Dynamic factor graphs for time series modeling

Piotr Mirowski, Yann Lecun

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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.

Original languageEnglish (US)
Title of host publicationMachine Learning and Knowledge Discovery in Databases - European Conference, ECML PKDD 2009, Proceedings
Number of pages16
EditionPART 2
StatePublished - 2009
EventEuropean Conference on Machine Learning and Knowledge Discovery in Databases, ECML PKDD 2009 - Bled, Slovenia
Duration: Sep 7 2009Sep 11 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 2
Volume5782 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


OtherEuropean Conference on Machine Learning and Knowledge Discovery in Databases, ECML PKDD 2009


  • Dynamic Bayesian networks
  • Expectation-maximization
  • Factor graphs
  • Recurrent networks
  • Time series

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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