Abstract
In this contribution we consider the problem of active learning in the regression setting. That is, choosing an optimal sampling scheme for the regression problem simultaneously with that of model selection. We consider a batch type approach and an on-line approach adapting algorithms developed for the classification problem. Our main tools are concentration-type inequalities which allow us to bound the supreme of the deviations of the sampling scheme corrected by an appropriate weight function.
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References
Beygelzimer, A., Dasgupta, S., & Langford, J. (2009). Importance weighted active learning. In Proceedings of the 26th Annual International Conference on Machine Learning (pp. 49–56). New York: ACM.
Birgé, L., & Massart, P. (1998). Minimum contrast estimators on sieves: Exponential bounds and rates of convergence. Bernoulli, 4, 329–395.
Fermin, A. K., & Ludeña, C. (2018). Probability bounds for active learning in the regression problem. arXiv: 1212.4457
Härdle, W., Kerkyacharian, G., Picard, D., & Tsybakov, A. (1998). Wavelets, approximation and statistical applications: Vol. 129. Lecture notes in statistics. New York: Springer.
Sugiyama, M. (2006). Active learning in approximately linear regression based on conditional expectation generalization error with model selection. Journal of Machine Learning Research, 7, 141–166.
Sugiyama, M., Krauledat, M., & Müller, K. R. (2007). Covariate shift adaptation by importance weighted cross validation. Journal of Machine Learning Research, 8, 985–1005.
Sugiyama, M., & Rubens, N. (2008). A batch ensemble approach to active learning with model selection. Neural Networks, 21(9), 1278–1286.
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Fermin, AK., Ludeña, C. (2018). Probability Bounds for Active Learning in the Regression Problem. In: Bertail, P., Blanke, D., Cornillon, PA., Matzner-Løber, E. (eds) Nonparametric Statistics. ISNPS 2016. Springer Proceedings in Mathematics & Statistics, vol 250. Springer, Cham. https://doi.org/10.1007/978-3-319-96941-1_14
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DOI: https://doi.org/10.1007/978-3-319-96941-1_14
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