Modeling the dependence between outputs is a fundamental challenge in multilabel classification. In this work we show that a generic regularized nonlinearity mapping independent predictions to joint predictions is sufficient to achieve state-of-the-art performance on a variety of benchmark problems. Crucially, we compute the joint predictions without ever obtaining any independent predictions, while incorporating low-rank and smoothness regularization. We achieve this by leveraging randomized algorithms for matrix decomposition and kernel approximation. Furthermore, our techniques are applicable to the multiclass setting. We apply our method to a variety of multiclass and multilabel data sets, obtaining state-of-the-art results.
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