Temporal Distributional Values for Probabilistic Forecasts

Probabilistic time-series forecasts describe a range of possible futures. When these forecasts inform health decisions, patients, clinicians and researchers need to understand how patient history shapes the predictions and their uncertainty. For example, in diabetes management individuals may wish to understand how behaviors (e.g., eating, exercise) shift predicted glucose trajectories and how they influence the range of future glycemic states. Specific patient behaviors may have similar effects on a predicted future glucose trajectory but induce substantially different levels of uncertainty in the range of glycemic outcomes predicted by the model. Scalar attribution methods explain a chosen summary of a forecast, such as its mean. However, a single aggregate statistic can conceal probabilistic information: an input may change the predicted variance without changing the mean, or shift the forecast from a uniform to a bimodal distribution. We introduce Temporal Distributional Values (TDV), a model-agnostic method that extends Shapley attribution to probabilistic time-series forecasting. TDV computes distributions of input contributions directly from the model's native probabilistic output, including quantiles and sampled trajectories. We evaluate TDV on four state of the art forecasting models using long-term glucose, meal, and activity data from type 1 diabetes, type 2 diabetes, and health and wellness populations. Experiments demonstrate accurate forecast reconstruction and close agreement between TDV average contributions and exact scalar Shapley values; stability under trajectory and order sampling; and practical computational cost. Case studies reveal previously hidden distributional effects of meals, activity, and glucose history, demonstrating the value of TDV for uncovering a richer understanding of probabilistic forecasts. These explanations give practitioners a new way to examine how patient history shapes the range of outcomes a forecasting model predicts.