论文标题
有效平均随机高斯 - 纽顿算法，用于估计非线性回归模型的参数
An efficient Averaged Stochastic Gauss-Newton algorithm for estimating parameters of non linear regressions models
论文作者
论文摘要
非线性回归模型是建模真实现象的标准工具，在机器学习，生态学，计量经济学中使用了一些应用...估计该模型的参数在很多年中引起了很多关注。我们在这里专注于一种递归方法，用于估计非线性回归的参数。确实，这些方法最著名的方法可能是随机梯度算法及其平均版本，因此可以有效地处理依次到达的大量数据。然而，在实践中，它们对我们想要最小化的功能性的Hessian的特征值非常敏感。为了避免此问题，我们首先引入了在线随机高斯 - 纽顿算法。为了改善初始化不良的估计行为，我们还引入了一种新的平均随机高斯 - 纽顿算法并证明其渐近效率。
Non linear regression models are a standard tool for modeling real phenomena, with several applications in machine learning, ecology, econometry... Estimating the parameters of the model has garnered a lot of attention during many years. We focus here on a recursive method for estimating parameters of non linear regressions. Indeed, these kinds of methods, whose most famous are probably the stochastic gradient algorithm and its averaged version, enable to deal efficiently with massive data arriving sequentially. Nevertheless, they can be, in practice, very sensitive to the case where the eigen-values of the Hessian of the functional we would like to minimize are at different scales. To avoid this problem, we first introduce an online Stochastic Gauss-Newton algorithm. In order to improve the estimates behavior in case of bad initialization, we also introduce a new Averaged Stochastic Gauss-Newton algorithm and prove its asymptotic efficiency.
