Variable Selection using the Pivotal Information Criterion // Sparse regression and classification via the Pivotal Information Criterion (PIC), an alternative to the Bayesian Information Criterion (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 Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) optimization for the L1, Smoothly Clipped Absolute Deviation (SCAD), and Minimax Concave Penalty (MCP) penalties across six response distributions: Gaussian, binomial, Poisson, exponential, Gumbel, and Cox. Under standard sparsity assumptions, the selector achieves a phase transition for exact support recovery, analogous to results in compressed sensing. See Sardy, van Cutsem and van de Geer (2026) doi:10.48550/arXiv.2603.04172.