cvLM 2.0.0

Major Changes & Breaking Updates

• New Default Behavior: Data centering (center = TRUE) is now the default. This ensures that the intercept is not penalized in ridge regression, aligning the package with standard statistical methodologies.
• API Cleanup: Removed the verbose argument from grid.search. The new C++ backend evaluates the lambda grid analytically, rendering progress bars unnecessary.
• Refined Object Inheritance: For lm and glm methods, subset and na.action are now handled by the model object prior to cross-validation, ensuring consistency with the original model fit.

Performance & Engine Overhaul

The engine has been transitioned from RcppEigen to RcppArmadillo, allowing the package to leverage high-performance LAPACK and BLAS libraries for large-scale matrix operations.

• SVD-Powered Grid Search: grid.search has been entirely rewritten in C++. It now utilizes a single Singular Value Decomposition (SVD) to evaluate the entire \(\lambda\) grid analytically.
  • Efficiency: Reduces computational complexity from \(O(np^2)\) per grid point to \(O(\min(n, p))\) after the initial decomposition.
• Parallel Computation: Refined and further integrated RcppParallel to distribute workloads.
  • For K-fold CV, threads are distributed across folds.
  • For GCV/LOOCV grid searches, threads are distributed across the \(\lambda\) grid.
• Optimized LOOCV/GCV: Implemented closed-form solutions for Leave-One-Out and Generalized Cross-Validation using the hat-matrix diagonal, avoiding \(n\) model refits.

Numerical Robustness

• OLS Evolution: Transitioned from Column-Pivoted QR decomposition to Complete Orthogonal Decomposition (COD). This enables the computation of the unique minimum \(L_2\) norm solution for column rank-deficient or underdetermined (\(p > n\)) systems.
• Ridge Evolution: Transitioned from Cholesky-based methods to Singular Value Decomposition (SVD). This avoids the numerical risks associated with forming the cross-product matrix \(X^TX\) and ensures stability in ill-conditioned settings.
• Precision Control: Added a tol (tolerance) parameter to define the threshold for numerical rank estimation during COD and SVD operations.

Internal Improvements

• Template Metaprogramming: Re-engineered core logic to utilize generic, templated C++ code, shifting significant computational evaluation to compile-time and reducing runtime overhead.
• C++17 Migration: Upgraded the package build standard to C++17, enabling more expressive syntax and modern compiler optimizations.
• Memory Optimization: Refactored multi-threaded workers to utilize pre-allocated buffers. By eliminating heap allocations within “hot loops” (specifically during data training and out-of-sample evaluation), the engine achieves significantly higher throughput and lower latency.
• Armadillo Expression Tuning: Optimized the use of Armadillo expression templates to maximize lazy evaluation. This minimizes the creation of temporary objects and allows the compiler to generate more efficient SIMD-augmented computation loops.
• Comprehensive Testing Suite:
  • R Integration: Implemented extensive testthat suites to validate cvLM and grid.search against manual matrix algebra and established packages like boot.
  • Numerical Validation: Tests specifically target edge cases including ill-conditioned, rank-deficient, and high-dimensional (\(p > n\)) datasets.
• Zero-Copy Interoperability: Utilizes Armadillo’s advanced memory mapping to interface directly with R-allocated memory, ensuring zero-copy data passing between R and C++.