Support vector machines for dynamic reconstruction of a chaotic system
Advances in kernel methods
Using support vector machines for time series prediction
Advances in kernel methods
Learning nonlinear dynamical systems using an EM algorithm
Proceedings of the 1998 conference on Advances in neural information processing systems II
Neural Networks: Tricks of the Trade, this book is an outgrowth of a 1996 NIPS workshop
Modeling systems with internal state using evolino
GECCO '05 Proceedings of the 7th annual conference on Genetic and evolutionary computation
Factor graphs and the sum-product algorithm
IEEE Transactions on Information Theory
Nonlinear dynamical factor analysis for state change detection
IEEE Transactions on Neural Networks
Energy-based temporal neural networks for imputing missing values
ICONIP'12 Proceedings of the 19th international conference on Neural Information Processing - Volume Part II
Training energy-based models for time-series imputation
The Journal of Machine Learning Research
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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.