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Life sciences · Preprint
arXiv · September 10, 2026
Raises a question worth testing. It does not answer one.
This preprint proposes a novel mathematical framework that extends feature-based explanation methods to time-dependent (functional) model outputs by using Hilbert-valued decomposition and kernel-based representations. The work is theoretical and algorithmic in nature, validated on synthetic and financial/energy forecasting datasets, but has not undergone peer review and does not address clinical or hard decision-relevant endpoints.
Preprint. Not applicable; this is a methodological framework. Validation datasets include synthetic data and real-world applications in financial and energy forecasting.. Intervention: Proposed Hilbert-valued functional decomposition framework for feature-based explanations with kernel-based output representations.
Framework generalizes functional decomposition to Hilbert-valued prediction functions Introduces kernel-based output representations for time-dependency-aware explanations at multiple temporal granularities Validation performed on intraday financial market volatility prediction and energy demand forecasting
Applications shown are in forecasting (finance, energy); generalizability to clinical or safety-critical domains not discussed.
The source did not state who this applies to in practice.
This is a methodological framework paper presenting novel mathematical theory for feature explanations in functional outputs, validated on synthetic and real data but without clinical endpoints, comparative effectiveness, or evidence of impact on decision-making.
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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.
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