论文标题
测量误差模型：从非参数方法到深神经网络
Measurement error models: from nonparametric methods to deep neural networks
论文作者
论文摘要
深度学习的成功激发了将神经网络应用于统计推断的最新兴趣。在本文中，我们研究了深层神经网络在非参数回归中使用测量误差。我们提出了一种有效的神经网络设计，用于估计测量误差模型，在该模型中，我们使用完全连接的前馈神经网络（FNN）近似回归函数$ f（x）$，一个归一化流量，以近似于$ x $的先前分布，并近似推理网络来近似$ x $的后验分布。我们的方法利用了深度神经网络的变异推断的最新进展，例如重要性权重自动编码器，双重重新处理梯度估计器和非线性独立组件估计。我们进行了一项广泛的数值研究，以将神经网络方法与经典的非参数方法进行比较，并观察到神经网络方法在适应不同类别的回归函数方面更加灵活，并且在几乎所有设置中都具有优越或可比性的最佳或可用方法。
The success of deep learning has inspired recent interests in applying neural networks in statistical inference. In this paper, we investigate the use of deep neural networks for nonparametric regression with measurement errors. We propose an efficient neural network design for estimating measurement error models, in which we use a fully connected feed-forward neural network (FNN) to approximate the regression function $f(x)$, a normalizing flow to approximate the prior distribution of $X$, and an inference network to approximate the posterior distribution of $X$. Our method utilizes recent advances in variational inference for deep neural networks, such as the importance weight autoencoder, doubly reparametrized gradient estimator, and non-linear independent components estimation. We conduct an extensive numerical study to compare the neural network approach with classical nonparametric methods and observe that the neural network approach is more flexible in accommodating different classes of regression functions and performs superior or comparable to the best available method in nearly all settings.
