# An efficient stochastic Newton algorithm for parameter estimation in logistic regressions

## TL;DR

This paper introduces a new stochastic Newton algorithm for efficient parameter estimation in logistic regression models with high-speed data streams, providing theoretical guarantees and numerical validation.

## Contribution

It proposes a novel recursive stochastic Newton algorithm for logistic regression, with proven convergence and asymptotic normality, suitable for sequential data processing.

## Key findings

- Algorithm converges almost surely.
- Estimates are asymptotically normal.
- Numerical experiments validate theoretical results.

## Abstract

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 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.