ExDBN: Learning Dynamic Bayesian Networks using Extended Mixed-Integer Programming Formulations

TL;DR

This paper introduces ExDBN, a novel score-based learning algorithm for dynamic Bayesian networks using extended mixed-integer programming, which improves accuracy over existing methods on synthetic data and is applicable to bioscience and finance.

Contribution

It presents a new mixed-integer quadratic programming formulation for learning dynamic Bayesian networks, avoiding exponential constraints via branch-and-cut, and demonstrates improved accuracy over state-of-the-art methods.

Findings

More accurate results on synthetic datasets up to 80 time series.

Effective application to bioscience and finance problems.

Avoids exponential acyclicity constraints with lazy constraint method.

Abstract

Causal learning from data has received much attention recently. Bayesian networks can be used to capture causal relationships. 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 80 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.