Learning Temporal Causal Graphs for Relational Time-Series Analysis

Learning temporal causal graph structures from multivariate time-series data reveals important dependency relationships between current observations and histories, and provides a better understanding of complex systems. In this paper, we examine learning tasks where one is presented with multiple multivariate time-series, as well as a relational graph among the different time-series. We propose an L1 regularized hidden Markov random field regression framework to leverage the information provided by the relational graph and jointly infer more accurate temporal causal structures for all time-series. We test the proposed model on climate modeling and cross-species microarray data analysis applications.

[1]  Yan Liu,et al.  Spatial-temporal causal modeling for climate change attribution , 2009, KDD.

[2]  Tom Burr,et al.  Causation, Prediction, and Search , 2003, Technometrics.

[3]  M. Yuan,et al.  Model selection and estimation in regression with grouped variables , 2006 .

[4]  R. Tibshirani,et al.  Sparse inverse covariance estimation with the graphical lasso. , 2008, Biostatistics.

[5]  Radford M. Neal.  Pattern Recognition and Machine Learning , 2007, Technometrics.

[6]  M. Yuan,et al.  Model selection and estimation in the Gaussian graphical model , 2007 .

[7]  Yan Liu,et al.  Temporal causal modeling with graphical granger methods , 2007, KDD '07.

[8]  Vincent R. Gray.  Climate Change 2007: The Physical Science Basis Summary for Policymakers , 2007 .

[9]  Jeff A. Bilmes,et al.  A gentle tutorial of the em algorithm and its application to parameter estimation for Gaussian mixture and hidden Markov models , 1998 .

[10]  H. Zou,et al.  Regularization and variable selection via the elastic net , 2005 .

[11]  Le Song,et al.  Time-Varying Dynamic Bayesian Networks , 2009, NIPS.

[12]  Naoki Abe,et al.  Grouped graphical Granger modeling for gene expression regulatory networks discovery , 2009, Bioinform..

[13]  W. Landman.  Climate change 2007: the physical science basis , 2010 .

[14]  Richard Scheines,et al.  Learning the Structure of Linear Latent Variable Models , 2006, J. Mach. Learn. Res..

[15]  Michael I. Jordan,et al.  Loopy Belief Propagation for Approximate Inference: An Empirical Study , 1999, UAI.

[16]  I. Simon,et al.  Combined analysis reveals a core set of cycling genes , 2007, Genome Biology.