Related papers: Mixtures and products in two graphical models

In this paper, we consider mixtures of multinomial logistic models (MNL), which are known to $\epsilon$-approximate any random utility model. Despite its long history and broad use, rigorous results are only available for learning a uniform…

The MIXANDMIX (mixtures by Anderson mixing) tool for the computation of the empirical spectral distribution of random matrices generated by mixtures of populations is described. Within the population mixture model the mapping between the…

This paper is about models for a vector of probabilities whose elements must have a multiplicative structure and sum to 1 at the same time; in certain applications, as basket analysis, these models may be seen as a constrained version of…

Forecasting with longitudinal data has been rarely studied. Most of the available studies are for continuous response and all of them are for univariate response. In this study, we consider forecasting multivariate longitudinal binary data.…

We propose a method for obtaining maximum likelihood estimates in a model with continuous and binary outcomes. Combinations of left and right censored observations are also naturally modeled in this framework. The model and estimation…

In this paper, we provide an explicit probability distribution for classification purposes. It is derived from the Bayesian nonparametric mixture of Dirichlet process model, but with suitable modifications which remove unsuitable aspects of…

Regularized regression models are well studied and, under appropriate conditions, offer fast and statistically interpretable results. However, large data in many applications are heterogeneous in the sense of harboring distributional…

In this note, we give an explicit expression for the quantile of a mixture of two random variables. We carefully examine all possible cases of discrete and continuous variables with possibly unbounded support. The result is useful for…

Maximum likelihood estimators are often of limited practical use due to the intensive computation they require. We propose a family of alternative estimators that maximize a stochastic variation of the composite likelihood function. Each of…

Existing statistical approaches to natural language problems are very coarse approximations to the true complexity of language processing. As such, no single technique will be best for all problem instances. Many researchers are examining…

Mixtures of product distributions are a powerful device for learning about heterogeneity within data populations. In this class of latent structure models, de Finetti's mixing measure plays the central role for describing the uncertainty…

Restricted Boltzmann Machines (RBMs) offer a versatile architecture for unsupervised machine learning that can in principle approximate any target probability distribution with arbitrary accuracy. However, the RBM model is usually not…

We consider the problem of classification when inputs correspond to sets of vectors. This setting occurs in many problems such as the classification of pieces of mail containing several pages, of web sites with several sections or of images…

We define a class of probability distributions that we call simplicial mixture models, inspired by simplicial complexes from algebraic topology. The parameters of these distributions represent their topology and we show that it is possible…

Restricted Boltzmann Machines are generative models that consist of a layer of hidden variables connected to another layer of visible units, and they are used to model the distribution over visible variables. In order to gain a higher…

When modeling the distribution of a set of data by a mixture of Gaussians, there are two possibilities: i) the classical one is using a set of parameters which are the proportions, the means and the variances; ii) the second is to consider…

A particularly important substructure in modeling joint linear chance-constrained programs with random right-hand sides and finite sample space is the intersection of mixing sets with common binary variables (and possibly a knapsack…

A Restricted Boltzmann Machine (RBM) is an unsupervised machine-learning bipartite graphical model that jointly learns a probability distribution over data and extracts their relevant statistical features. As such, RBM were recently…

Expanding a lower-dimensional problem to a higher-dimensional space and then projecting back is often beneficial. This article rigorously investigates this perspective in the context of finite mixture models, namely how to improve inference…

We begin by reviewing some probabilistic results about the Dirichlet Process and its close relatives, focussing on their implications for statistical modelling and analysis. We then introduce a class of simple mixture models in which…