### 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.

Original language | English (US) |
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Title of host publication | Machine Learning and Knowledge Discovery in Databases - European Conference, ECML PKDD 2009, Proceedings |

Pages | 128-143 |

Number of pages | 16 |

Volume | 5782 LNAI |

Edition | PART 2 |

DOIs | |

State | Published - 2009 |

Event | European Conference on Machine Learning and Knowledge Discovery in Databases, ECML PKDD 2009 - Bled, Slovenia Duration: Sep 7 2009 → Sep 11 2009 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Number | PART 2 |

Volume | 5782 LNAI |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | European Conference on Machine Learning and Knowledge Discovery in Databases, ECML PKDD 2009 |
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Country | Slovenia |

City | Bled |

Period | 9/7/09 → 9/11/09 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Machine Learning and Knowledge Discovery in Databases - European Conference, ECML PKDD 2009, Proceedings*(PART 2 ed., Vol. 5782 LNAI, pp. 128-143). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5782 LNAI, No. PART 2). https://doi.org/10.1007/978-3-642-04174-7_9

**Dynamic factor graphs for time series modeling.** / Mirowski, Piotr; LeCun, Yann.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Machine Learning and Knowledge Discovery in Databases - European Conference, ECML PKDD 2009, Proceedings.*PART 2 edn, vol. 5782 LNAI, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), no. PART 2, vol. 5782 LNAI, pp. 128-143, European Conference on Machine Learning and Knowledge Discovery in Databases, ECML PKDD 2009, Bled, Slovenia, 9/7/09. https://doi.org/10.1007/978-3-642-04174-7_9

}

TY - GEN

T1 - Dynamic factor graphs for time series modeling

AU - Mirowski, Piotr

AU - LeCun, Yann

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

KW - Dynamic Bayesian networks

KW - Expectation-maximization

KW - Factor graphs

KW - Recurrent networks

KW - Time series

UR - http://www.scopus.com/inward/record.url?scp=70349961665&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70349961665&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-04174-7_9

DO - 10.1007/978-3-642-04174-7_9

M3 - Conference contribution

AN - SCOPUS:70349961665

SN - 3642041736

SN - 9783642041730

VL - 5782 LNAI

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 128

EP - 143

BT - Machine Learning and Knowledge Discovery in Databases - European Conference, ECML PKDD 2009, Proceedings

ER -