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We study the problem of learning with label proportions in which the trainingdata is provided in groups and only the proportion of each class in each groupis known. We propose a new method called proportion-SVM, or $\propto$SVM, whichexplicitly models the latent unknown instance labels together with the knowngroup 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 orderto solve it efficiently, we propose two algorithms: one based on simplealternating optimization and the other based on a convex relaxation. Extensiveexperiments on standard datasets show that $\propto$SVM outperforms thestate-of-the-art, especially for larger group sizes.

$\propto$SVM for learning with label proportions