Deep Learning for Functional Data Analysis with Adaptive Basis Layers
Deep Learning for Functional Data Analysis with Adaptive Basis Layers
复制标题
DOI：
--
复制
发表时间：
2021-06
期刊：
影响因子：
--
通讯作者：
Ju Yao;Jonas W. Mueller;Jane-ling Wang
中科院分区：
文献类型：
--
作者：
Ju Yao;Jonas W. Mueller;Jane-ling Wang
尽管深度神经网络取得了广泛的成功，但在功能数据中的应用至今仍然很少。函数数据的无限维度意味着只有在适当降维之后才能应用标准学习算法，这通常是通过基扩展实现的。目前，这些基础是在没有手头任务信息的情况下先验地选择的，因此对于指定的任务可能无效。相反，我们建议以端到端的方式适应性地学习这些基础。我们引入了神经网络，它采用了一个新的基本层，其隐藏单元是每个基本函数本身，实现为一个微神经网络。我们的体系结构学习将简约降维应用于只关注与目标相关的信息的函数输入，而不是输入函数中不相关的变化。在大量使用函数数据的分类/回归任务中，我们的方法在经验上优于其他类型的神经网络，并且我们证明了我们的方法在统计上是一致的，并且泛化误差很小。代码位于：\url{https://github.com/jwyyy/AdaFNN}.
Despite their widespread success, the application of deep neural networks to functional data remains scarce today. The infinite dimensionality of functional data means standard learning algorithms can be applied only after appropriate dimension reduction, typically achieved via basis expansions. Currently, these bases are chosen a priori without the information for the task at hand and thus may not be effective for the designated task. We instead propose to adaptively learn these bases in an end-to-end fashion. We introduce neural networks that employ a new Basis Layer whose hidden units are each basis functions themselves implemented as a micro neural network. Our architecture learns to apply parsimonious dimension reduction to functional inputs that focuses only on information relevant to the target rather than irrelevant variation in the input function. Across numerous classification/regression tasks with functional data, our method empirically outperforms other types of neural networks, and we prove that our approach is statistically consistent with low generalization error. Code is available at: \url{https://github.com/jwyyy/AdaFNN}.