Dynamic Factor Graphs for Time Series Modeling

Piotr Mirowski, Courant Institute of Mathematical Science, New York University, USA
Yann LeCun, Courant Institute of Mathematical Science, New York University, USA

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Abstract

This article presents a method for training Dynamic Factor Graphs (DFG) with continuous latent state variables. A DFG includes factors modeling joint
probabilities between hidden and observed variables, and factors modeling
dynamical constraints on hidden variables. The DFG assigns a scalar energy to each configuration of hidden and observed variables. A gradient-based inference procedure finds the minimum-energy state sequence for a given
observation sequence. Because the factors are designed to ensure a constant
partition function, they can be trained by minimizing the expected energy over training sequences with respect to the factors’ parameters. These alternated inference and parameter updates can be seen as a deterministic EM-like procedure. Using smoothing regularizers, DFGs are shown to reconstruct chaotic attractors and to separate a mixture of independent oscillatory sources perfectly. DFGs outperform the best known algorithm on the CATS competition benchmark for time series prediction. DFGs also successfully reconstruct missing motion capture data.