Optimal Subset Cardinality Regression (OSCAR) Models Using the L0-Pseudonorm

Optimal Subset Cardinality Regression (OSCAR) models offer regularized linear regression using the L0-pseudonorm, conventionally known as the number of non-zero coefficients. The package estimates an optimal subset of features using the L0-penalization via cross-validation, bootstrapping and visual diagnostics. Effective Fortran implementations are offered along the package for finding optima for the DC-decomposition, which is used for transforming the discrete L0-regularized optimization problem into a continuous non-convex optimization task. These optimization modules include DBDC ('Double Bundle method for nonsmooth DC optimization' as described in Joki et al. (2018) ) and LMBM ('Limited Memory Bundle Method for large-scale nonsmooth optimization' as in Haarala et al. (2004) ). The OSCAR models are comprehensively exemplified in Halkola et al. (2023) ). Multiple regression model families are supported: Cox, logistic, and Gaussian.