We explore a novel approach to upper bound the misclassification error for problems with data comprising a small number of positive samples and a large number of negative samples. We assign the hinge-loss to upper bound the misclassification error of the positive examples and use the minimax risk to upper bound the misclassification error with respect to the worst case distribution that generates the negative examples. This approach is computationally appealing since the majority of training examples (belonging to the negative class) are represented by the statistics of their distribution, in contrast to kernel SVM which produces a very large number of support vectors in such settings. We derive empirical risk bounds for linear and non-linear classification and show that they are dimensionally independent and decay as 1/√m for m samples. We propose an efficient algorithm for training an intersection of finite number of hyperplanes and demonstrate its effectiveness on real data, including letter and scene recognition.
|Title of host publication||32nd International Conference on Machine Learning, ICML 2015|
|Editors||David Blei, Francis Bach|
|Publisher||International Machine Learning Society (IMLS)|
|Number of pages||9|
|State||Published - 2015|
|Event||32nd International Conference on Machine Learning, ICML 2015 - Lile, France|
Duration: 6 Jul 2015 → 11 Jul 2015
|Name||32nd International Conference on Machine Learning, ICML 2015|
|Conference||32nd International Conference on Machine Learning, ICML 2015|
|Period||6/07/15 → 11/07/15|
Bibliographical noteFunding Information:
This work has been supported by Israel Science Foundation 839/12 and the European Union's Seventh Framework Programme FP7-ICT-2013-11 under grant agreement No 619435.
Copyright © 2015 by the author(s).
ASJC Scopus subject areas
- Human-Computer Interaction
- Computer Science Applications