Density Ratio Estimation in Machine Learning
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- Masashi Sugiyama, University of Tokyo
- Taiji Suzuki, University of Tokyo
- Takafumi Kanamori, Nagoya University, Japan
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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 also 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.Read more
- The first book to cover the entire framework of density ratio estimation
- Allows readers to solve various machine learning problems systematically
- Includes source code (mostly in MATLAB®)
Reviews & endorsements
"There is no doubt that this book will change the way people think about machine learning and stimulate many new directions for research."
From the Foreword by Thomas G. DietterichSee more reviews
"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."
Shrisha Rao, Computing Reviews
"This book is clear and well written, and it is an excellent introduction to density ratio estimation in both theory and practice. It presents the state-of-the-art methodology on this topic and in this regard it is really nice that the bibliography is so exhaustive and well commented."
Pierre Alquir, Mathematical Reviews
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- Date Published: June 2012
- format: Adobe eBook Reader
- isbn: 9781139227285
- contains: 79 b/w illus. 18 tables
- availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
Part I. Density Ratio Approach to Machine Learning:
Part II. Methods of Density Ratio Estimation:
2. Density estimation
3. Moment matching
4. Probabilistic classification
5. Density fitting
6. Density-ratio fitting
7. Unified framework
8. Direct density-ratio estimation with dimensionality reduction
Part III. Applications of Density Ratios in Machine Learning:
9. Importance sampling
10. Distribution comparison
11. Mutual information estimation
12. Conditional probability estimation
Part IV. Theoretical Analysis of Density Ratio Estimation:
13. Parametric convergence analysis
14. Non-parametric convergence analysis
15. Parametric two-sample test
16. Non-parametric numerical stability analysis
Part V. Conclusions:
17. Conclusions and future directions.
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