The Pivotal Information Criterion

Sylvain Sardy; Maxime van Cutsem; Sara van de Geer

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arXiv · 2603.04172

The Pivotal Information Criterion

Sylvain Sardy·Maxime van Cutsem·Sara van de Geer

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Abstract

The Bayesian and Akaike information criteria aim at finding a good balance between under- and over-fitting. They are extensively used every day by practitioners. Yet we contend they suffer from at least two afflictions: their penalty parameter $\lambda=\log n$ and $\lambda=2$ are too small, leading to many false discoveries, and their inherent (best subset) discrete optimization is infeasible in high dimension. We alleviate these issues with the pivotal information criterion: PIC is defined as a continuous optimization problem, and the PIC penalty parameter $\lambda$ is selected at the detection boundary (under pure noise). PIC's choice of $\lambda$ is the quantile of a statistic that we prove to be (asymptotically) pivotal, provided the loss function is appropriately transformed. As a result, simulations show a phase transition in the probability of exact support recovery with PIC, a phenomenon studied with no noise in compressed sensing. Applied on real data, for similar predictive performances, PIC selects the least complex model among state-of-the-art learners.

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Sylvain Sardy, Maxime van Cutsem, Sara van de Geer. 2026-03-04. The Pivotal Information Criterion. https://arxiv.org/abs/2603.04172

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