Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 218 / 2 / e / Solution

The successful hard-margin fit proves that the transformed observations are separable. This creates complete separation in unpenalized logistic regression: scaling a separating coefficient vector continually raises the likelihood, so no finite maximum-likelihood estimate exists. The nearly singular observed information produces the enormous reported standard errors.

A ridge-penalized logistic regression, or equivalently a Bayesian logistic model with a proper Gaussian prior, gives finite, stable coefficients. Firth bias reduction is another standard remedy.