Causality is a very interesting research topic, but it is only recently that people have begun to use mathematical methods to study it, and there are still many conceptual issues that are hotly debated.

This book summarizes the author’s ten years of research into causality. There are others who have been working in the field longer than the author and have published several books on causality, including Pearl, Spirtes, Imbens, Rubin, and others. The authors hope that this book will complement existing work in two ways.

First, the book addresses what might be considered the most fundamental and unrealistic sub-problem of causality, namely that the system being analyzed consists of only two observations. Over the past decade, the author has studied this issue in detail. This part will describe much of their work, and the authors hope to try to place it in the context of a larger, deeper understanding of causality. Although it might be more instructive to look at bivariate cases in the order of the chapters in this book, we could have just started reading the chapter on multivariate variables.

In addition, the authors are inspired and influenced by the field of machine learning and computational statistics. They’re interested in ways that they can help us infer causal structures, and even how causal reasoning can guide us in machine learning. Furthermore, the authors feel that some of the most profound open problems in machine learning are best understood not using random experiments under probability distributions as a starting point, but based on the causal structure behind the distribution.

The author attempts to provide a systematic introduction to this topic for the benefit of readers familiar with probability theory and statistics or the fundamentals of machines.

In order to make the book easy to read and to focus on conceptual issues, the author is forced to devote only a small amount of space to the important issues of causality, focusing instead on theoretical insights into specific Settings and various methods of practical importance.

In addition, the authors say their book has many shortcomings. Some of these are inherited from domains, such as theoretical results that are often limited to situations where there is an infinite amount of data. Although there are algorithms for limited data, the statistical properties of these methods are not discussed. In addition, in some places, the authors ignore the measurement theory problem, usually by assuming the existence of density. While the authors consider these issues relevant and interesting, they had to make this choice in order to keep the book short and to consider the breadth of the audience.

The authors argue that the method of calculating causality is still in its infancy. In particular, learning causal structures from data can be done only in fairly limited circumstances. The authors try to include specific algorithms as much as possible, but they also realize that many problems of causal reasoning are more difficult to solve than typical machine learning problems, so the authors make no promises about whether these algorithms will work for the real problems we encounter.

Well, we all want a book or an article that tells us directly what to do when we have a problem. But when faced with complex problems, the reality is often that the authors do not know how to do, they can only provide their own ideas for exploration and research, so, the author of this book says please don’t be discouraged, this is a fascinating subject.