Modelling mechanisms with causal cycles
- 507 Downloads
Mechanistic philosophy of science views a large part of scientific activity as engaged in modelling mechanisms. While science textbooks tend to offer qualitative models of mechanisms, there is increasing demand for models from which one can draw quantitative predictions and explanations. Casini et al. (Theoria 26(1):5–33, 2011) put forward the Recursive Bayesian Networks (RBN) formalism as well suited to this end. The RBN formalism is an extension of the standard Bayesian net formalism, an extension that allows for modelling the hierarchical nature of mechanisms. Like the standard Bayesian net formalism, it models causal relationships using directed acyclic graphs. Given this appeal to acyclicity, causal cycles pose a prima facie problem for the RBN approach. This paper argues that the problem is a significant one given the ubiquity of causal cycles in mechanisms, but that the problem can be solved by combining two sorts of solution strategy in a judicious way.
KeywordsBayesian nets Recursive Bayesian nets Cyclic causality Mechanisms Feedback Causal models Causation Mechanistic modelling
We would like to thank Lorenzo Casini, George Darby, Phyllis Illari, Mike Joffe, Federica Russo, and Michael Wilde for their helpful comments on this paper. Jon Williamson’s research is supported by the UK Arts and Humanities Research Council. Bert Leuridan is Postdoctoral Fellow of the Research Foundation—Flanders (FWO).
- Bechtel, W., & Abrahamsen, A. (2005). Explanation: A mechanist alternative. Studies in History and Philosophy of Biological and Biomedical Sciences, 36(2), 421–441.Google Scholar
- Bernard, A., & Hartemink, A. (2005). Informative structure priors: Joint learning of dynamic regulatory networks from multiple types of data. In R. Altman, A. K. Dunker, L. Hunter, T. Jung, & T. Klein (Eds.), Proceedings of the Pacific symposium on biocomputing (PSB05) (pp. 459–470). Hackensack, NJ: World Scientific.Google Scholar
- Boon, N. A., Colledge, N. R., Walker, B. R., & Hunter, J. A. (Eds.). (2006). Davidson’s principles & practice of medicine (20th ed.). Edinburgh: Churchill Livingstone.Google Scholar
- Bouchaffra, D. (2010). Topological dynamic Bayesian networks. In Proceedings of the twentieth IEEE international conference on pattern recognition (pp. 898–901).Google Scholar
- Cartwright, N. (2002). Against modularity, the causal Markov condition, and any link between the two: Comments on Hausman and Woodward. The British Journal for the Philosophy of Science, 53(3), 411–453.Google Scholar
- Casini, L., Illari, P. M., Russo, F., & Williamson, J. (2011). Models for prediction, explanation and control: Recursive Bayesian networks. Theoria, 26(1), 5–33.Google Scholar
- Cowell, R. G., Dawid, A. P., Lauritzen, S. L., & Spiegelhalter, D. J. (1999). Probabilistic networks and expert systems. Berlin: Springer.Google Scholar
- Doshi-Velez, F., Wingate, D., Tenenbaum, J., & Roy, N. (2011). Infinite dynamic bayesian networks. In L. Getoor & T. Scheffer (Eds.), Proceedings of the 28th international conference on machine learning (ICML) (pp. 913–920). Montreal: Omnipress.Google Scholar
- Friedman, N., Murphy, K. P., & Russell, S. J. (1998). Learning the structure of dynamic probabilistic networks. In G. F. Cooper & S. Moral (Eds.), Proceedings of the fourteenth conference on uncertainty in artificial intelligence (UAI) (pp. 139–147), San Mateo, CA. Morgan Kaufmann.Google Scholar
- Gebharter, A., & Kaiser, M. I. (2012). Causal graphs and mechanisms. In A. Hüttemann, M. I. Kaiser, & O. Scholz (Eds.), Explanation in the special sciences. The case of biology and history. Synthese Library. Dordrecht: Springer.Google Scholar
- Ghahramani, Z. (1998). Learning dynamic bayesian networks. In C. Giles & M. Gori (Eds.), Adaptive processing of sequences and data structures. Lecture notes in computer science (Vol. 1387, pp. 168–197). Berlin: Springer. doi: 10.1007/BFb0053999.
- Glennan, S. S. (2005). Modeling mechanisms. Studies in History and Philosophy of Biological and Biomedical Sciences, 36(2), 443–464.Google Scholar
- Hausman, D. M., & Woodward, J. (2004a). Manipulation and the causal Markov condition. Philosophy of Science, 55(5), 147–161.Google Scholar
- Koster, J. T. A. (1996). Markov properties of nonrecursive causal models. Annals of Statistics, 24(5), 2148–2177.Google Scholar
- Leuridan, B. (2014). The structure of scientific theories, explanation, and unification. A causal-structural account. The British Journal for the Philosophy of Science doi: 10.1093/bjps/axt015.
- Murphy, K. P. (2002). Dynamic Bayesian networks: Representation, inference and learning. PhD thesis, Computer Science, University of California, Berkeley.Google Scholar
- Neal, R. (2000).On deducing conditional independence from \(d\)-separation in causal graphs with feedback: The uniqueness condition is not suffient. Journal of Artificial Intelligence Research, 12, 87–91.Google Scholar
- Neapolitan, R. E. (1990). Probabilistic reasoning in expert systems: Theory and algorithms. New York: Wiley.Google Scholar
- Pearl, J. (1988). Probabilistic reasoning in intelligent systems: Networks of plausible inference. San Mateo, CA: Morgan Kaufmann.Google Scholar
- Pearl, J. (2000). Causality: Models, reasoning, and inference. Cambridge: Cambridge University Press.Google Scholar
- Pearl, J., & Dechter, R. (1996). Identifying independencies in causal graphs with feedback. In Uncertainty in artificial intelligence: Proceedings of the twelfth conference (pp. 420–426). San Mateo, CA. Morgan Kaufmann.Google Scholar
- Seidenfeld, T. (1987). Entropy and uncertainty. In I. B. MacNeill & G. J. Umphrey (Eds.), Foundations of statistical inference (pp. 259–287). Dordrecht: Reidel.Google Scholar
- Spirtes, P. (1995). Directed cyclic graphical representation of feedback models. In P. Besnard & S. Hanks (Eds.), Proceedings of the eleventh conference on uncertainty in artificial intelligence (pp. 491–498). San Mateo, CA: Morgan Kaufmann.Google Scholar
- Spirtes, P., Glymour, C., & Scheines, R. (2000). Causation, prediction, and search. Cambridge, MA: MIT Press.Google Scholar
- Spirtes, P., Glymour, C., Scheines, R., & Tillman, R. (2010). Automated search for causal relations—Theory and practice. In R. Dechter, H. Geffner, & J. Y. Halpern (Eds.), Heuristics, probability and causality: A tribute to Judea Pearl (pp. 467–506). London: College Publications.Google Scholar
- Williamson, J. (2005). Bayesian nets and causality: Philosophical and computational foundations. Oxford: Oxford University Press.Google Scholar
- Woodward, J. (2003). Making things happen. A theory of causal explanation. New York: Oxford University Press.Google Scholar