Causal learning from data has received much 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, which is utilized in the present contribution to formulate a score-based learning approach. 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 excellent results when applied to small and medium-sized synthetic instances of up to 25 time-series. Lastly, two interesting applications in bio-science and finance, to which the method is directly applied, further stress the opportunities in developing highly accurate, globally convergent solvers that can handle modest instances.

翻译：近年来，从数据中学习因果关系受到广泛关注。捕捉因果关系的一种方法是利用贝叶斯网络。该方法可恢复一个带权重的有向无环图，其中随机变量由顶点表示，每条边关联的权重代表变量间因果关系的强度。为捕捉动态效应，本研究引入对历史数据的依赖性，这可通过结构方程模型实现。本文利用该模型构建了一种基于评分的学习方法。我们建立了混合整数二次规划模型并提出了算法解决方案，通过采用分支切割（"惰性约束"）方法避免了指数级数量的无环约束的预生成。与现有技术相比，新方法在最多包含25个时间序列的中小规模合成实例中表现出优异性能。最后，在生物科学和金融领域的两个直接应用案例进一步表明，开发能够处理中等规模实例的高精度全局收敛求解器具有广阔前景。