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2021 | OriginalPaper | Buchkapitel

Recent Advances in Counting and Sampling Markov Equivalent DAGs

verfasst von : Marcel Wienöbst, Max Bannach, Maciej Liśkiewicz

Erschienen in: KI 2021: Advances in Artificial Intelligence

Verlag: Springer International Publishing

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Abstract

Counting and sampling directed acyclic graphs (DAGs) from a Markov equivalence class are fundamental tasks in graphical causal analysis. In this paper, we discuss recently proposed polynomial-time algorithms for these tasks. The presented result solves a long-standing open problem in graphical modelling. Experiments show that the proposed algorithms are implementable and effective in practice. Our paper is an extended abstract of the work [24], honored as an AAAI-21 Distinguished Paper at the 35th AAAI Conference on Artificial Intelligence.

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Literatur
1.
Zurück zum Zitat AhmadiTeshnizi, A., Salehkaleybar, S., Kiyavash, N.: Lazyiter: a fast algorithm for counting Markov equivalent DAGs and designing experiments. In: Proceedings of the 37th International Conference on Machine Learning, ICML 2020 (2020) AhmadiTeshnizi, A., Salehkaleybar, S., Kiyavash, N.: Lazyiter: a fast algorithm for counting Markov equivalent DAGs and designing experiments. In: Proceedings of the 37th International Conference on Machine Learning, ICML 2020 (2020)
2.
Zurück zum Zitat Andersson, S.A., Madigan, D., Perlman, M.D.: A characterization of Markov equivalence classes for acyclic digraphs. Ann. Stat. 25(2), 505–541 (1997)MathSciNetMATH Andersson, S.A., Madigan, D., Perlman, M.D.: A characterization of Markov equivalence classes for acyclic digraphs. Ann. Stat. 25(2), 505–541 (1997)MathSciNetMATH
3.
Zurück zum Zitat Chickering, D.M.: Learning equivalence classes of Bayesian-network structures. J. Mach. Learn. Res. 2, 445–498 (2002)MathSciNetMATH Chickering, D.M.: Learning equivalence classes of Bayesian-network structures. J. Mach. Learn. Res. 2, 445–498 (2002)MathSciNetMATH
4.
Zurück zum Zitat Chickering, D.M.: Optimal structure identification with greedy search. J. Mach. Learn. Res. 3, 507–554 (2002)MathSciNetMATH Chickering, D.M.: Optimal structure identification with greedy search. J. Mach. Learn. Res. 3, 507–554 (2002)MathSciNetMATH
5.
Zurück zum Zitat Ganian, R., Hamm, T., Talvitie, T.: An efficient algorithm for counting Markov equivalent dags. In: Proccedings of the 34th Conference on Artificial Intelligence, AAAI 2020, pp. 10136–10143 (2020) Ganian, R., Hamm, T., Talvitie, T.: An efficient algorithm for counting Markov equivalent dags. In: Proccedings of the 34th Conference on Artificial Intelligence, AAAI 2020, pp. 10136–10143 (2020)
6.
Zurück zum Zitat Ghassami, A., Salehkaleybar, S., Kiyavash, N., Bareinboim, E.: Budgeted experiment design for causal structure learning. In: Proceedings of the 35th International Conference on Machine Learning, ICML 2018, pp. 1719–1728 (2018) Ghassami, A., Salehkaleybar, S., Kiyavash, N., Bareinboim, E.: Budgeted experiment design for causal structure learning. In: Proceedings of the 35th International Conference on Machine Learning, ICML 2018, pp. 1719–1728 (2018)
7.
Zurück zum Zitat Ghassami, A., Salehkaleybar, S., Kiyavash, N., Zhang, K.: Counting and sampling from Markovv equivalent dags using clique trees. In: Proceedings of the 33th Conference on Artificial Intelligence, AAAI 2019, pp. 3664–3671 (2019) Ghassami, A., Salehkaleybar, S., Kiyavash, N., Zhang, K.: Counting and sampling from Markovv equivalent dags using clique trees. In: Proceedings of the 33th Conference on Artificial Intelligence, AAAI 2019, pp. 3664–3671 (2019)
