论文标题
部分可观测时空混沌系统的无模型预测
Conditional Distribution Function Estimation Using Neural Networks for Censored and Uncensored Data
论文作者
论文摘要
神经网络中的大多数工作都侧重于估计一组协变量的连续响应变量的条件平均值。在本文中，我们考虑使用神经网络对审查和未经审查的数据估算条件分布函数。该算法建立在与时间依赖性协变量有关COX回归的数据结构上。在不施加任何模型假设的情况下，我们考虑了基于有条件危害函数的全部可能性的损失函数，该函数是唯一未知的非参数参数，可以应用不强调的优化方法。通过仿真研究，我们显示了所提出的方法具有理想的性能，而部分似然方法和传统的神经网络，当违反模型假设时，$ L_2 $损失产量的偏向估计值有偏见。我们进一步用几个现实世界数据集说明了提出的方法。提出的方法的实现可在https://github.com/bingqing0729/nncde上获得。
Most work in neural networks focuses on estimating the conditional mean of a continuous response variable given a set of covariates.In this article, we consider estimating the conditional distribution function using neural networks for both censored and uncensored data. The algorithm is built upon the data structure particularly constructed for the Cox regression with time-dependent covariates. Without imposing any model assumption, we consider a loss function that is based on the full likelihood where the conditional hazard function is the only unknown nonparametric parameter, for which unconstraint optimization methods can be applied. Through simulation studies, we show the proposed method possesses desirable performance, whereas the partial likelihood method and the traditional neural networks with $L_2$ loss yield biased estimates when model assumptions are violated. We further illustrate the proposed method with several real-world data sets. The implementation of the proposed methods is made available at https://github.com/bingqing0729/NNCDE.
