Geometry of Covariate Shift with Applications to Active Learning
Geometry of Covariate Shift with Applications to Active Learning
This chapter examines learning algorithms under the covariate shift in which training and test data are drawn from different distributions. Using a naive estimator under the covariate shift, such as the maximum likelihood estimator (MLE), results in serious estimation bias when the assumed statistical model is misspecified. To correct this estimation bias, the chapter introduces the maximum weighted log-likelihood estimator (MWLE) with an information criterion to determine an optimal weight function for samples. It also investigates active learning in which the covariate shift is used to improve prediction, and shows that by incorporating the MWLE into active learning, one can reduce estimation bias and obtain a consistent estimator even under model misspecification.
Keywords: learning algorithms, covariate shift, log-likelihood estimator, estimation bias, active learning
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