{"paper":{"title":"Strong log-concavity in probit regression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Giacomo Zanella, Martin Chak","submitted_at":"2026-05-29T12:24:02Z","abstract_excerpt":"We show that strong log-concavity emerges in probit regression likelihoods without ridge penalization (i.e. Gaussian priors), unlike for the logistic case. Specifically, we provide: (a) a characterization of strong log-concavity for fixed designs, similar to that for the existence of the maximum likelihood estimator (MLE) and (b) an analysis for Gaussian design, dependent on the proportionality $d/n = r\\in [0, 1)$ between the sample size $n$ and the number of covariates $d$. In the latter case we show that, with high probability, provided $r$ is small enough, the resulting condition number is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.31218","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.31218/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}