Cross-Validation for Linear & Ridge Regression Models (RcppArmadillo & RcppParallel)

This package provides efficient implementations of cross-validation techniques for linear and ridge regression models, leveraging C++17 with RcppArmadillo and RcppParallel. It supports leave-one-out, generalized, and K-fold cross-validation methods, utilizing Singular Value Decomposition (SVD) and Complete Orthogonal Decomposition (COD) for high performance and numerical stability in high-dimensional settings.

Dependencies

• Rcpp: Integration between R and C++.
• RcppParallel: Parallel computing support for Rcpp.
• RcppArmadillo: Integration between R and the Armadillo C++ library.
• RhpcBLASctl: Control of BLAS/LAPACK thread counts.

Requirements

• R
• Rcpp
• RcppParallel
• RcppArmadillo
• C++17 compatible compiler

Acknowledgments

This code is adapted and extended from various sources, leveraging the capabilities of the following:

• Rcpp by Dirk Eddelbuettel, Romain Francois, et al., for R and C++ integration.
• RcppParallel by JJ Allaire, Romain Francois, et al., for parallel computing support.
• RcppArmadillo by Dirk Eddelbuettel, Conrad Sanderson, et al., for high-performance linear algebra.

Please refer to the source files for detailed information and licenses.

Contributors

• [Philip Nye]: GitHub Profile

License

This code is under MIT License.

Example Usage

library(cvLM)
data(mtcars)

# 10-fold CV for a linear regression model
cvLM(mpg ~ ., data = mtcars, K.vals = 10)

# Comparing 5-fold, 10-fold, and Leave-One-Out CV configurations using 2 threads
cvLM(mpg ~ ., data = mtcars, K.vals = c(5, 10, nrow(mtcars)), n.threads = 2)

# Ridge regression with analytic GCV (using lm interface)
fitted.lm <- lm(mpg ~ ., data = mtcars)
cvLM(fitted.lm, data = mtcars, lambda = 0.5, generalized = TRUE)

grid.search(
  formula = mpg ~ ., 
  data = mtcars,
  K = 5L,           # Use 5-fold CV
  max.lambda = 100, # Search values between 0 and 100
  precision = 0.01  # Increment in steps of 0.01
)