Feature-based explanations capture time-dependent model outputs better
A Hilbert-Valued Functional Decomposition Framework for Explaining Time-Dependent Outputs
Machine Learning
Summary
Many computer models produce results that change over time, like forecasting energy use or stock volatility, but current explanation methods treat each time point separately. The authors developed a new technique that explains how input features affect the entire time-dependent output as a whole, considering how different moments in time relate to each other. Their method uses math tools called Hilbert spaces and kernels to provide explanations that work at different time scales, from specific moments to overall trends. They tested their approach with simulated data and real-world cases to show it works.
What this means in practice
- •For energy demand analysts: Explain how different factors influence predicted energy use over daily or hourly periods with a cohesive view rather than separate time points.
- •For financial risk managers: Understand the time-dependent influence of market features on intraday volatility forecasts using unified explanation methods.
Authors
Sophie Hanna Langbein, Niklas Koenen, Marvin N. Wright, Julia Herbinger
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.