Variable selection using the Pivotal Information Criterion.
Sparse regression and classification via the Pivotal Information Criterion (PIC), an alternative to BIC, cross-validation, and Lasso-based tuning. The regularisation parameter is selected from a pivotal null-distribution statistic, eliminating the need for cross-validation and yielding sharper support recovery.
Provides FISTA optimisation for the L1, SCAD, and MCP penalties across six response distributions:
| Family | family = |
Response |
|---|---|---|
| Gaussian | "gaussian" |
continuous |
| Binomial | "binomial" |
0/1 binary |
| Poisson | "poisson" |
count |
| Exponential | "exponential" |
positive cont. |
| Gumbel | "gumbel" |
continuous |
| Cox PH | "cox" |
(time, event) |
Under standard sparsity assumptions, the selector achieves a phase transition for exact support recovery, analogous to results in compressed sensing.
The development version can be installed from GitHub:
# install.packages("remotes")
remotes::install_github("VcMaxouuu/picreg")library(picreg)
data(QuickStartExample)
fit <- pic(QuickStartExample$X, QuickStartExample$y)
fit$selected # names of selected variables
fit$lambda # PDB-selected lambda
coef(fit) # coefficients on the original scaleThe full walk-through - fitting across all six families, predicting,
visualising, choosing penalties, and running diagnostics
(phase_transition(), pdb_asymptotic()) - lives
in the package vignette:
vignette("vignette", package = "picreg")Sardy, van Cutsem, and van de Geer. The Pivotal Information Criterion. https://arxiv.org/abs/2603.04172 (doi:10.48550/arXiv.2603.04172)