Hierarchical Industrial Demand Forecasting with Temporal and Uncertainty Explanations

Harshavardhan Kamarthi; Shangqing Xu; Xinjie Tong; Xingyu Zhou; James Peters; Joseph Czyzyk; B. Aditya Prakash

cs.LGMar 6, 2026

Hierarchical Industrial Demand Forecasting with Temporal and Uncertainty Explanations

Authors: Harshavardhan Kamarthi, Shangqing Xu, Xinjie Tong, Xingyu Zhou, James Peters, Joseph Czyzyk, B. Aditya Prakash

Organizations: Georgia Institute of Technology Atlanta, USA · Aspen Technology Houston, USA · The Dow Chemical Company Houston, USA · The Dow Chemical Company Midland, USA

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.

Figures & tables

Fig. 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.

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

Fig. 4: Adapting to any probabilistic forecast by deriving importance scores from quantiles of the forecasts

Dataset	No. of Nodes	Levels of	Horizon	Obs.
Dow	20022	8	24	1.2 M
M5	3914	12	12	7.7 M
Tourism-L	555	4,5	12	126k
Wiki	207	5	1	696k

TABLE I: Summary of demand datasets used in benchmark establishment. We covered a variety of node capacity, number of hierarchical levels, and horizon sizes in the selection of such datasets.

Dataset	Dow’s Demand								M5
Metric	IAS				EVDA				IAS				EVDA
Int. Method	LIME	IG	FO	SG	LIME	IG	FO	SG	LIME	IG	FO	SG	LIME	IG	FO	SG
FreqShapes	$0.39$	$0.42$	$0.37$	$0.22$	$0.38$	$0.44$	$0.48$	$0.27$	$0.56$	$0.62$	$0.37$	$0.77$	$0.52$	$0.62$	$0.54$	$0.77$
- w/o subtree	$0.11$	$0.17$	$0.23$	$0.17$	$0.16$	$0.32$	$0.39$	$0.28$	$0.24$	$0.36$	$0.26$	$0.49$	$0.21$	$0.37$	$0.32$	$0.46$
SeqComb	$0.39$	$0.33$	$0.38$	$0.29$	$0.39$	$0.42$	$0.44$	$0.32$	0.47	0.54	0.33	0.73	0.58	0.74	0.37	0.64
- w/o subtree	$0.27$	$0.24$	$0.35$	$0.28$	$0.21$	$0.24$	$0.31$	$0.29$	0.22	0.39	0.18	0.53	0.33	0.31	0.24	0.35

TABLE II: Cross-variable deterministic hierarchical evaluation results on Dow’s Demand and M5, averaged across all HTSF models. Subtree approximation improved 34 of 36 Dow experiments with relatively

40.4\%

in EVDA and

62.0\%

in IAS, and improved all M5 experiment with relatively

92.5\%

in EVDA and

78.0\%

in IAS.

	Correlation Type	Same Series				Cross Series				Cross Levels
	Int. Method	LIME	IG	FO	SG	LIME	IG	FO	SG	LIME	IG	FO	SG
Dow’s Demand	FreqShapes	0.32	0.35	0.37	0.31	0.15	0.17	0.19	0.18	0.18	0.19	0.17	0.11
	- w/o subtree	0.29	0.37	0.34	0.33	0.13	0.18	0.17	0.15	0.15	0.19	0.17	0.09
	SeqComb	0.35	0.34	0.39	0.39	0.13	0.16	0.22	0.24	0.16	0.18	0.24	0.25
	- w/o subtree	0.25	0.36	0.32	0.39	0.17	0.21	0.19	0.15	0.19	0.24	0.2	0.11
	LowVar	0.21	0.24	0.24	0.23	0.11	0.24	0.18	0.19	0.1	0.12	0.12	0.11

TABLE III: Same-variable evaluation results on Dow’s Demand, M5, Tourism-L, and Wiki. Among all the 36 experiments in each dataset, subtree approximation improved 22 Dow experiments with average

12.3\%

improvement, 24 M5 experiments with average

8.0\%

improvement, 26 Tourism experiments with average

7.5\%

improvement, and 26 Wiki experiments with average

10.7\%

improvement.

