Strong log-concavity in probit regression
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866916065361002496 |
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| author | Chak, Martin Zanella, Giacomo |
| author_facet | Chak, Martin Zanella, Giacomo |
| contents | 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 finite and, in the asymptotic regime $n, d\rightarrow \infty$, independent of $r$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_31218 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Strong log-concavity in probit regression Chak, Martin Zanella, Giacomo Statistics Theory 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 finite and, in the asymptotic regime $n, d\rightarrow \infty$, independent of $r$. |
| title | Strong log-concavity in probit regression |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2605.31218 |