ExDBN: Exact learning of Dynamic Bayesian Networks
Keywords: causal lerning, bayesian network, structural equation model
TL;DR: Mixed-integer formulations can used to learn dynamic Bayesian nets very fast, when valid violated inequalities are generated dynamically.
Abstract: Causal learning from data has received a lot of attention in recent years. One way of capturing causal relationships is by utilizing Bayesian networks. There, one recovers a weighted directed acyclic graph in which random variables are represented by vertices, and the weights associated with each edge represent the strengths of the causal relationships between them.
This concept is extended to capture dynamic effects by introducing a dependency on past data, which may be captured by the structural equation model. This formalism is utilized in the present contribution to propose a score-based learning algorithm. A mixed-integer quadratic program is formulated and an algorithmic solution proposed, in which the pre-generation of exponentially many acyclicity constraints is avoided by utilizing the so-called branch-and-cut (``lazy constraint'') method.
Comparing the novel approach to the state-of-the-art, we show that the proposed approach turns out to produce more accurate results when applied to small and medium-sized synthetic instances containing up to 25 time series. Lastly, two interesting applications in bioscience and finance, to which the method is directly applied, further stress the importance of developing highly accurate, globally convergent solvers that can handle instances of modest size.
Primary Area: causal reasoning
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Submission Number: 10168
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