Shinichi Nakajima is a senior researcher at Technische Universität Berlin. His research interests include the theory and applications of machine learning, and he has published papers at numerous conferences and in journals such as the Journal of Machine Learning Research, the Machine Learning Journal, Neural Computation, and IEEE Transactions on Signal Processing. He currently serves as an area chair for NIPS and an action Editor for Digital Signal Processing.

Kazuho Watanabe is a lecturer at Toyohashi University of Technology. His research interests include statistical machine learning and information theory, and he has published papers at numerous conferences and in journals such as the Journal of Machine Learning Research, the Machine Learning Journal, IEEE Transactions on Information Theory, and IEEE Transactions on Neural Networks and Learning Systems.

Masashi Sugiyama is Director of the RIKEN Center for Advanced Intelligence Project and Professor of Complexity Science and Engineering at the University of Tokyo. His research interests include the theory, algorithms, and applications of machine learning. He has written several books on machine learning, including Density Ratio Estimation in Machine Learning (Cambridge, 2012). He served as program co-chair and general co-chair of the NIPS conference in 2015 and 2016, respectively, and received the Japan Academy Medal in 2017.

Designed for researchers and graduate students in machine learning, this book introduces the theory of variational Bayesian learning, a popular machine learning method, and suggests how to make use of it in practice. Detailed derivations allow readers to follow along without prior knowledge of the specific mathematical techniques.