8.
Zurück zum Zitat Hauser, A., Bühlmann, P.: Characterization and greedy learning of interventional Markov equivalence classes of directed acyclic graphs. J. Mach. Learn. Res. 13, 2409–2464 (2012)MathSciNetMATH Hauser, A., Bühlmann, P.: Characterization and greedy learning of interventional Markov equivalence classes of directed acyclic graphs. J. Mach. Learn. Res. 13, 2409–2464 (2012)MathSciNetMATH
9.
Zurück zum Zitat He, Y.B., Geng, Z.: Active learning of causal networks with intervention experiments and optimal designs. J. Mach. Learn. Res. 9(Nov), 2523–2547 (2008) He, Y.B., Geng, Z.: Active learning of causal networks with intervention experiments and optimal designs. J. Mach. Learn. Res. 9(Nov), 2523–2547 (2008)
10.
Zurück zum Zitat He, Y., Jia, J., Yu, B.: Counting and exploring sizes of Markov equivalence classes of directed acyclic graphs. J. Mach. Learn. Res. 16(79), 2589–2609 (2015)MathSciNetMATH He, Y., Jia, J., Yu, B.: Counting and exploring sizes of Markov equivalence classes of directed acyclic graphs. J. Mach. Learn. Res. 16(79), 2589–2609 (2015)MathSciNetMATH
11.
Zurück zum Zitat Heckerman, D., Geiger, D., Chickering, D.M.: Learning Bayesian networks: the combination of knowledge and statistical data. Mach. Learn. 20(3), 197–243 (1995)MATH Heckerman, D., Geiger, D., Chickering, D.M.: Learning Bayesian networks: the combination of knowledge and statistical data. Mach. Learn. 20(3), 197–243 (1995)MATH
12.
Zurück zum Zitat Koller, D., Friedman, N.: Probabilistic Graphical Models - Principles and Techniques. MIT Press, Cambridge (2009) Koller, D., Friedman, N.: Probabilistic Graphical Models - Principles and Techniques. MIT Press, Cambridge (2009)
13.
Zurück zum Zitat Maathuis, M.H., Kalisch, M., Bühlmann, P.: Estimating high-dimensional intervention effects from observational data. Ann. Stat. 37(6A), 3133–3164 (2009)MathSciNetCrossRef Maathuis, M.H., Kalisch, M., Bühlmann, P.: Estimating high-dimensional intervention effects from observational data. Ann. Stat. 37(6A), 3133–3164 (2009)MathSciNetCrossRef
14.
Zurück zum Zitat Madigan, D., Andersson, S.A., Perlman, M.D., Volinsky, C.T.: Bayesian model averaging and model selection for Markov equivalence classes of acyclic digraphs. Commun. Stat. Theory Methods 25(11), 2493–2519 (1996)CrossRef Madigan, D., Andersson, S.A., Perlman, M.D., Volinsky, C.T.: Bayesian model averaging and model selection for Markov equivalence classes of acyclic digraphs. Commun. Stat. Theory Methods 25(11), 2493–2519 (1996)CrossRef
15.
Zurück zum Zitat Meek, C.: Causal inference and causal explanation with background knowledge. In: Proceedings of the 11th Conference on Uncertainty in Artificial Intelligence, UAI 1995, pp. 403–410 (1995) Meek, C.: Causal inference and causal explanation with background knowledge. In: Proceedings of the 11th Conference on Uncertainty in Artificial Intelligence, UAI 1995, pp. 403–410 (1995)
16.
Zurück zum Zitat Meek, C.: Graphical Models: Selecting Causal and Statistical Models. Ph.D. thesis, Carnegie Mellon University (1997) Meek, C.: Graphical Models: Selecting Causal and Statistical Models. Ph.D. thesis, Carnegie Mellon University (1997)
17.
Zurück zum Zitat Pearl, J.: Causality. Cambridge University Press, Cambridge (2009) Pearl, J.: Causality. Cambridge University Press, Cambridge (2009)
