Sparse Additive Text Models with Low Rank Background

The sparse additive model for text modeling involves the sum-of-exp computing, whose cost is consuming for large scales. Moreover, the assumption of equal background across all classes/topics may be too strong. This paper extends to propose sparse additive model with low rank background (SAM-LRB) and obtains simple yet efficient estimation. Particularly, employing a double majorization bound, we approximate log-likelihood into a quadratic lower-bound without the log-sumexp terms. The constraints of low rank and sparsity are then simply embodied by nuclear norm and l1-norm regularizers. Interestingly, we find that the optimization task of SAM-LRB can be transformed into the same form as in Robust PCA. Consequently, parameters of supervised SAM-LRB can be efficiently learned using an existing algorithm for Robust PCA based on accelerated proximal gradient. Besides the supervised case, we extend SAM-LRB to favor unsupervised and multifaceted scenarios. Experiments on three real data demonstrate the effectiveness and efficiency of SAM-LRB, compared with a few state-of-the-art models.