High-Dimensional Density Ratio Estimation with Extensions to Approximate Likelihood Computation

Understand

The ratio between two probability density functions is an important component of various tasks, including selection bias correction, novelty detection and classification.

• Recently, several estimators of this ratio have been proposed.
• Most of these methods fail if the sample space is high-dimensional, and hence require a dimension reduction step, the result of which can be a significant loss of information.
• Here we propose a simple-to-implement, fully nonparametric density ratio estimator that expands the ratio in terms of the eigenfunctions of a kernel-based operator; these functions reflect the underlying geometry of the data (e.g., submanifold structure), often leading to better estimates without an explicit dimension reduction step.