jmlr jmlr2012 jmlr2012-91 jmlr2012-91-reference knowledge-graph by maker-knowledge-mining

91 jmlr-2012-Plug-in Approach to Active Learning


Source: pdf

Author: Stanislav Minsker

Abstract: We present a new active learning algorithm based on nonparametric estimators of the regression function. Our investigation provides probabilistic bounds for the rates of convergence of the generalization error achievable by proposed method over a broad class of underlying distributions. We also prove minimax lower bounds which show that the obtained rates are almost tight. Keywords: active learning, selective sampling, model selection, classification, confidence bands


reference text

J.-Y. Audibert and A. B. Tsybakov. Fast learning rates for plug-in classifiers. Preprint, 2005. Available at: http://imagine.enpc.fr/publications/papers/05preprint_AudTsy.pdf. M.-F. Balcan, S. Hanneke, and J. Wortman. The true sample complexity of active learning. In Proceedings of the Conference on Learning Theory, pages 45–56, 2008. M.-F. Balcan, A. Beygelzimer, and J. Langford. Agnostic active learning. J. Comput. System Sci., 75(1):78–89, 2009. R. M. Castro and R. D. Nowak. Minimax bounds for active learning. IEEE Trans. Inform. Theory, 54(5):2339–2353, 2008. S. Dasgupta, D. Hsu, and C. Monteleoni. A general agnostic active learning algorithm. In Advances in Neural Information Processing Systems 20, pages 353–360. MIT Press, 2008. S. Ga¨ffas. Sharp estimation in sup norm with random design. Statist. Probab. Lett., 77(8):782–794, ı 2007. E. Gin´ and R. Nickl. Confidence bands in density estimation. Ann. Statist., 38(2):1122–1170, e 2010. S. Hanneke. Rates of convergence in active learning. Ann. Statist., 39(1):333–361, 2011. M. Hoffmann and R. Nickl. On adaptive inference and confidence bands. The Annals of Statistics, to appear. V. Koltchinskii. Rademacher complexities and bounding the excess risk in active learning. J. Mach. Learn. Res., 11:2457–2485, 2010. V. Koltchinskii. Oracle inequalities in empirical risk minimization and sparse recovery problems. Springer, 2011. Lectures from the 38th Probability Summer School held in Saint-Flour, 2008, ´ ´ e Ecole d’Et´ de Probabilit´ s de Saint-Flour. e M. G. Low. On nonparametric confidence intervals. Ann. Statist., 25(6):2547–2554, 1997. A. B. Tsybakov. Introduction to Nonparametric Estimation. Springer, 2009. 90