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Felix Yu, Dong Liu, Sanjiv Kumar, Tony Jebara, Shih-Fu Chang. $\propto$SVM for learning with label proportions. In International Conference on Machine Learning (ICML) (full oral), Atlanta, GA, June 2013.

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We study the problem of learning with label proportions in which the training data is provided in groups and only the proportion of each class in each group is known. We propose a new method called proportion-SVM, or $\propto$SVM, which explicitly models the latent unknown instance labels together with the known group label proportions in a large-margin framework. Unlike the existing works, our approach avoids making restrictive assumptions about the data. The $\propto$SVM model leads to a non-convex integer programming problem. In order to solve it efficiently, we propose two algorithms: one based on simple alternating optimization and the other based on a convex relaxation. Extensive experiments on standard datasets show that $\propto$SVM outperforms the state-of-the-art, especially for larger group sizes


FelixX. Yu
Dong Liu
Shih-Fu Chang

BibTex Reference

   Author = {Yu, Felix and Liu, Dong and Kumar, Sanjiv and Jebara, Tony and Chang, Shih-Fu},
   Title = {$\propto$SVM for learning with label proportions},
   BookTitle = {International Conference on Machine Learning (ICML) (full oral)},
   Address = {Atlanta, GA},
   Month = {June},
   Year = {2013}

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