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Direct Importance Estimation with Model Selection and Its Application to Covariate Shift Adaptation
Masashi Sugiyama · Shinichi Nakajima · Hisashi Kashima · Paul von Buenau · Motoaki Kawanabe

Tue Dec 04 10:30 AM -- 10:40 AM (PST) @

When training and test samples follow different input distributions (i.e., the situation called \emph{covariate shift}), the maximum likelihood estimator is known to lose its consistency. For regaining consistency, the log-likelihood terms need to be weighted according to the \emph{importance} (i.e., the ratio of test and training input densities). Thus, accurately estimating the importance is one of the key tasks in covariate shift adaptation. A naive approach is to first estimate training and test input densities and then estimate the importance by the ratio of the density estimates. However, since density estimation is a hard problem, this approach tends to perform poorly especially in high dimensional cases. In this paper, we propose a direct importance estimation method that does not require the input density estimates. Our method is equipped with a natural model selection procedure so tuning parameters such as the kernel width can be objectively optimized. This is an advantage over a recently developed method of direct importance estimation. Simulations illustrate the usefulness of our approach.

Author Information

Masashi Sugiyama (RIKEN / University of Tokyo)
Shinichi Nakajima (TU Berlin)
Hisashi Kashima (IBM Research)
Paul von Buenau (TU Berlin)
Motoaki Kawanabe (Fraunhofer FIRST)

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