Frisky CALF sometimes outruns LASSO

Regularized regression analysis is a mature analytic approach to identify weighted sums of variables that predict outcomes. Typically, the number of subjects (N) is smaller than the number of predictors (p). Here, we present a novel coarse approximation linear function (CALF) to frugally select important predictors, build linear models, and discover causality. CALF is a linear regression strategy applied to normalized data that employs only a few (such as 2 to 20) nonzero weights, each +1 or -1. Metrics can be Welch t-test p-value, area under curve (AUC) of receiver operating characteristic, or Pearson correlation, depending upon data type and user preferences. For quantitative approximations, a linear fit (adding an intercept value and rescaling {+/-}1 weights by a common multiplier) can be added to optimize mean squared error (MSE). Real medical data of five types were used to generate examples with goals of binary classification or real variable approximation. Predictors considered were real, sets of integers, or ternary values of single nucleotide polymorphisms. When applied to real data, CALF approximations outperformed in p-value, AUC, correlation, or MSE a popular regularized linear regression algorithm, namely, basic LASSO. It appears that using LASSO without considering CALF might risk wasting resources. AvailabilityR version: Comprehensive R Archive (CRAN): https://cran.r-project.org/web/packages/CALF/index.html Python 3.x version: GitHub: https://github.com/jorufo/CALF_Python Contactclark_jeffries@med.unc.edu