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Scalable Structure Learning of Continuous-Time Bayesian Networks from Incomplete Data

Authors: Linzner, Dominik; Schmidt, Michael; Koeppl, Heinz;

Scalable Structure Learning of Continuous-Time Bayesian Networks from Incomplete Data

Abstract

Continuous-time Bayesian Networks (CTBNs) represent a compact yet powerful framework for understanding multivariate time-series data. Given complete data, parameters and structure can be estimated efficiently in closed-form. However, if data is incomplete, the latent states of the CTBN have to be estimated by laboriously simulating the intractable dynamics of the assumed CTBN. This is a problem, especially for structure learning tasks, where this has to be done for each element of a super-exponentially growing set of possible structures. In order to circumvent this notorious bottleneck, we develop a novel gradient-based approach to structure learning. Instead of sampling and scoring all possible structures individually, we assume the generator of the CTBN to be composed as a mixture of generators stemming from different structures. In this framework, structure learning can be performed via a gradient-based optimization of mixture weights. We combine this approach with a new variational method that allows for a closed-form calculation of this mixture marginal likelihood. We show the scalability of our method by learning structures of previously inaccessible sizes from synthetic and real-world data.

Comment: Accepted at NeurIPS2019

Keywords

FOS: Computer and information sciences, Computer Science - Machine Learning, Statistics - Machine Learning, Machine Learning (stat.ML), Machine Learning (cs.LG)

22 references, page 1 of 3

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[2] Claudia Battistin, Benjamin Dunn, and Yasser Roudi. Learning with unknowns: Analyzing biological data in the presence of hidden variables. Current Opinion in Systems Biology, 1:122-128, 2017.

[3] Irene Cantone, Lucia Marucci, Francesco Iorio, Maria Aurelia Ricci, Vincenzo Belcastro, Mukesh Bansal, Stefania Santini, Mario Di Bernardo, Diego di Bernardo, and Maria Pia Cosma. A Yeast Synthetic Network for In Vivo Assessment of Reverse-Engineering and Modeling Approaches. Cell, 137(1):172-181, apr 2009.

[4] Ido Cohn, Tal El-Hay, Nir Friedman, and Raz Kupferman. Mean field variational approximation for continuous-time Bayesian networks. Journal Of Machine Learning Research, 11:2745-2783, 2010.

[5] Tal El-Hay, Ido Cohn, Nir Friedman, and Raz Kupferman. Continuous-Time Belief Propagation. Proceedings of the 27th International Conference on Machine Learning, pages 343-350, 2010.

[6] Tal El-Hay, R Kupferman, and N Friedman. Gibbs sampling in factorized continuous-time Markov processes. Proceedings of the 22th Conference on Uncertainty in Artificial Intelligence, 2011.

[7] Yu Fan and CR Shelton. Sampling for approximate inference in continuous time Bayesian networks. AI and Math, 2008.

[8] Jerome Friedman, Trevor Hastie, and Robert Tibshirani. Sparse covariance estimation. Biostatistics2, 9(3):432-441, 2008.

[9] Roy J Glauber. Time-Dependent Statistics of the Ising Model. J. Math. Phys., 4(1963):294-307, 1963.

[10] Daphne Koller and Nir Friedman. Probabilistic graphical models principles and techniques. MIT Press, 2010.

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