The Pivotal Information Criterion
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866908901190926336 |
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| author | Sardy, Sylvain van Cutsem, Maxime van de Geer, Sara |
| author_facet | Sardy, Sylvain van Cutsem, Maxime van de Geer, Sara |
| contents | 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 $λ=\log n$ and $λ=2$ 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 $λ$ is selected at the detection boundary (under pure noise). PIC's choice of $λ$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_04172 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Pivotal Information Criterion Sardy, Sylvain van Cutsem, Maxime van de Geer, Sara Statistics Theory Information Theory Methodology 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 $λ=\log n$ and $λ=2$ 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 $λ$ is selected at the detection boundary (under pure noise). PIC's choice of $λ$ 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. |
| title | The Pivotal Information Criterion |
| topic | Statistics Theory Information Theory Methodology |
| url | https://arxiv.org/abs/2603.04172 |