Abstract
Discovery of temporal structures and finding causal interactions among time series have recently attracted attention of the data mining community. Among various causal notions graphical Granger causality is well-known due to its intuitive interpretation and computational simplicity. Most of the current graphical approaches are designed for homogeneous datasets i.e. the interacting processes are assumed to have the same data distribution. Since many applications generate heterogeneous time series, the question arises how to leverage graphical Granger models to detect temporal causal dependencies among them. Profiting from the generalized linear models, we propose an efficient Heterogeneous Graphical Granger Model (HGGM) for detecting causal relation among time series having a distribution from the exponential family which includes a wider common distributions e.g. Poisson, gamma. To guarantee the consistency of our algorithm we employ adaptive Lasso as a variable selection method. Extensive experiments on synthetic and real data confirm the effectiveness and efficiency of HGGM.
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I.e. the resulting sequence of estimates does not have to converge in probability to the optimal solution for variable selection under certain conditions (Sect. 2 in [20]).
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References
Arnold, A., Liu, Y., Abe, N.: Temporal causal modelling with graphical Granger methods. In: KDD (2007)
Bacsó, N.: Das Klima des Donauraumes. Geoforum (1971)
Bahadori, M.T., Liu, Y.: Granger causality analysis in irregular time series. In: SDM (2012)
Budhathoki, K., Vreeken, J.: Causal inference by compression. In: ICDM (2016)
Budhathoki, K., Vreeken, J.: MDL for causal inference on discrete data. In: ICDM (2017)
Budhathoki, K., Vreeken, J.: Causal inference on event sequences. In: SDM (2018)
Cheng, D., Bahadori, M.T., Liu, Y.: FBLG: a simple and effective approach for temporal dependence discovery from time series data. In: KDD (2014)
Granger, C.W.: Investigating causal relations by econometric models and cross-spectral methods. Econometrica, 424–438 (1969)
Kim, S., Putrino, D., Ghosh, S., Brown, E.: A Granger causality measure for point process models of ensemble neural spiking activity. PLOS Comput. Biol. 7, 1–13 (2011)
Marx, A., Vreeken, J.: Causal inference on multivariate and mixed-type data. In: Berlingerio, M., Bonchi, F., Gärtner, T., Hurley, N., Ifrim, G. (eds.) ECML PKDD 2018. LNCS, vol. 11052, pp. 655–671. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-10928-8_39
McIlhagga, W.: penalized: a MATLAB toolbox for fitting generalized linear models with penalties. J. Stat. Softw. (2016). Articles
Mooij, J.M., Peters, J., Janzing, D., Zscheischler, J., Schölkopf, B.: Distinguishing cause from effect using observational data: methods and benchmarks. J. Mach. Learn. Res. 17, 1103–1204 (2016)
Nelder, J.A., Baker, R.J.: Generalized linear models. In: Encyclopedia of Statistical Sciences (1972)
Peters, J., Janzing, D., Schölkopf, B.: Causal inference on discrete data using additive noise models. IEEE Trans. Pattern Anal. Mach. Intell. 33, 2436–2450 (2011)
Qiu, H., Liu, Y., Subrahmanya, N.A., Li, W.: Granger causality for time-series anomaly detection. In: ICDM (2012)
Schreiber, T.: Measuring information transfer. Phys. Rev. Lett. 85(2), 461 (2000)
Shimizu, S., Hoyer, P.O., Hyvärinen, A., Kerminen, A.: A linear non-Gaussian acyclic model for causal discovery. J. Mach. Learn. Res. 7(Oct), 2003–2030 (2006)
Shojaie, A., Michailidis, G.: Discovering graphical Granger causality using the truncating lasso penalty. Bioinformatics 26, i517–i523 (2010)
Tibshirani, R.: Regression shrinkage and selection via the Lasso. J. Roy. Stat. Soc. Ser. B (Methodol.) 58, 267–288 (1996)
Zou, H.: The adaptive Lasso and its Oracle property. J. Am. Stat. Assoc. 101, 1418–1429 (2008)
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Behzadi, S., Hlaváčková-Schindler, K., Plant, C. (2019). Granger Causality for Heterogeneous Processes. In: Yang, Q., Zhou, ZH., Gong, Z., Zhang, ML., Huang, SJ. (eds) Advances in Knowledge Discovery and Data Mining. PAKDD 2019. Lecture Notes in Computer Science(), vol 11441. Springer, Cham. https://doi.org/10.1007/978-3-030-16142-2_36
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