Local Causal and Markov Blanket Induction for Causal Discovery and Feature Selection for Classification Part II: Analysis and Extensions

In part I of this work we introduced and evaluated the Generalized Local Learning (GLL) framework for producing local causal and Markov blanket induction algorithms. In the present second part we analyze the behavior of GLL algorithms and provide extensions to the core methods. Specifically, we investigate the empirical convergence of GLL to the true local neighborhood as a function of sample size. Moreover, we study how predictivity improves with increasing sample size. Then we investigate how sensitive are the algorithms to multiple statistical testing, especially in the presence of many irrelevant features. Next we discuss the role of the algorithm parameters and also show that Markov blanket and causal graph concepts can be used to understand deviations from optimality of state-of-the-art non-causal algorithms. The present paper also introduces the following extensions to the core GLL framework: parallel and distributed versions of GLL algorithms, versions with false discovery rate control, strategies for constructing novel heuristics for specific domains, and divide-and-conquer local-to-global learning (LGL) strategies. We test the generality of the LGL approach by deriving a novel LGL-based algorithm that compares favorably c ©2010 Constantin F. Aliferis, Alexander Statnikov, Ioannis Tsamardinos, Subramani Mani and Xenofon D. Koutsoukos. ALIFERIS, STATNIKOV, TSAMARDINOS, MANI AND KOUTSOUKOS to the state-of-the-art global learning algorithms. In addition, we investigate the use of non-causal feature selection methods to facilitate global learning. Open problems and future research paths related to local and local-to-global causal learning are discussed.