are undirected graphical models with two-state stochastic variables, in which the logarithms of the clique potentials are quadratic functions of the node states. They have been widely studied in the neural computing…