Cost-based Reweighting for Principal L_q Support Vector Machines for Sufficient Dimension Reduction

In this work we try to address the imbalance of the number of points which naturally occurs when slicing the response in Sufficient Dimension Reduction methods (SDR). Specifically, some recently proposed support vector machine based (SVM-based) methodology suffers a lot more due to the properties of the SVM algorithm. We target a recently proposed algorithm called Principal LqSVM and we propose the reweighting based on a different cost. We demonstrate that our reweighted proposal works better than the original algorithm in simulated and real data.