arXiv:2410.05430cs.LGstat.AP2024-10NeurIPS

将可解释的结构化网络扩展至函数型数据,兼顾模型可解释性与预测性能。

A Functional Extension of Semi-Structured Networks

  • 将半结构化网络拓展到函数型数据,保留可解释性。
  • 在真实生物力学数据上准确恢复信号,提升预测精度。
  • 适合处理大规模函数型数据的科研与工程场景。

半结构化网络(SSNs)结合了加法模型的结构与深度神经网络,能够在保持部分特征效应可解释性的同时捕捉高阶非线性关系。然而,如何维持加法模型部分的可解释性仍是关键挑战。受大规模生物力学数据启发,本文探索将SSN扩展至函数型数据。现有函数数据分析方法虽具潜力,但表达能力有限,难以建模全部交互与非线性关系,且在大规模数据上扩展性差。尽管SSN具有显著优势,其向函数型数据的适配仍较复杂。本文提出一种功能性半结构化网络方法,在保留经典函数回归优点的基础上提升了可扩展性。数值实验表明,该方法能准确恢复潜在信号,增强预测性能,并优于对比方法。

原文摘要 · Abstract (English)

Semi-structured networks (SSNs) merge the structures familiar from additive models with deep neural networks, allowing the modeling of interpretable partial feature effects while capturing higher-order non-linearities at the same time. A significant challenge in this integration is maintaining the interpretability of the additive model component. Inspired by large-scale biomechanics datasets, this paper explores extending SSNs to functional data. Existing methods in functional data analysis are promising but often not expressive enough to account for all interactions and non-linearities and do not scale well to large datasets. Although the SSN approach presents a compelling potential solution, its adaptation to functional data remains complex. In this work, we propose a functional SSN method that retains the advantageous properties of classical functional regression approaches while also improving scalability. Our numerical experiments demonstrate that this approach accurately recovers underlying signals, enhances predictive performance, and performs favorably compared to competing methods.

函数型数据可解释模型半结构化网络

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