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

Using Latent Binary Variables for Online Reconstruction of Large Scale Systems