OSCAR: Optimal subset cardinality regression using the L0-pseudonorm with applications to prognostic modelling of prostate cancer

Abstract

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.

Nonsmooth Optimization-Based Hyperparameter-Free Neural Networks for Large-Scale Regression

“…However, there are some successful exceptions. For example, abs-linear forms of prediction tasks are solved using a successive piecewise linearization method in [12,13], a primal-dual prox method for problems in which both the loss function and the regularizer are nonsmooth is developed in [14], various nonsmooth optimization methods are applied to solve clustering, classification, and regression problems in [5,6,[15][16][17], and finally, nonsmooth optimization approaches are combined with support vector machines in [18][19][20].…”

“…We use this method since it is one of the few algorithms capable of handling large dimensions, nonconvexity, and nonsmoothness all at once. In addition, the LMBM has already proven itself in solving machine learning problems such as clustering [5], cardinality and clusterwise linear regression [6,7], and missing value imputation [8].…”