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

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.

Machine Learning (stat.ML); Machine Learning (cs.LG)

arXiv:2609.11295 [stat.ML]

(or arXiv:2609.11295v1 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2609.11295 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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