Causality, Probability, and Time

Causality is a key part of many fields and facets of life, from finding the relationship between diet and disease to discovering the reason for a particular stock market crash. Despite centuries of work in philosophy and decades of computational research, automated inference and explanation remains an open problem. In particular, the timing and complexity of relationships has been largely ignored even though this information is critically important for prediction, explanation and intervention. However, given the growing availability of large observational datasets including those from electronic health records and social networks, it is a practical necessity. This book presents a new approach to inference (finding relationships from a set of data) and explanation (assessing why a particular event occurred), addressing both the timing and complexity of relationships. The practical use of the method developed is illustrated through theoretical and experimental case studies, demonstrating its feasibility and success. "This new book on causality is a wonderful combination surveying past work and moving on to develop useful new concepts such as probabilistic temporal logic to give new definitions and results about the nature of causes. Formal theorems and practical case studies about causality are given equally detailed attention." Patrick Suppes, Stanford University "This book presents an exciting new approach to causality based on temporal logic. Kleinberg does an excellent job in integrating a thorough understanding of present-day philosophical approaches to causality with formal and computational considerations, to deliver an approach that is both well motivated and practically oriented. It is recommended to those interested in theories of causality as well as those concerned with the practice of causal inference." Jon Williamson, University of Kent1. Introduction; 2. A brief history of causality; 3. Probability, logic and probabilistic temporal logic; 4. Defining causality; 5. Inferring causality; 6. Token causality; 7. Case studies; 8. Conclusion; Appendix A. A little bit of statistics; Appendix B. Proofs.