It is well known that the man-machine ratio between humans and computers has decreased very significantly in recent decades (and continues to do so). Unlike the early days of computing when there were many designers, maintainers, and users per computer, now there are often many computers per user, and hardly any human wishes to spend time maintaining a computer or teaching it to carry out tasks. Along with this decrease in man-machine ratio comes the expectations of speed that are placed on modern computerized systems (for example, in the financial services industry), which all but preclude the inputs of slow-moving humans for critical functions. For these reasons, it is increasingly necessary to devise systems that can receive raw empirical data (either stored or streamed from live sources) and derive conclusions. This is aptly described as machine learning.

Classical machine learning uses logical approaches such as decision trees, association rules, and inductive logic, and present research also relies on probability and statistics, with approaches like clusters (achieved by various means), support vector machines, and Bayesian networks. This book may be seen in this context. As the lucid foreword by Thomas G. Dietterich notes, estimating probability distributions is often considered a key question in machine learning. The authors of this book propose estimating probability density ratios, that is, the ratio of two probability densities; this different view of machine learning is in line with their past and ongoing research.

The book consists of 17 chapters, divided into five parts, and more than 300 pages. The first part consists of a single introductory chapter that gives an overview of the whole field from the perspective of this approach. Part 2 (seven chapters) presents the basic approaches and mathematical tools of density ratio estimation. Part 3 (four chapters) discusses applications of density ratio estimation in machine learning, and Part 4 (four chapters) explores theoretical analyses of density ratio estimation. Part 5’s single chapter presents the authors’ conclusions and perspectives for the future.

I have one small quibble with the authors concerning the flow diagram on page 19, which shows the layout and dependence of the chapters. It would probably be rather difficult for a graduate student--or any other reader--to jump straight from Part 1, the introductory chapter, to Part 3’s chapters on applications. The authors provide links to the MATLAB code for certain problems discussed in the book; thus, knowledge of MATLAB is desirable.

The book is well written and produced, and will probably be seen in retrospect as a significant addition to the literature in this important area--at least to the extent that density ratio estimation as a technique proves useful in real-world applications. Future work and applications using the theory presented should indicate to what extent this happens.