Special Session 129: Mathematics of Data Science and Applications

Unbounded Density Ratio Estimation and Its Application to Covariate Shift Adaptation
Zhengchu Guo
Zhejiang University
Peoples Rep of China
Co-Author(s):    Ren-Rui Liu, Jun Fan, Lei Shi
Abstract:
This talk addresses unbounded density ratio estimation--an underexplored yet critical challenge in statistical learning--and its application to covariate shift adaptation. We propose a three-step procedure utilizing unlabeled data from both source and target distributions: (1) estimating a relative density ratio; (2) truncating to control unboundedness; and (3) transforming the estimate back to the standard density ratio, which is then used as importance weights for regression. We establish non-asymptotic convergence guarantees for both the density ratio estimator and the resulting regression estimator, showing that under mild conditions, both achieve optimal or near-optimal rates. This work provides new theoretical insights into density ratio estimation and learning under covariate shift, extending classical theory to more practical settings.