Convex Mixed-Integer Programming for Causal Additive Models with Optimization and Statistical Guarantees
具有优化与统计保证的因果加性模型凸混合整数规划
We study the problem of learning a directed acyclic graph from data generated according to an additive, non-linear structural equation model with Gaussian noise. We express each non-linear function through a basis expansion, and derive a maximum likelihood estimator with a group l0-regularization that penalizes the number of edges in the graph. The resulting estimator is formulated through a convex mixed-integer program, enabling the use of branch-and-bound methods to obtain…