We propose a probabilistic graphical model realizing a minimal encoding of real variables dependencies based on possibly incomplete observation and an empirical cumulative distribution function per variable. The target application is a large scale partially observed system, like e.g. a traffic network, where a small proportion of real valued variables are observed, and the other variables have to be predicted. Our design objective is therefore to have good scalability in a real-time setting. Instead of attempting to encode the dependencies of the system directly in the description space, we propose a way to encode them in a latent space of binary variables, reflecting a rough perception of the observable (congested/non-congested for a traffic road). The method relies in part on message passing algorithms, i.e. belief propagation, but the core of the work concerns the definition of meaningful latent variables associated to the variables of interest and their pairwise dependencies. Numerical experiments demonstrate the applicability of the method in practice.

A directed generative model for binary data using a small number of hidden continuous units is investigated. The relationships between the correlations of the underlying continuous Gaussian variables and the binary output variables are utilized to learn the appropriate weights of the network. The advantages of this approach are illustrated on a translationally invariant binary distribution and on handwritten digit images. Introduction Principal Components Analysis (PCA) is a widely used statistical technique for representing data with a large number of variables [1]. It is based upon the assumption that although the data is embedded in a high dimensional vector space, most of the variability in the data is captured by a much lower climensional manifold.

A directed generative model for binary data using a small number of hidden continuous units is investigated. The relationships between the correlations of the underlying continuous Gaussian variables and the binary output variables are utilized to learn the appropriate weights of the network. The advantages of this approach are illustrated on a translationally invariant binary distribution and on handwritten digit images. Introduction Principal Components Analysis (PCA) is a widely used statistical technique for representing data with a large number of variables [1]. It is based upon the assumption that although the data is embedded in a high dimensional vector space, most of the variability in the data is captured by a much lower climensional manifold.

A directed generative model for binary data using a small number of hidden continuous units is investigated. The relationships between the correlations of the underlying continuousGaussian variables and the binary output variables are utilized to learn the appropriate weights of the network. The advantages of this approach are illustrated on a translationally invariant binarydistribution and on handwritten digit images. Introduction Principal Components Analysis (PCA) is a widely used statistical technique for representing datawith a large number of variables [1]. It is based upon the assumption that although the data is embedded in a high dimensional vector space, most of the variability in the data is captured by a much lower climensional manifold.

I} when the probability distribution that generates the input examples is member of a family that we call k-blocking distributions. Such distributions represent an important step beyond the case where each input variable is statistically independent since the 2k-blocking family contains all the Markov distributions of order k. By stochastic percept ron we mean a perceptron which, upon presentation of input vector x, outputs 1 with probability fCLJi WiXi - B).

Such distributions represent an important stepbeyond the case where each input variable is statistically independent since the 2k-blocking family contains all the Markov distributions of order k. By stochastic perceptron we mean a perceptron which,upon presentation of input vector x, outputs 1 with probability fCLJi WiXi - B).