This chapter discusses the problem of importance estimation. Importance-weighting techniques play essential roles in covariate shift adaptation. However, the importance values are usually unknown a priori, so they must be estimated from data samples. The chapter introduces importance estimation methods, including importance estimation via kernel density estimation, the kernel mean matching method, a logistic regression approach, the Kullback–Leibler importance estimation procedure, and the least-squares importance fitting methods. The latter methods allow one to estimate the importance weights without performing through density estimation. Since density estimation is known to be difficult, the direct importance estimation approaches would be more accurate and preferable in practice. The numerical behavior of direct importance estimation methods is illustrated through experiments. Characteristics of importance estimation methods are also discussed.
Keywords: importance-weighting techniques, covariate shift adaptation, kernel density estimation, kernel mean matching, logistic regression, Kullback–Leibler importance estimation, least-squares importance fitting
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