Learning LWF Chain Graphs: A Markov Blanket Discovery Approach

This paper provides a graphical characterization of Markov blankets in chain graphs (CGs) under the Lauritzen-Wermuth-Frydenberg (LWF) interpretation. The characterization is different from the well-known one for Bayesian networks and generalizes it. We provide a novel scalable and sound algorithm for Markov blanket discovery in LWF CGs and prove that the Grow-Shrink algorithm, the IAMB algorithm, and its variants are still correct for Markov blanket discovery in LWF CGs under the same assumptions as for Bayesian networks. We provide a sound and scalable constraint-based framework for learning the structure of LWF CGs from faithful causally sufficient data and prove its correctness when the Markov blanket discovery algorithms in this paper are used. Our proposed algorithms compare positively/competitively against the state-of-the-art LCD (Learn Chain graphs via Decomposition) algorithm, depending on the algorithm that is used for Markov blanket discovery. Our proposed algorithms make a broad range of inference/learning problems computationally tractable and more reliable because they exploit locality.Comment: This is an extended version of the accepted paper for UAI 202

Multi-label Causal Variable Discovery: Learning Common Causal Variables and Label-specific Causal Variables

Causal variables in Markov boundary (MB) have been widely applied in extensive single-label tasks. While few researches focus on the causal variable discovery in multi-label data due to the complex causal relationships. Since some variables in multi-label scenario might contain causal information about multiple labels, this paper investigates the problem of multi-label causal variable discovery as well as the distinguishing between common causal variables shared by multiple labels and label-specific causal variables associated with some single labels. Considering the multiple MBs under the non-positive joint probability distribution, we explore the relationships between common causal variables and equivalent information phenomenon, and find that the solutions are influenced by equivalent information following different mechanisms with or without existence of label causality. Analyzing these mechanisms, we provide the theoretical property of common causal variables, based on which the discovery and distinguishing algorithm is designed to identify these two types of variables. Similar to single-label problem, causal variables for multiple labels also have extensive application prospects. To demonstrate this, we apply the proposed causal mechanism to multi-label feature selection and present an interpretable algorithm, which is proved to achieve the minimal redundancy and the maximum relevance. Extensive experiments demonstrate the efficacy of these contributions

Causality-based Feature Selection: Methods and Evaluations

Feature selection is a crucial preprocessing step in data analytics and machine learning. Classical feature selection algorithms select features based on the correlations between predictive features and the class variable and do not attempt to capture causal relationships between them. It has been shown that the knowledge about the causal relationships between features and the class variable has potential benefits for building interpretable and robust prediction models, since causal relationships imply the underlying mechanism of a system. Consequently, causality-based feature selection has gradually attracted greater attentions and many algorithms have been proposed. In this paper, we present a comprehensive review of recent advances in causality-based feature selection. To facilitate the development of new algorithms in the research area and make it easy for the comparisons between new methods and existing ones, we develop the first open-source package, called CausalFS, which consists of most of the representative causality-based feature selection algorithms (available at https://github.com/kuiy/CausalFS). Using CausalFS, we conduct extensive experiments to compare the representative algorithms with both synthetic and real-world data sets. Finally, we discuss some challenging problems to be tackled in future causality-based feature selection research