18.
Zurück zum Zitat Perković, E., Textor, J., Kalisch, M., Maathuis, M.H.: Complete graphical characterization and construction of adjustment sets in Markov equivalence classes of ancestral graphs. J. Mach. Learn. Res. 18, 220:1–220:62 (2017) Perković, E., Textor, J., Kalisch, M., Maathuis, M.H.: Complete graphical characterization and construction of adjustment sets in Markov equivalence classes of ancestral graphs. J. Mach. Learn. Res. 18, 220:1–220:62 (2017)
19.
Zurück zum Zitat Shanmugam, K., Kocaoglu, M., Dimakis, A.G., Vishwanath, S.: Learning causal graphs with small interventions. In: Processing of the 28th Annual Conference on Neural Information Processing Systems, NIPS 2015, pp. 3195–3203 (2015) Shanmugam, K., Kocaoglu, M., Dimakis, A.G., Vishwanath, S.: Learning causal graphs with small interventions. In: Processing of the 28th Annual Conference on Neural Information Processing Systems, NIPS 2015, pp. 3195–3203 (2015)
20.
Zurück zum Zitat Spirtes, P., Glymour, C., Scheines, R.: Causation, Prediction, and Search, Second Edition. MIT Press, Cambridge (2000) Spirtes, P., Glymour, C., Scheines, R.: Causation, Prediction, and Search, Second Edition. MIT Press, Cambridge (2000)
21.
Zurück zum Zitat Talvitie, T., Koivisto, M.: Counting and sampling Markov equivalent directed acyclic graphs. In: Proceedings of the 33th Conference on Artificial Intelligence, AAAI 2019, pp. 7984–7991 (2019) Talvitie, T., Koivisto, M.: Counting and sampling Markov equivalent directed acyclic graphs. In: Proceedings of the 33th Conference on Artificial Intelligence, AAAI 2019, pp. 7984–7991 (2019)
22.
Zurück zum Zitat Verma, T., Pearl, J.: Equivalence and synthesis of causal models. In: Proceedings of the 6th Annual Conference on Uncertainty in Artificial Intelligence, UAI 1990, pp. 255–270 (1990) Verma, T., Pearl, J.: Equivalence and synthesis of causal models. In: Proceedings of the 6th Annual Conference on Uncertainty in Artificial Intelligence, UAI 1990, pp. 255–270 (1990)
23.
Zurück zum Zitat Verma, T., Pearl, J.: An algorithm for deciding if a set of observed independencies has a causal explanation. In: Proceedings of the 8th Annual Conference on Uncertainty in Artificial Intelligence, UAI 1992, pp. 323–330 (1992) Verma, T., Pearl, J.: An algorithm for deciding if a set of observed independencies has a causal explanation. In: Proceedings of the 8th Annual Conference on Uncertainty in Artificial Intelligence, UAI 1992, pp. 323–330 (1992)
24.
Zurück zum Zitat Wienöbst, M., Bannach, M., Liśkiewicz, M.: Polynomial-time algorithms for counting and sampling Markov equivalent dags. In: Proccedings of the 35th Conference on Artificial Intelligence, AAAI 2021 (2021, in press) Wienöbst, M., Bannach, M., Liśkiewicz, M.: Polynomial-time algorithms for counting and sampling Markov equivalent dags. In: Proccedings of the 35th Conference on Artificial Intelligence, AAAI 2021 (2021, in press)
25.
Zurück zum Zitat van der Zander, B., Liśkiewicz, M.: Separators and adjustment sets in Markov equivalent dags. In: Proceedings of the 30th Conference on Artificial Intelligence, AAAI 2016, pp. 3315–3321 (2016) van der Zander, B., Liśkiewicz, M.: Separators and adjustment sets in Markov equivalent dags. In: Proceedings of the 30th Conference on Artificial Intelligence, AAAI 2016, pp. 3315–3321 (2016)
Metadaten
Titel
Recent Advances in Counting and Sampling Markov Equivalent DAGs
verfasst von
Marcel Wienöbst
Max Bannach
Maciej Liśkiewicz
Copyright-Jahr
2021
DOI
https://doi.org/10.1007/978-3-030-87626-5_20