Abstract
Causality is increasingly integrated into decision-making processes. Often, the goal is to optimize over causal interventions to achieve specific policy objectives. However, research into causal optimization has bifurcated into either the online optimization of interventions in causal models or the offline optimization of decision rules in causal influence diagrams. This paper introduces an approximate method for offline optimizing interventions in arbitrary hybrid Bayesian networks using observational data. The optimization problem is approached by compiling discretized Bayesian networks as binary decision diagrams, whereafter running interventional queries is very efficient. This efficiency is exploited by running heuristic optimization algorithms to optimize over the interventional queries. By running experiments on a variety of large hybrid Bayesian networks, we demonstrate the practical utility of our method and discuss policy relevance.
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Notes
- 1.
In this case, we consider a one-dimensional outcome variable, although the proposed methodology is generalizable to multiple outcome variables.
- 2.
The methodology is available on https://github.com/sebastiaanbrand/bn-dd.
- 3.
Because of the nature of the do-operator and the adjustment formula of Eq. 2, nodes that are not marginalized or conditioned upon in the optimization step can be eliminated from the compilation.
References
Aglietti, V., Dhir, N., González, J., Damoulas, T.: Dynamic causal bayesian optimization. In: NeurIPS, vol. 34, pp. 10549–10560 (2021)
Aglietti, V., Lu, X., Paleyes, A., González, J.: Causal Bayesian optimization. In: AISTATS, pp. 3155–3164. PMLR (2020)
Aglietti, V., Malek, A., Ktena, I., Chiappa, S.: Constrained causal Bayesian optimization. arXiv preprint arXiv:2305.20011 (2023)
Arsenyan, V., Grosnit, A., Bou-Ammar, H.: Contextual causal Bayesian optimisation. arXiv preprint arXiv:2301.12412 (2023)
Athey, S., Wager, S.: Policy learning with observational data. Econometrica 89(1), 133–161 (2021)
Bäck, T., et al.: Evolutionary algorithms for parameter optimization–thirty years later. Evol. Comput. 31(2), 81–122 (2023)
Bareinboim, E., Correa, J.D., Ibeling, D., Icard, T.F.: On Pearl’s hierarchy and the foundations of causal inference. In: Probabilistic and Causal Inference (2022)
Bareinboim, E., Forney, A., Pearl, J.: Bandits with unobserved confounders: a causal approach. In: NeurIPS, vol. 28 (2015)
Beuzen, T., Marshall, L., Splinter, K.D.: A comparison of methods for discretizing continuous variables in Bayesian networks. Environ. Model. Software 108, 61–66 (2018)
Beyer, H.G., Schwefel, H.P.: Evolution strategies-a comprehensive introduction. Nat. Comput. 1, 3–52 (2002)
Broyden, C.: The convergence of a class of double-rank minimization algorithms: 2. The new algorithm. IMA J. Appl. Math. 6(3) (1970)
Bryant, R.E.: Graph-based algorithms for Boolean function manipulation. Trans. Comput. 100(8), 677–691 (1986)
Chavira, M., Darwiche, A.: On probabilistic inference by weighted model counting. Artif. Intell. 172(6–7), 772–799 (2008)
Dal, G., Lucas, P.: Weighted positive binary decision diagrams for exact probabilistic inference. Int. J. Approximate Reasoning 90, 411–432 (2017)
Everitt, T., Carey, R., Langlois, E.D., Ortega, P.A., Legg, S.: Agent incentives: a causal perspective. In: AAAI, vol. 35, no. 13, pp. 11487–11495 (2021)
Fletcher, R.: A new approach to variable metric algorithms. The Computer Journal 13(3), 317–322 (1970). https://doi.org/10.1093/comjnl/13.3.317
Geffner, T., et al.: Deep end-to-end causal inference. arXiv preprint arXiv:2202.02195 (2022)
Goldfarb, D.: A family of variable-metric methods derived by variational means. Math. Comput. 24(109), 23–26 (1970)
Gultchin, L., Aglietti, V., Bellot, A., Chiappa, S.: Functional causal Bayesian optimization. arXiv preprint arXiv:2306.06409 (2023)
Koller, D., Friedman, N.: Probabilistic Graphical Models: Principles and Techniques. MIT Press (2009)
Kreif, N., DiazOrdaz, K.: Machine learning in policy evaluation: new tools for causal inference. arXiv (2019). https://doi.org/10.48550/arXiv.1903.00402
