SIAM Journal on Control and Optimization, Volume 58, Issue 1, Page 348-367, January 2020.
Logistic regression is a well-known statistical model which is commonly used in the situation where the output is a binary random variable. It has a wide range of applications including machine learning, public health, social sciences, ecology, and econometry. In order to estimate the unknown parameters of logistic regression with data streams arriving sequentially and at high speed, we focus our attention on a recursive stochastic algorithm. More precisely, we investigate the asymptotic behavior of a new stochastic Newton algorithm. It enables us to easily update the estimates when the data arrive sequentially and to have research steps in all directions. We establish the almost sure convergence of our stochastic Newton algorithm as well as its asymptotic normality. All our theoretical results are illustrated by numerical experiments.

中文翻译：

---

Logistic回归中有效的参数估计随机牛顿算法

SIAM控制与优化杂志，第58卷，第1期，第348-367页，2020年1月。
Logistic回归是一种众所周知的统计模型，通常在输出是二进制随机变量的情况下使用。它具有广泛的应用，包括机器学习，公共卫生，社会科学，生态学和计量经济学。为了估计数据流顺序且高速到达的逻辑回归的未知参数，我们将注意力集中在递归随机算法上。更准确地说，我们研究了一种新的随机牛顿算法的渐近行为。它使我们能够在数据按顺序到达时轻松更新估计值，并在各个方向进行研究。我们建立了随机牛顿算法及其渐近正态性的几乎确定的收敛性。数值实验说明了我们所有的理论结果。