Abstract Pairwise learning is a specialized form of supervised learning that focuses on predicting outcomes for pairs of objects. In this paper, we formulate the pairwise learning problem as a difference of convex (DC) optimization problem using the Kronecker product kernel, $$\ell _1$$ ℓ 1 - and $$\ell _0$$ ℓ 0 -regularizations, and various, possibly nonsmooth, loss functions. Our aim is to develop an efficient learning algorithm, SparsePKL, that produces accurate predictions with the desired sparsity level. In addition, we propose a novel limited memory bundle DC algorithm (LMB-DCA) for large-scale nonsmooth DC optimization and apply it as an underlying solver in the SparsePKL. The performance of the SparsePKL-algorithm is studied in seven real-world drug-target interaction data and the results are compared with those of the state-of-art methods in pairwise learning.

In many real-world applications, such as those based on electronic health records, prognostic prediction of patient survival is based on heterogeneous sets of clinical laboratory measurements. To address the trade-off between the predictive accuracy of a prognostic model and the costs related to its clinical implementation, we propose an optimized L0-pseudonorm approach to learn sparse solutions in multivariable regression. The model sparsity is maintained by restricting the number of nonzero coefficients in the model with a cardinality constraint, which makes the optimization problem NP-hard. In addition, we generalize the cardinality constraint for grouped feature selection, which makes it possible to identify key sets of predictors that may be measured together in a kit in clinical practice. We demonstrate the operation of our cardinality constraint-based feature subset selection method, named OSCAR, in the context of prognostic prediction of prostate cancer patients, where it enables one to determine the key explanatory predictors at different levels of model sparsity. We further explore how the model sparsity affects the model accuracy and implementation cost. Lastly, we demonstrate generalization of the presented methodology to high-dimensional transcriptomics data.