Overcoming Saturation in Density Ratio Estimation by Iterated Regularization
This work addresses a bottleneck in density ratio estimation for machine learning practitioners, offering an incremental improvement over existing methods.
The paper tackles the problem of error saturation in kernel methods for density ratio estimation, which hinders fast error convergence rates, and introduces iterated regularization to overcome this issue, achieving improved performance on benchmarks and large-scale domain adaptation evaluations.
Estimating the ratio of two probability densities from finitely many samples, is a central task in machine learning and statistics. In this work, we show that a large class of kernel methods for density ratio estimation suffers from error saturation, which prevents algorithms from achieving fast error convergence rates on highly regular learning problems. To resolve saturation, we introduce iterated regularization in density ratio estimation to achieve fast error rates. Our methods outperform its non-iteratively regularized versions on benchmarks for density ratio estimation as well as on large-scale evaluations for importance-weighted ensembling of deep unsupervised domain adaptation models.