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

arXiv · AI, language, vision and robotics · article · Sep 10, 2026 · UTC

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 func

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