Finite-Sample Performance of Gradient Descent in Logistic Regression with Gaussian Design (opens in new tab)

We consider the parameter estimation problem in logistic regression with Gaussian design: the estimation of a fixed unknown parameter $\theta^*\in \mathbb{R}^d$ ($\|\theta^*\|_2\ge 1$) from $n$ i.i.d. samples $\{(x_i,y_i)\}_{i=1}^n$, where $x_i\sim N(0,I_d)$ and $y_i|x_i \sim {\rm Bernoulli}(1/(1+\exp(-x_i^\top \theta^*)))$. Our main aim is to characterize the finite-sample estimation performance and convergence behavior of gradient descent (GD)...