论文检索

高斯设计 Logistic 回归的极小极大最优估计与 MLE 误差界改进AI 解读

We study finite-sample parameter estimation in logistic regression with Gaussian design, where the goal is to estimate $\mathbfθ^*\in \mathbb{R}^d$ with $R=\|\mathbfθ^*\|_2\ge 1$ from i.i.d. samples $\{(\mathbf{x}_i,y_i)\}_{i=1}^n,$ $\mathbf{x}_i \sim N(0,\mathbf{I}_d)$, $y_i\mid \mathbf{x}_i \sim \mathrm{Bernoulli}((1+\exp(-\mathbf{x}_i^\top \mathbfθ^*))^{-1})$. In this paper, we provide the first minimax optimal estimator, and improve on the best known finite-sample error…

基于迭代硬阈值的学习二元结果稀疏广义线性模型AI 解读

In statistics, generalized linear models (GLMs) are widely used for modeling data and can expressively capture potential nonlinear dependence of the model's outcomes on its covariates. Within the broad family of GLMs, those with binary outcomes, which include logistic and probit regressions, are motivated by common tasks such as binary classification with (possibly) non-separable data. In addition, in modern machine learning and statistics, data is often high-dimensional yet…