部分线性模型的半线性神经网络估计

Semi-Linear Neural Networks Estimation of Partially Linear Model

鉴于传统的神经网络可解释性差且同时概括数据全局趋势和局部变化的能力有限,其不适合直接用于估计部分线性模型的回归函数.针对该问题,本文首先构建了同时具备线性部分和非线性部分的半线性神经网络结构,其次在一些必要条件下证明了基于经验风险最小化的网络估计量的相合性,并设计了基于梯度下降的半线性网络参数估计算法—–局部反向传播算法.随机模拟实验验证了大样本性质,实例分析结果说明了对于此问题在神经网络中引入线性部分的必要性,特别地,实验表明在波士顿房价数据集上该方法估计效果略优于N-W核估计方法.

Based on the poor interpretability and the limitation of summarizing the overall trends and local changes at the same time of the traditional neural network,it is not suitable for estimating the regression function of the partial linear model directly.In response to this problem,the semi-linear neural network structure that has both linear and non-linear parts is constructed firstly.Then,the consistency of the network estimator based on empirical risk minimization is proved under some necessary conditions,and the semi-linear network parameter estimation algorithm based on gradient descent is designed,which is called as the local back propagation algorithm.The random simulation experiments verify the large sample property,the results of the case analysis explain the necessity of introducing a linear part in the neural network.In particular,the experiment shows that the estimation effect of this method is slightly better than the N-W kernel estimation method based on the Boston House Price Dataset.