Abstract
We consider causally sufficient acyclic causal models in which the relationship among the variables is nonlinear while disturbances have linear effects, and show that three principles, namely, the causal Markov condition (together with the independence between each disturbance and the corresponding parents), minimum disturbance entropy, and mutual independence of the disturbances, are equivalent. This motivates new and more efficient methods for some causal discovery problems. In particular, we propose to use multichannel blind deconvolution, an extension of independent component analysis, to do Granger causality analysis with instantaneous effects. This approach gives more accurate estimates of the parameters and can easily incorporate sparsity constraints. For additive disturbance-based nonlinear causal discovery, we first make use of the conditional independence relationships to obtain the equivalence class; undetermined causal directions are then found by nonlinear regression and pairwise independence tests. This avoids the brute-force search and greatly reduces the computational load.
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References
Cichocki, A., Amari, S.: Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications. John Wiley & Sons, UK (2003) (corrected and revisited edition)
Cover, T.M., Thomas, J.A.: Elements of Information Theory. Wiley, Chichester (1991)
Gibbs, P.: Event-Symmetric Space-Time. Weburbia Press, Great Britain (1998)
Granger, C.: Testing for causality: A personal viewpoint. Journal of Economic Dynamics and Control 2 (1980)
Gretton, A., Fukumizu, K., Teo, C.H., Song, L., Schölkopf, B., Smola, A.J.: A kernel statistical test of independence. In: NIPS 20, pp. 585–592. MIT Press, Cambridge (2008)
Hoyer, P.O., Janzing, D., Mooji, J., Peters, J., Schölkopf, B.: Nonlinear causal discovery with additive noise models. In: NIPS 21, Vancouver, B.C., Canada (2009)
Hyvärinen, A.: Fast and robust fixed-point algorithms for independent component analysis. IEEE Transactions on Neural Networks 10(3), 626–634 (1999)
Hyvärinen, A., Karhunen, J., Oja, E.: Independent Component Analysis. John Wiley & Sons, Inc., Chichester (2001)
Hyvärinen, A., Ramkumar, P., Parkkonen, L., Hari, R.: Independent component analysis of short-time Fourier transforms for spontaneous EEG/MEG analysis (2008) (submitted manuscript)
Hyvärinen, A., Shimizu, S., Hoyer, P.O.: Causal modelling combining instantaneous and lagged effects: an identifiable model based on non-gaussianity. In: ICML 2008, Helsinki, Finland, pp. 424–431 (2008)
Liu, R.W., Luo, H.: Direct blind separation of independent non-Gaussian signals with dynamic channels. In: Proc. Fifth IEEE Workshop on Cellular Neural Networks and their Applications, London, England, April 1998, pp. 34–38 (1998)
Margaritis, D.: Distribution-free learning of bayesian network structure in continuous domains. In: Proceedings of the 20th Conference on Artificial Intelligence (AAAI 2005), Pittsburgh, PA, July 2005, pp. 825–830 (2005)
Pearl, J.: Causality: Models, Reasoning, and Inference. Cambridge University Press, Cambridge (2000)
Pellet, J.P., Elisseeff, A.: Using markov blankets for causal structure learning. Journal of Machine Learning Research 9, 1295–1342 (2008)
Rasmussen, C.E., Williams, C.K.I.: Gaussian Processes for Machine Learning. MIT Press, Cambridge (2006)
Reale, M., Tunnicliffe Wilson, G.: Identification of vector ar models with recursive structural errors using conditional independence graphs. Statistical Methods and Applications 10(1-3), 49–65 (2001)
Schwarz, G.: Estimating the dimension of a model. The Annals of Statistics 6, C461–C464 (1978)
Shimizu, S., Hoyer, P.O., Hyvärinen, A., Kerminen, A.J.: A linear non-Gaussian acyclic model for causal discovery. Journal of Machine Learning Research 7, 2003–2030 (2006)
Spirtes, P., Glymour, C., Scheines, R.: Causation, Prediction, and Search, 2nd edn. MIT Press, Cambridge (2001)
Zhang, K., Peng, H., Chan, L., Hyvärinen, A.: ICA with sparse connections: Revisisted. In: Proc. 8rd Int. Conf. on Independent Component Analysis and Blind Signal Separation (ICA 2009), Paraty, Brazil, pp. 195–202 (2009)
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Zhang, K., Hyvärinen, A. (2009). Causality Discovery with Additive Disturbances: An Information-Theoretical Perspective. In: Buntine, W., Grobelnik, M., Mladenić, D., Shawe-Taylor, J. (eds) Machine Learning and Knowledge Discovery in Databases. ECML PKDD 2009. Lecture Notes in Computer Science(), vol 5782. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04174-7_37
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DOI: https://doi.org/10.1007/978-3-642-04174-7_37
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