AI 中文总结
该研究拓展传统函数对标量回归，采用深度算子网络结合卷积神经网络，实现任意算子下的条件分布估计，在复杂数据场景中鲁棒性优于均值回归神经网络。
AI 中文摘要
函数线性模型常用于分析带标量响应的函数数据，尤其用于建模给定函数协变量时响应的条件均值。本研究从两方面拓展了传统的函数对标量回归：1. 估计条件分布函数而非条件均值等特定特征；2. 考虑任意算子，不施加函数线性性或任何模型假设。我们采用似然方法处理条件风险函数，应用卷积神经网络近似函数输入的效应，并使用深度算子网络估计条件分布。通过模拟和真实数据示例，结果表明与均值回归神经网络相比，所提方法具有良好的鲁棒性，在复杂数据场景中能实现更优的条件分布估计和区间预测。
英文摘要
Functional linear models are commonly used for analyzing functional data with scalar responses, particularly for modeling the conditional mean of the response given functional covariates. In this work, we extend the traditional scalar-on-function regression in two major aspects: 1. estimating the conditional distribution function instead of a particular characteristic such as the conditional mean; 2. considering an arbitrary operator without imposing functional linearity or any model assumption. We use a likelihood approach for the conditional hazard function and apply convolutional neural networks to approximate the effects of functional inputs and estimate the conditional distribution using deep operator networks. Through simulations and a real world data example, we show the desirable robustness of the proposed method in comparison with the mean regression neural networks, demonstrating that our approach achieves better conditional distribution estimation and interval prediction in complex data settings.
