Directed Acyclic Graphs Structure Learning with the Absorbing Markov Chain

Bayesian networks are of paramount significance in modeling joint probability distributions and have garnered extensive applications across diverse domains. The continuous optimization method formulates the structure learning problem as a purely continuous optimization problem within the space of real matrices, thereby offering a novel avenue for learning directed acyclic graphs (DAGs). In our quest to enhance performance and interpretability, we introduce a groundbreaking continuous optimization approach for learning the structures of DAGs, namely Directed Acyclic Graphs structure learning with Absorbing Markov Chain (DAG-AMC). DAG-AMC ingeniously transforms the acyclic constraint into a node transition challenge, effectively recasting it as a Markov chain problem with absorbing states. This innovative transformation reconceptualizes the graph structure as a state transition matrix within the framework of an absorbing Markov chain. The absorption time intrinsic to this chain provides an elegant representation of the acyclic constraint in DAG structure learning. We leverage the augmented Lagrangian method, incorporating the constructed smooth function as a constraint throughout the optimization process. Empirical experiments conducted on both synthetic and real-world datasets highlight the remarkable efficacy of our proposed DAG-AMC. Our results consistently surpass those of baseline methods across a wide array of evaluation metrics, thus underscoring the superior potential of DAG-AMC as a preeminent solution for DAG structure learning.