Compressed learning with regular concept

Authors:
Jiawei Lv;Jianwen Zhang;Fei Wang;Zheng Wang;Changshui Zhang
Affiliations:
State Key Laboratory on Intelligent Technology and Systems, Tsinghua National Laboratory for Information Science and Technology, Department of Automation, Tsinghua University, Beijing, China;State Key Laboratory on Intelligent Technology and Systems, Tsinghua National Laboratory for Information Science and Technology, Department of Automation, Tsinghua University, Beijing, China;Department of Statistical Science, Cornell University;State Key Laboratory on Intelligent Technology and Systems, Tsinghua National Laboratory for Information Science and Technology, Department of Automation, Tsinghua University, Beijing, China;State Key Laboratory on Intelligent Technology and Systems, Tsinghua National Laboratory for Information Science and Technology, Department of Automation, Tsinghua University, Beijing, China
Venue:
ALT'10 Proceedings of the 21st international conference on Algorithmic learning theory
Year:
2010

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Abstract

We revisit compressed learning in the PAC learning framework. Specifically, we derive error bounds for learning halfspace concepts with compressed data. We propose the regularity assumption over a pair of concept and data distribution to greatly generalize former assumptions. For a regular concept we define a robust factor to characterize the margin distribution and show that such a factor tightly controls the generalization error of a learned classifier. Moreover, we extend our analysis to the more general linearly non-separable case. Empirical results on both toy and real world data validate our analysis.