Lattimore, F., Lattimore, T., Reid, M.D.: Causal bandits: learning good interventions via causal inference. In: NeurIPS, vol. 29 (2016)
Lee, S., Bareinboim, E.: Structural causal bandits: where to intervene? In: Advances in Neural Information Processing Systems, vol. 31 (2018)
Lee, S., Bareinboim, E.: Structural causal bandits with non-manipulable variables. In: AAAI, vol. 33, pp. 4164–4172 (2019)
Li, H., Hubbard, A., van der Laan, M.: Targeted learning on variable importance measure for heterogeneous treatment effect. preprint arXiv:2309.13324 (2023)
Malekovic, N., Vonk, M., Birkman, L., Sweijs, T., Kononova, A., Bäck, T.: Angling for causality behind security: natural causes of armed conflict in Iraq. Preprints (2024). https://doi.org/10.20944/preprints202402.0556.v1
Malenica, I., Coyle, J., van der Laan, M.J.: tmle3mopttx: Targeted learning and variable importance with optimal individualized categorical treatment (2022). https://github.com/tlverse/tmle3mopttx, r package version 1.0.0
Meunier, L., et al.: Black-box optimization revisited: Improving algorithm selection wizards through massive benchmarking. IEEE Trans. Evol. Comput. 26(3) (2022)
Neil, M., Tailor, M., Marquez, D.: Inference in hybrid Bayesian networks using dynamic discretization. Stat. Comput. 17(3), 219–233 (2007)
de Nobel, J., Ye, F., Vermetten, D., Wang, H., Doerr, C., Bäck, T.: IOHexperimenter: Benchmarking platform for iterative optimization heuristics. CoRR abs/2111.04077 (2021), arXiv:2111.04077
Nojavan, F., Qian, S.S., Stow, C.A.: Comparative analysis of discretization methods in Bayesian networks. Environ. Model. Software 87, 64–71 (2017)
Opgen-Rhein, R., Strimmer, K.: From correlation to causation networks: a simple approximate learning algorithm and its application to high-dimensional plant gene expression data. BMC Syst. Biol. 1(1), 1–10 (2007)
Pearl, J.: Causality. Cambridge University Press, Cambridge (2009)
Powell, M.: An efficient method for finding the minimum of a function of several variables without calculating derivatives. Comput. J. 7(2) (1964)
Rapin, J., Teytaud, O.: Nevergrad - a gradient-free optimization platform (2018). https://GitHub.com/FacebookResearch/Nevergrad
Salmerón, A., Rumí, R., Langseth, H., Nielsen, T.D., Madsen, A.L.: A review of inference algorithms for hybrid Bayesian networks. J. Artif. Intell. Res. 62, 799–828 (2018). https://doi.org/10.1613/jair.1.11228
Scutari, M.: Learning Bayesian networks with the BNLearn R package. J. Stat. Softw. 35(3), 1–22 (2010)
Shanno, D.F.: Conditioning of quasi-newton methods for function minimization. Math. Comput. 24(111), 647–656 (1970)
Storn, R., Price, K.: Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces. J. Global Optim. 11(4), 341–359 (1997)
Sussex, S., Sessa, P.G., Makarova, A., Krause, A.: Adversarial causal Bayesian optimization (2023)
van der Zander, B., Liśkiewicz, M., Textor, J.: Separators and adjustment sets in causal graphs: complete criteria and an algorithmic framework. Artif. Intell. 270, 1–40 (2019)
Vermetten, D., de Nobel, J., Ye, F., Wang, H., Doerr, C., Bäck, T.: IOHprofiler: iterative Optimization Heuristics Profiler (2018). https://github.com/IOHprofiler, wiki available at https://iohprofiler.github.io/
Vitolo, C., Scutari, M., Ghalaieny, M., Tucker, A., Russell, A.: Modeling air pollution, climate, and health data using Bayesian networks: a case study of the English regions. Earth Space Sci. 5(4), 76–88 (2018)
Vonk, M.C., Brand, S., Malekovic, N., Bäck, T., Laarman, A., Kononova, A.V.: Efficient inference in Bayesian networks with continuous variables a discretization and knowledge compilation approach. Available at SSRN 4620451 (2023)
Vonk, M.C., Malekovic, N., Bäck, T., Kononova, A.V.: Disentangling causality: assumptions in causal discovery and inference. Artif. Intell. Rev. 1–37 (2023)
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Vonk, M.C. et al. (2024). Optimizing Causal Interventions in Hybrid Bayesian Networks. In: Lesot, MJ., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2024. Lecture Notes in Networks and Systems, vol 1174. Springer, Cham. https://doi.org/10.1007/978-3-031-74003-9_20
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