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The support vector machine (SVM) is a widely used method for classification.Although many efforts have been devoted to develop efficient solvers, itremains challenging to apply SVM to large-scale problems. A nice property ofSVM is that the non-support vectors have no effect on the resulting classifier.Motivated by this observation, we present fast and efficient screening rules todiscard non-support vectors by analyzing the dual problem of SVM viavariational inequalities (DVI). As a result, the number of data instances to beentered into the optimization can be substantially reduced. Some appealingfeatures of our screening method are: (1) DVI is safe in the sense that thevectors discarded by DVI are guaranteed to be non-support vectors; (2) the dataset needs to be scanned only once to run the screening, whose computationalcost is negligible compared to that of solving the SVM problem; (3) DVI isindependent of the solvers and can be integrated with any existing efficientsolvers. We also show that the DVI technique can be extended to detectnon-support vectors in the least absolute deviations regression (LAD). To thebest of our knowledge, there are currently no screening methods for LAD. Wehave evaluated DVI on both synthetic and real data sets. Experiments indicatethat DVI significantly outperforms the existing state-of-the-art screeningrules for SVM, and is very effective in discarding non-support vectors for LAD.The speedup gained by DVI rules can be up to two orders of magnitude.

Scaling SVM and Least Absolute Deviations via Exact Data Reduction