[Paper Review] Hierarchical Industrial Demand Forecasting with Temporal and Uncertainty Explanations

Harshavardhan Kamarthi, Shangqing Xu+5 more|arXiv (Cornell University)|Mar 6, 2026

Forecasting Techniques and Applications0 citations

TL;DR

The paper introduces HiereInterpret, a generalizable method to provide explanations for hierarchical probabilistic time-series forecasts by (1) a subtree approximation to respect hierarchy, and (2) a quantile-based deterministic surrogate for probabilistic outputs, evaluated on synthetic and real industrial data with substantial explainability gains.

ABSTRACT

Hierarchical time-series forecasting is essential for demand prediction across various industries. While machine learning models have obtained significant accuracy and scalability on such forecasting tasks, the interpretability of their predictions, informed by application, is still largely unexplored. To bridge this gap, we introduce a novel interpretability method for large hierarchical probabilistic time-series forecasting, adapting generic interpretability techniques while addressing challenges associated with hierarchical structures and uncertainty. Our approach offers valuable interpretative insights in response to real-world industrial supply chain scenarios, including 1) the significance of various time-series within the hierarchy and external variables at specific time points, 2) the impact of different variables on forecast uncertainty, and 3) explanations for forecast changes in response to modifications in the training dataset. To evaluate the explainability method, we generate semi-synthetic datasets based on real-world scenarios of explaining hierarchical demands for over ten thousand products at a large chemical company. The experiments showed that our explainability method successfully explained state-of-the-art industrial forecasting methods with significantly higher explainability accuracy. Furthermore, we provide multiple real-world case studies that show the efficacy of our approach in identifying important patterns and explanations that help stakeholders better understand the forecasts. Additionally, our method facilitates the identification of key drivers behind forecasted demand, enabling more informed decision-making and strategic planning. Our approach helps build trust and confidence among users, ultimately leading to better adoption and utilization of hierarchical forecasting models in practice.

Motivation & Objective

• Address the lack of interpretability in large-scale hierarchical probabilistic time-series forecasting for industrial demand.
• Develop a generalizable explanation method that respects hierarchical coherency and probabilistic outputs.
• Create a semi-synthetic benchmark with ground-truth explanations and validate on real-world industrial data.
• Demonstrate how explanations reveal key drivers, important time steps, and sensitivity to data changes to aid decision-making.

Proposed method

• Propose subtree approximation to decompose cross-hierarchy importance into adjacent-hierarchy importance, reducing computation and aligning with hierarchical coherency.
• Introduce a deterministic surrogate for probabilistic forecasts by using quantiles of the output distribution, enabling post-hoc interpretability with existing methods.
• Establish a synthetic benchmark by generating hierarchical series with known ground-truth explanations and grafting them onto real-world datasets to evaluate explainability metrics.
• Evaluate explanations with metrics such as Importance Accuracy Score (IAS) and External Variable Detection Accuracy (EVDA) across deterministic and probabilistic settings.
• Provide case studies on real-world Dow demand data to illustrate practical interpretability gains and stakeholder utility.

Figure 1: In real-world HTSF tasks, stakeholders and planners want to know: RQ1: which input variable(s) contribute most to the prediction; RQ2: which time steps of each variable contribute most to the prediction; RQ3: why prediction results change when input data changes.

Experimental results

Research questions

• RQ1 RQ1: Which variables contribute most to HTSF predictions under a hierarchy?
• RQ2 RQ2: Which time steps in input histories are most influential for hierarchical forecasts?
• RQ3 RQ3: How do forecast explanations change when input data are modified?
• RQ4 RQ4: How can probabilistic HTSF outputs be explained using deterministic surrogate methods?
• RQ5 RQ5: Do the proposed explanations scale to large industrial hierarchies and real-world datasets?

Key findings

• Subtree approximation yields substantial explainability gains and scales to large hierarchies, with notable improvements in deterministic and probabilistic settings.
• Deterministic quantile surrogates enable applying standard explainability methods to probabilistic forecasts, achieving consistent explanations.
• Across synthetic benchmarks, subtree approximation improves point-forecast explanations (IAS) by up to 62.0% and probabilistic explanations (IAS) by up to 26.0% on average.
• On real-world Dow data and other benchmarks (M5, Tourism-L, Wiki), the method improves explainability metrics across multiple baselines and HTSF models.
• Case studies demonstrate the approach helps identify key drivers, patterns, and uncertainty changes relevant to stakeholders and decision-making.

Figure 2: Subtree approximation allows HiereInterpret to accurately capture importance scores of any time-series across the hierarchy