In the big data era, data have become an important source of automatically generated knowledge which, in turn, is able to help to change the system to achieve a certain objective, to make predictions under interventions, or to assist decision making in various fields. To this end, it is crucial that the knowledge encodes causal information. As a consequence, more and more data mining researchers are interested in causal discovery.

In acknowledging the increasing interest in causal discovery in the data mining community, and to facilitate further development of this research area, in August 2016 we organized the Workshop on Causal Discovery with ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD 2016). The aim of the workshop is to provide a forum for data mining researchers and researchers in causal modeling and inference to communicate, understand each others’ problems, and to create stronger synergy between the research communities to solve real, large-scale problems. This KDD workshop follows the success of the Causal Discovery Workshop held in conjunction with the IEEE International Conference on Data Mining 2013 (ICDM 2013) and the Special Issue on Causal Discovery and Inference of ACM Transactions on Intelligent Systems and Technology. The workshop attracted wide interest at KDD 2016. Around 200 KDD participants attended the workshop keynote speech and regular presentations.

This special issue includes a collection of the extended version of some selected papers from the KDD workshop and some invited contributions as well.

Structural causal models make use of directed acyclic graphs to represent the causal mechanisms underlying a certain phenomenon, which entail probabilistic and causal relationships among a set of random variables in the observational data set. Estimating the underlying causal structures from observational data is one of the central challenges of causal discovery. In the invited paper, “Introduction to the foundations of causal discovery,” Frederick Eberhardt, keynote speaker of the KDD workshop, presents an introduction to various graphical causal models and their assumptions.

“Causal faithfulness” is one of the essential assumptions made by many structural learning algorithms. In practice, however, this assumption may not be satisfied, and there is a growing interest in investigating how violations of faithfulness affect the performance of causal discovery algorithms. The paper “Weakening faithfulness: some heuristic causal discovery algorithms” studies to what extent two of the most well-known algorithms for causal learning rely on this assumption. The paper also considers alternative strategies for weakening faithfulness, which come accompanied with a few heuristic algorithms that present relative reasonable results in practice.

In real-world medical data, hybrid types of data and missing values are pervasive. The paper “Handling hybrid and missing data in constraint-based causal discovery to study the etiology of ADHD” develops an effective procedure for causal discovery in medical applications when a significant number of discrete and continuous values are missing. The proposed method has been assessed with both real-world and simulated data sets.

Given the prevalence of high-dimensional data sets, it is essential to improve the scalability of causal learning algorithms to solve a wider range of problems. The paper “A million variables and more: The FAST GREEDY SEARCH algorithm for learning high-dimensional graphical causal models, with an application to functional magnetic resonance Images” extends some classical algorithms for causal discovery to large-scale settings. One of the algorithms was applied to a medical imaging data set with one million variables to find local causal structures, with the running time in 14 h.

Dynamic Bayesian networks (DBNs) are one of the most popular extensions of Bayesian networks to allow dependencies of variables between different time stamps. The paper “Identifiability and transportability in dynamic causal networks” extends DBNs to incorporate causal semantics in settings with recurrent temporal behaviors. It introduces an algorithm for computing the effects of interventions in dynamic causal networks, and then develops a procedure for the transportability (i.e., extrapolation) of causal effects from one domain to another with generalizability guarantees.

We hope the collection of papers in this special issue can provide a glance at the current developments in causal discovery. We also hope that the work presented here can motivate more exciting future works from readers to push the research and applications of causal discovery to a new height.

Finally, we would like to express our gratitude to all the people who have contributed to this special issue. In particular, we would like to thank all authors for submitting their papers to the KDD workshop and this special issue, all reviewers for providing timely and high-quality reviews, and Professor Longbing Cao, editor-in-chief of JDSA for his support and help with making this special issue successful.