Active Learning in Approximately Linear Regression Based on Conditional Expectation of Generalization Error

摘要

The goal of active learning is to determine the locations of traininginput points so that the generalization error is minimized. Wediscuss the problem of active learning in linear regression scenarios.Traditional active learning methods using least-squares learning oftenassume that the model used for learning is correctly specified. Inmany practical situations, however, this assumption may not befulfilled. Recently, active learning methods using"importance"-weighted least-squares learning have been proposed, whichare shown to be robust against misspecification of models. In thispaper, we propose a new active learning method also using the weightedleast-squares learning, which we call ALICE (Active Learningusing the Importance-weighted least-squares learning based onConditional Expectation of the generalization error). An importantdifference from existing methods is that we predict theconditional expectation of the generalization error giventraining input points, while existing methods predict the fullexpectation of the generalization error. Due to this difference, thetraining input design can be fine-tuned depending on the realizationof training input points. Theoretically, we prove that the proposedactive learning criterion is a more accurate predictor of thesingle-trial generalization error than the existing criterion.Numerical studies with toy and benchmark data sets show that theproposed method compares favorably to existing methods. color="gray">