This book introduces theories, methods and applications of density ratio estimation, a newly emerging paradigm in the machine learning community.

Masashi Sugiyama is an Associate Professor in the Department of Computer Science at the Tokyo Institute of Technology.

Part I. Density Ratio Approach to Machine Learning: 1. Introduction; 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.