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The multi-label classification problem has generated significant interest inrecent years. However, existing approaches do not adequately address two keychallenges: (a) the ability to tackle problems with a large number (saymillions) of labels, and (b) the ability to handle data with missing labels. Inthis paper, we directly address both these problems by studying the multi-labelproblem in a generic empirical risk minimization (ERM) framework. Ourframework, despite being simple, is surprisingly able to encompass severalrecent label-compression based methods which can be derived as special cases ofour method. To optimize the ERM problem, we develop techniques that exploit thestructure of specific loss functions - such as the squared loss function - tooffer efficient algorithms. We further show that our learning framework admitsformal excess risk bounds even in the presence of missing labels. Our riskbounds are tight and demonstrate better generalization performance for low-rankpromoting trace-norm regularization when compared to (rank insensitive)Frobenius norm regularization. Finally, we present extensive empirical resultson a variety of benchmark datasets and show that our methods performsignificantly better than existing label compression based methods and canscale up to very large datasets such as the Wikipedia dataset.

Large-scale Multi-label Learning with Missing Labels