A Recursive Markov Boundary-Based Approach to Causal Structure Learning

Abstract

One of the main approaches for causal structure learning is constraint-based methods. These methods are particularly valued as they are guaranteed to asymptotically find a structure which is statistically equivalent to the ground truth. However, they may require exponentially large number of conditional independence (CI) tests in the number of variables of the system. In this paper, we propose a novel recursive constraint-based method for causal structure learning. The key idea of the proposed approach is to recursively use Markov blanket information in order to identify a variable that can be removed from the set of variables without changing the statistical relations among the remaining variables. Once such a variable is found, its neighbors are identified, the removable variable is removed, and the Markov blanket information of the remaining variables is updated. Our proposed approach reduces the required number of conditional independence tests for structure learning compared to the state of the art. We also provide a lower bound on the number of CI tests required by any constraint-based method. Comparing this lower bound to our achievable bound demonstrates the efficiency of our approach. We evaluate and compare the performance of the proposed method on both synthetic and real world structures against the state of the art.

On Distributed Computing Continuum Systems

“…Few improvements made on these learning algorithms to overcome this challenge. A recursive MBL algorithm is introduced in [54] for learning the BN and removing the states in which the statistical dependencies do not affect the other states of the system. The primary goal of the MBL is feature selection or discovering the best set of MBs) [55]- [57].…”