  The logistic regression model is one of the most popular data generation
model in noisy binary classification problems. In this work, we study the
sample complexity of estimating the parameters of the logistic regression model
up to a given $\ell_2$ error, in terms of the dimension and the inverse
temperature, with standard normal covariates. The inverse temperature controls
the signal-to-noise ratio of the data generation process. While both
generalization bounds and asymptotic performance of the maximum-likelihood
estimator for logistic regression are well-studied, the non-asymptotic sample
complexity that shows the dependence on error and the inverse temperature for
parameter estimation is absent from previous analyses. We show that the sample
complexity curve has two change-points in terms of the inverse temperature,
clearly separating the low, moderate, and high temperature regimes.
