Density Ratio Estimation in Machine Learning

Machine learning sits where mathematics meets engineering, concerned with the theory behind systems that improve from data and with their real-world uses. This book focuses on density ratio estimation, a relatively recent approach that has gained traction among machine learning researchers. It explains the ideas, techniques and applications involved.

A wide range of tasks can be tackled by estimating the ratio between two probability densities. These include adapting to non-stationary data, spotting outliers, reducing dimensionality, independent component analysis, clustering, classification, and estimating conditional densities. The authors survey the main families of estimators: those built on density estimation, moment matching, probabilistic classification, density fitting, and density ratio fitting. For each, they show how it is applied in machine learning.

The book also covers the mathematics underneath these methods. Its theoretical chapters address convergence analysis for both parametric and non-parametric estimators, along with the numerical stability of the computations. Together these parts aim to cover the whole framework of density ratio estimation in machine learning.