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Introduction to the Special Section on Advances in Causal Discovery and Inference

Identification of cause and effect is the ultimate goal for most scientific and social discoveries. Controlled experiments are an effective approach to such discoveries, but they are expensive and sometimes infeasible to conduct. With the advent of big data availability in many areas, finding causal relationships using automated procedures is increasingly possible. With its focus on this challenge, causal discovery and inference is now a fast growing area in machine learning. Graphical causal models, the potential outcome model, and structural equation models are the three major modelling approaches to representation of causal relations and identification of causal effects. They have achieved many successes in various applications. More importantly, the principles and insights of causal inference help to solve several challenging machine-learning problems, such as model explainability, transfer learning, domain adaptation, and lifelong learning [1]. However, causal discovery and inference faces many challenges in theory and practice. They need strong assumptions, some of which are not verifiable in data. There is a lack of ground truth data for real-world evaluation of causal discovery and inference methods. Some of the algorithms whose results have asymptotic theoretical guarantees are not scalable to large and/or highdimensional data. More research is still needed to solve fundamental problems in causal discovery and inference, such as structure learning, false discovery control, assessment of causal discoveries, hidden variables, and nonlinear and/or heterogeneous causal relationships. More real-world applications of causal discovery and inference are also vital. Many workshops and symposia have been organized to meet the increasing research interests and demands in causal discovery and inference. Some associate editors of this special issue have organized four KDD Causal Discovery workshops, from 2016 to 2019. More than 10 other workshops and symposia have been organized in the same period, such as NeurIPS Workshop From “What If?” To “What Next?”: Causal Inference and Machine Learning for Intelligent Decision Making in 2017; NeurIPS Workshop Machine Learning and Causal Inference for Improved Decision Making in 2019; UAI Workshop Causation: Foundation to Application, 2016; UAI Workshop Causality: Learning, Inference, and Decision-Making, 2017; and UAI Workshop on Causal Inference, 2018. We edit this special issue to showcase the research achievements in the past few years since the previous special issue on the same topic in 2016 was published in this journal. This special issue collects seven articles that fall into two groups: fundamental problems and applications. The five articles in the first group study the fundamental problems in causal discovery and inference and present novel solutions for false discovery control in structure learning, causal relationship detection in simulation models, causal structure search in the presence of latent confounders, the shortest causal path discovery by local search, and conditional independence test for causal structure learning. Discovering causal relationships from observational data is a fundamental problem. Little research work has studied the strategies for controlling false discovery rates in causal structure learning. The article “Estimating and controlling the false discovery rate of the PC algorithm using edge-specific p-values,” by E. Strobl, P. Spirtes, and S. Visweswaran, presents an extension