Density Ratio Estimation in Machine Learning

Machine learning is an interdisciplinary field of science and engineering that studies mathematical theories and practical applications of systems that learn. This book introduces theories, methods and applications of density ratio estimation, which is a newly emerging paradigm in the machine learning community. Various machine learning problems such as non-stationarity adaptation, outlier detection, dimensionality reduction, independent component analysis, clustering, classification and conditional density estimation can be systematically solved via the estimation of probability density ratios. The authors offer a comprehensive introduction of various density ratio estimators including methods via density estimation, moment matching, probabilistic classification, density fitting and density ratio fitting, as well as describing how these can be applied to machine learning. The book provides mathematical theories for density ratio estimation including parametric and non-parametric convergence analysis and numerical stability analysis to complete the first and definitive treatment of the entire framework of density ratio estimation in machine learning.

'There is no doubt that this book will change the way people think about machine learning and stimulate many new directions for research.' Thomas G. Dietterich, from the Foreword

Masashi Sugiyama is an Associate Professor in the Department of Computer Science at the Tokyo Institute of Technology. Taiji Suzuki is an Assistant Professor in the Department of Mathematical Informatics at the University of Tokyo, Japan. Takafumi Kanamori is an Associate Professor in the Department of Computer Science and Mathematical Informatics at Nagoya University, Japan.