A Hilbert-Valued Functional Decomposition Framework for Explaining Time-Dependent Outputs

2026-09-10

AI Summary

本文针对时间依赖性输出的解释问题，提出了一种基于希尔伯特值函数分解框架的方法，能够提供考虑时间依赖性的多粒度解释。

Abstract

Feature-based explanations quantify features' influence on model predictions, but are primarily designed for scalar outputs. In many applications, however, outputs are functional or multivariate, such as time-dependent trajectories in demand forecasting. Consequently, existing approaches typically explain each output location independently, ignoring dependencies across the output components. We address this limitation by developing a unified framework for feature-based explanations of time-dependent outputs. Specifically, we generalize functional decomposition to Hilbert-valued prediction functions and extend an existing feature-based explanation framework to this setting. Our framework introduces kernel-based output representations that enable time-dependency-aware explanations at multiple levels of temporal granularity, including time-specific, time-resolved, and time-aggregated, while providing a unified view in which existing methods arise as special cases. We validate our framework on synthetic and real-world data, including intraday financial market volatility prediction and energy demand forecasting.

Problem

• time-dependent outputs
• feature-based explanations
• Hilbert-valued functions
• output dependencies
• functional decomposition

Innovation

• Hilbert-valued Functional Decomposition
• Time-dependent Outputs
• Feature-based Explanations
• Kernel-based Output Representations