Temporal causal modeling with graphical granger methods

ABSTRACT

The need for mining causality, beyond mere statistical correlations, for real world problems has been recognized widely. Many of these applications naturally involve temporal data, which raises the challenge of how best to leverage the temporal information for causal modeling. Recently graphical modeling with the concept of "Granger causality", based on the intuition that a cause helps predict its effects in the future, has gained attention in many domains involving time series data analysis. With the surge of interest in model selection methodologies for regression, such as the Lasso, as practical alternatives to solving structural learning of graphical models, the question arises whether and how to combine these two notions into a practically viable approach for temporal causal modeling. In this paper, we examine a host of related algorithms that, loosely speaking, fall under the category of graphical Granger methods, and characterize their relative performance from multiple viewpoints. Our experiments show, for instance, that the Lasso algorithm exhibits consistent gain over the canonical pairwise graphical Granger method. We also characterize conditions under which these variants of graphical Granger methods perform well in comparison to other benchmark methods. Finally, we apply these methods to a real world data set involving key performance indicators of corporations, and present some concrete results.

REFERENCES

• 1: T. Chu and C. Glymour. Semi-parametric Causal Inference for Nonlinear Time Series Data. J. of Machine Learning Res., submitted, 2006.
• 2: T. Chu, D. Danks, and C. Glymour. Data Driven Methods for Nonlinear Granger Causality: Climate Teleconnection Mechanisms, 2004.
• 3: Don Coppersmith , Shmuel Winograd, Matrix multiplication via arithmetic progressions, Journal of Symbolic Computation, v.9 n.3, p.251-280, March 1990 [doi>10.1016/S0747-7171(08)80013-2]
• 4: Adrian Dobra , Chris Hans , Beatrix Jones , Joseph R. Nevins , Guang Yao , Mike West, Sparse graphical models for exploring gene expression data, Journal of Multivariate Analysis, v.90 n.1, p.196-212, July 2004 [doi>10.1016/j.jmva.2004.02.009]
• 5: M. Drton and M. D. Perlman. A SINful Approach to Gaussian Graphical Model Selection. Department of Statistics, University of Washington, Technical Report 457, 2004.
• 6: B. Efron, T. Hastie, I. Johnstone and R. Tibshirani. Least Angle Regression (with discussion). Annals of Statistics, 2003.
• 7: M. Eichler. Graphical modeling of multivariate time series with latent variables. Preprint, Universiteit Maastricht, 2006.
• 8: N. Friedman, I. Nachman, and D. Peer. Learning Bayesian network structure from massive datasets: The "sparse candidate" algorithm. In (UAI'99), 1999.
• 9: P. D. Gilbert. Combining VAR Estimation and State Space Model Reduction for Simple Good Predictions. J. of Forecasting: Special Issue on VAR Modelling, 14:229250, 1995.
• 10: G. Golub, M. Heath, and G. Wahba. Generalized cross validation as a method for choosing a good ridge parameter. Technometrics, 21: 215--224.
• 11: C. W. J. Granger. Investigating causal relations by econometric models and cross-spectral methods. Econometrica, 37: 424--438l, 1969.
• 12: David Heckerman, A tutorial on learning with Bayesian networks, Learning in graphical models, MIT Press, Cambridge, MA, 1999
• 13: P. O. Hoyer, S. Shimizu, and A. J. Kerminen. Estimation of linear, non-gaussian causal models in the presence of confounding latent variables. In (PGM'06), pp. 155--162, 2006.
• 14: M. Kalisch and P. Buehlmann. Estimating high-dimensional directed acyclic graphs with the PC algorithm. Technical report No. 130, ETH Zurich, 2005.
• 15: R. Kaplan and D. Norton. The Balanced Scorecard - Measures that Drive Performance. Harvard Business Review. 71--79, 1992.
• 16: R. Kaplan and D. Norton. The Balanced Scorecard: Translating Strategy into Action. Harvard Business School Press. Boston, MA, 1996.
• 17: S. Lauritzen. Graphical Models. Oxford University Press. 1996.
• 18: C. Meek. Graphical Models: Selecting Causal and Statistical Models. PhD thesis, Carnegie Mellon University, Philosophy Department, 1996.
• 19: N. Meinshausen and P. Buhlmann. High dimensional graphs and variable selection with the Lasso. Annals of Statistics, 34(3), 1436--1462, 2006.
• 20: A. Moneta and P. Spirtes. Graphical models for the identification of causal structures in multivariate time series models. In Proc. Fifth Intl. Conf. on Computational Intelligence in Economics and Finance, 2006.
• 21: R. Opgen-Rhein and K. Strimmer. Learning causal networks from systems biology time course data: an effective model selection procedure for the vector autoregressive process. BMC Bioinformatics 8 (suppl.) in press, 2007.
• 22: J. Pearl. Causality. Cambridge University Press, Cambridge, UK, 2000.
• 23: Sam Roweis , Zoubin Ghahramani, A unifying review of linear Gaussian models, Neural Computation, v.11 n.2, p.305-345, Feb. 15, 1999 [doi>10.1162/089976699300016674]
• 24: S. Shimizu, A. Hyvärinen, P. O. Hoyer, and Y. Kano. Finding a causal ordering via independent component analysis. Computational Statistics & Data Analysis, 50(11): 3278--3293, 2006.
• 25: Ricardo Silva , Richard Scheine , Clark Glymour , Peter Spirtes, Learning the Structure of Linear Latent Variable Models, The Journal of Machine Learning Research, 7, p.191-246, 12/1/2006
• 26: P. Spirtes, C. Glymour, and R. Scheines. Causation, Prediction, and Search. MIT Press, New York, NY, second edition, 2000.
• 27: Standard & Poor's Compustat Data. Available from http://www.compustat.com.
• 28: R. Scheines, P. Spirtes, C. Glymour, and C. Meek". TETRAD II: Tools for Discovery. Lawrence Erlbaum Associates, Hillsdale, NJ. 1994.
• 29: R. Tibshirani. Regression shrinkage and selection via the lasso. J. Royal. Statist. Soc B., Vol. 58, No. 1, pages 267--288, 1996.
• 30: P. A. Valdes-Sosa et. al.. Estimating brain functional connectivity with sparse multivariate autoregression. Philos Trans R Soc Lond B Biol Sci. 2005 May 29; 360(1457): 969--81, 2005.

INDEX TERMS

Primary Classification:
  H. Information Systems
  H.2 DATABASE MANAGEMENT
      H.2.8 Database applications
          Subjects: Data mining

General Terms:
Algorithms, Design, Performance

Keywords:
causal modeling, graphical models, time series data