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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 regularization parameter is selected from a pivotal null-distribution statistic, eliminating the need for cross-validation and yielding sharper support recovery.
Provides FISTA optimization 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.
Install the released version from CRAN:
install.packages("picreg")Or the development version from GitHub:
# install.packages("remotes")
remotes::install_github("VcMaxouuu/picreg")library(picreg)
data(QuickStartExample)
fit <- pic(QuickStartExample$X, QuickStartExample$y)
fit$selected # names of the selected variables
fit$lambda # PDB-selected lambda (no cross-validation)
summary(fit) # family, penalty, lambda, and non-zero coefficients
coef(fit) # coefficients (sparse matrix, original scale of X)
predict(fit, newx = QuickStartExample$X[1:5, ])The design deliberately mirrors glmnet: a single
pic() fitting function returning an object equipped with
print(), summary(), coef(),
predict(), plot(), and assess()
methods that behave consistently across all six families.
The full walk-through — fitting across all six families, predicting,
visualizing, 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)
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.