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<b:Sources SelectedStyle="" xmlns:b="http://schemas.openxmlformats.org/officeDocument/2006/bibliography"  xmlns="http://schemas.openxmlformats.org/officeDocument/2006/bibliography" >
<b:Source>
<b:Tag>Mirowski+LeCun2009</b:Tag>
<b:SourceType>Misc</b:SourceType>
<b:Year>2009</b:Year>
<b:Author>
<b:Author><b:NameList>
<b:Person><b:Last>Mirowski</b:Last><b:First>P.</b:First></b:Person>
<b:Person><b:Last>LeCun</b:Last><b:First>Y.</b:First></b:Person>
</b:NameList></b:Author>
</b:Author>
<b:Title>Dynamic Factor Graphs for Time Series Modeling</b:Title>
<b:Comments>This article presents a method for training Dynamic Fac- tor Graphs (DFG) with continuous latent state variables. A DFG in- cludes factors modeling joint probabilities between hidden and observed variables, and factors modeling dynamical constraints on hidden vari- ables. 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. Be- cause 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&#8217; parameters. These alternated in- ference 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 suc- cessfully reconstruct missing motion capture data.</b:Comments>
</b:Source>
</b:Sources>