On the Sparse DAG Structure Learning Based on Adaptive Lasso
This work improves DAG structure learning for Bayesian Networks, which is crucial for evidential reasoning, but it is incremental as it builds on existing methods like NOTEARS.
The paper tackles the problem of learning sparse directed acyclic graphs (DAGs) from observational data by addressing the non-sparsity issue in continuous optimization methods like NOTEARS, resulting in a method that consistently outperforms NOTEARS in experiments on synthetic and real-world datasets.
Learning the underlying Bayesian Networks (BNs), represented by directed acyclic graphs (DAGs), of the concerned events from purely-observational data is a crucial part of evidential reasoning. This task remains challenging due to the large and discrete search space. A recent flurry of developments followed NOTEARS[1] recast this combinatorial problem into a continuous optimization problem by leveraging an algebraic equality characterization of acyclicity. However, the continuous optimization methods suffer from obtaining non-spare graphs after the numerical optimization, which leads to the inflexibility to rule out the potentially cycle-inducing edges or false discovery edges with small values. To address this issue, in this paper, we develop a completely data-driven DAG structure learning method without a predefined value to post-threshold small values. We name our method NOTEARS with adaptive Lasso (NOTEARS-AL), which is achieved by applying the adaptive penalty method to ensure the sparsity of the estimated DAG. Moreover, we show that NOTEARS-AL also inherits the oracle properties under some specific conditions. Extensive experiments on both synthetic and a real-world dataset demonstrate that our method consistently outperforms NOTEARS.