Using Latent Binary Variables for Online Reconstruction of Large Scale Systems
This work addresses the challenge of real-time prediction in large-scale systems like traffic networks, but it appears incremental as it builds on existing message-passing algorithms with a novel latent variable encoding.
The paper tackles the problem of reconstructing large-scale partially observed systems, such as traffic networks, by predicting unobserved real-valued variables from a small set of observations, achieving good scalability in real-time settings through a probabilistic graphical model with latent binary variables.
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.