非线性回归模型参数估计的一种有效平均随机Gauss-Newton算法
An efficient Averaged Stochastic Gauss-Newton algorithm for estimating parameters of non linear regressions models
摘要：
非线性回归模型是对真实现象建模的标准工具，在机器学习、生态学、计量经济学等领域有多种应用..多年来，模型参数的估计已经引起了人们的广泛关注。本文主要讨论非线性回归参数估计的一种递推方法。事实上，这些方法，其中最著名的可能是随机梯度算法及其平均版本，能够有效地处理大量数据顺序到达。然而，在实践中，它们可能对我们想要最小化的泛函的Hessian的特征值处于不同尺度的情况非常敏感。为了避免这个问题，我们首先介绍了一个在线的随机高斯-牛顿算法。为了改善在初始化不好的情况下的估计行为，我们还引入了一种新的平均随机高斯-牛顿算法，并证明了它的渐近有效性。
英文摘要：
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.
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