Zhenxing Wang
ABSTRACT
Bayesian network learning algorithms have been widely used for causal discovery since the pioneer work [13,18]. Among all existing algorithms, three-phase dependency analysis algorithm (TPDA) [5] is the most efficient one in the sense that it has polynomial-time complexity. However, there are still some limitations to be improved. First, TPDA depends on mutual information-based conditional independence (CI) tests, and so is not easy to be applied to continuous data. In addition, TPDA uses two phases to get approximate skeletons of Bayesian networks, which is not efficient in practice. In this paper, we propose a two-phase algorithm with partial correlation-based CI tests: the first phase of the algorithm constructs a Markov random field from data, which provides a close approximation to the structure of the true Bayesian network; at the second phase, the algorithm removes redundant edges according to CI tests to get the true Bayesian network. We show that two-phase algorithm with partial correlation-based CI tests can deal with continuous data following arbitrary distributions rather than only Gaussian distribution.
- S. Andreassen, A. Rosenfalck, B. Falck, K. G. Olesen, and S. K. Andersen. Evaluation of the diagnostic performance of the expert emg assistant munin. Electroencephalography and Clinical Neurophysiology/Electromyography and Motor Control, 101(2):129--144, 1996.Google Scholar
Cross Ref
- K. Baba, R. Shibata, and M. Sibuya. Partial correlation and conditional correlation as measures of conditional independence. Australian & New Zealand Journal of Statistics, 46(4):657--664, December 2004.Google ScholarCross Ref
- I. A. Beinlich, H. J. Suermondt, R. M. Chavez, and G. F. Cooper. The ALARM Monitoring System: A Case Study with Two Probabilistic Inference Techniques for Belief Networks. In Second European Conf. on Artif. Intell. in Medicine, volume 38, pages 247--256, London, Great Britain, 1989.Google Scholar
- J. Binder, D. Koller, S. Russell, and K. Kanazawa. Adaptive probabilistic networks with hidden variables. Machine Learning, 29(2):213--244, 1997. Google ScholarDigital Library
- J. Cheng, R. Greiner, J. Kelly, D. A. Bell, and W. Liu. Learning bayesian networks from data: An information-theory based approach. Artif. Intell., 137(1-2):43--90, 2002. Google ScholarDigital Library
- P. Hoyer, A. Hyvarinen, R. Scheines, P. Spirtes, J. Ramsey, G. Lacerda, and S. Shimizu. Causal discovery of linear acyclic models with arbitrary distributions. In Proc. 24th Conf. on Uncertainty in Artif. Intell. (UAI-08), pages 282--289, Corvallis, Oregon, 2008. AUAI Press.Google Scholar
- A. Hyvarinen, S. Shimizu, and P. Hoyer. Causal modelling combining instantaneous and lagged effects: an identifiable model based on non-gaussianity. In Proc. of the 25th Int. Conf. on Mach. learn., pages 424--431, Helsinki, Finland, 2008. ACM. Google ScholarDigital Library
- A. L. Jensen and F. V. Jensen. Midas: An influence diagram for management of mildew in winter wheat. In Proc. of the Twelfth Annual Conf. on Uncertainty in Artif. Intell., pages 349--356, San Francisco, CA, USA, 1996. Morgan Kaufmann Publishers. Google ScholarDigital Library
- R. Kindermann and J. L. Snell. Markov Random Fields and Their Applications. American Mathematical Society, 1980.Google ScholarCross Ref
- K. Kristensen and I. A. Rasmussen. The use of a bayesian network in the design of a decision support system for growing malting barley without use of pesticides. Computers and Electronics in Agriculture, 33(3):197--217, 2002.Google ScholarCross Ref
- R. Opgen-Rhein and K. Strimmer. From correlation to causation networks: a simple approximate learning algorithm and its application to high-dimensional plant gene expression data. BMC Systems Biology, 1(37):334--353, 2007.Google Scholar
- J. Pearl. Causality : Models, Reasoning, and Inference. Cambridge University Press, March 2000. Google ScholarDigital Library
- J. Pearl and T. Verma. A theory of inferred causation. In Proc. of the Second Int. Conf. on Principles of Knowledge Representation and Reasoning, 1991.Google ScholarDigital Library
- J.-P. Pellet and A. Elisseeff. A partial correlation-based algorithm for causal structure discovery with continuous variables. In IDA, pages 229--239, 2007. Google ScholarDigital Library
- S. Shimizu, P. O. Hoyer, A. Hyvarinen, and A. Kerminen. A linear non-gaussian acyclic model for causal discovery. J. Mach. Learn. Res., 7:2003--2030, 2006. Google ScholarDigital Library
- P. Spirtes and C. Glymour. An algorithm for fast recovery of sparse causal graphs. Social Science Computer Review, 9(1):62--72, October 1991.Google ScholarCross Ref
- P. Spirtes, C. Glymour, and R. Scheines. From probability to causality. In Proc. of Advanced Computing for the Social Sciences, 1990.Google Scholar
- P. Spirtes, C. Glymour, and R. Scheines. Causation, Prediction, and Search. Springer Verlag, Berlin, 1993.Google ScholarCross Ref
- Z. Wang and L. Chan. A heuristic partial correlation-based algorithm for causal relationship discovery. In Intell. Data Engineering and Automated Learning - IDEAL 2009, pages 234--241, 2009. Google ScholarDigital Library
Index Terms
- An efficient causal discovery algorithm for linear models
Recommendations
Learning bayesian networks from Markov random fields: An efficient algorithm for linear models
Dependency analysis is a typical approach for Bayesian network learning, which infers the structures of Bayesian networks by the results of a series of conditional independence (CI) tests. In practice, testing independence conditioning on large sets ...
An Introduction to Variational Methods for Graphical Models
This paper presents a tutorial introduction to the use of variational methods for inference and learning in graphical models (Bayesian networks and Markov random fields). We present a number of examples of graphical models, including the QMR-DT database, ...
Learning Causal Relations in Multivariate Time Series Data
Many applications naturally involve time series data and the vector autoregression (VAR), and the structural VAR (SVAR) are dominant tools to investigate relations between variables in time series. In the first part of this work, we show that the SVAR ...
Comments