	Correlation Type	Same Series				Cross Series				Cross Levels
	Int. Method	LIME	IG	FO	SG	LIME	IG	FO	SG	LIME	IG	FO	SG
Dow’s Demand	FreqShapes	0.28	0.26	0.34	0.23	0.08	0.19	0.14	0.13	0.08	0.14	0.12	0.07
	- w/o subtree	0.22	0.22	0.27	0.17	0.07	0.14	0.10	0.09	0.06	0.14	0.08	0.07
	SeqComb	0.25	0.42	0.29	0.43	0.20	0.27	0.18	0.17	0.14	0.15	0.19	0.16
	- w/o subtree	0.18	0.33	0.24	0.28	0.16	0.22	0.16	0.16	0.13	0.14	0.17	0.11
	LowVar	0.16	0.26	0.21	0.29	0.13	0.22	0.16	0.13	0.11	0.06	0.16	0.13

TABLE IV: Probabilistic hierarchical explanation results on Dow’s Demand, M5, Tourism-L, and Wiki, averaged across all HTSF models and three quantiles. Of all 36 experiments on each dataset, subtree approximation improved 34 Dow experiments with an average

26.0\%

improvement, 29 M5 experiments with an average

18.1\%

improvement, 29 Tourism experiments with an average

16.5\%

improvement, and 31 Wiki experiments with average

25.3\%

improvement.

Panel of Figure 8 — Fig. 5: Probabilistic evaluation results of each quantile. While the 70th quantile with subtree has the best absolute performance, the 90th quantile receives the most improvement by introducing subtree approximation.

Panel of Figure 9 — Fig. 6: Performance improvement of HiereInterpret with Subtree approximation. Point forecasts see up to 16% improvements, whereas probabilistic forecasts show over 25% improvements

Panel of Figure 10 — Fig. 7: Degradation of performance with increase in hierarchy size with and without subtree approximation

Panel of Figure 11 — Fig. 8: After accessing new data without periodic spikes, HAILS tend to give high uncertainty in its prediction. HiereInterpret shows that such high uncertainty output comes from the focus on two types of data – with and without periodic spikes.

Panel of Figure 12 — Fig. 9: As the model anticipates the beginning of the periodic trends, HiereInterpret notes the increased importance of the periodic trends from the past.

Fig. 10: Running time of explanation models on HAILS considering hierarchies up to different levels. Our proposed subtree approximation greatly cuts down the time complexity.

Panel of Figure 14 — Fig. 11: The downward spike observed in the second forecast causes HiereInterpret to interpret that the important economic variable’s previous downward trend may have a significant impact on the change in forecast trend.

Explainable Time Series Forecasting

Explainable time series forecasting makes predictions over time interpretable through attributions, structured models, causal reasoning, and counterfactuals.

See all 61 papers

Aug 25, 2026

NVExplain: Explaining Time Series Forecasting with Latent Trajectory Analysis and Structure-Preserving Surrogates

Time series forecasting models are widely used in high-stakes settings, yet their predictions remain difficult to interpret because existing post-hoc methods often ignore temporal dependence and fail to provide horizon-specific explanations. We propose a model-agnostic explainability framework that explains forecasting predictions by attributing each forecast horizon to temporally relevant historical lags. The framework models forecasting as a latent trajectory and introduces semantic flow to quantify how information evolves across time in the model's internal representations. By aggregating semantic flow, it constructs a lag-horizon attribution matrix that captures horizon-resolved temporal influence. To improve explainability, we further generate structure-preserving perturbations and fit sparse local surrogate models, producing human-readable and temporally coherent explanations. We evaluate the method using faithfulness and stability diagnostics across multiple benchmark datasets. Results show that the semantic-flow variant achieves competitive or superior faithfulness compared to standard post-hoc baselines, while being substantially more computationally efficient. Stability analysis further demonstrates that the explanations are robust and identifies regimes where interpretation should be applied with caution.

Muyan Anna Li, Manikandan Ravikiran, Aditi Gautam

NVIDIA, USA

Explainable Time Series Forecasting Interpretable ML Feature Attribution

Ask PDF

Jul 30, 2026

Information Bottleneck Learning for Faithful Time Series Forecasting Explanations

As forecasts increasingly drive decisions in fields such as energy, transportation, and healthcare, understanding the historical data behind these predictions has become as crucial as the predictions themselves. Although existing interpretable-by-design forecasters reveal their internal structures, they offer no guarantee that these structures faithfully reflect the underlying evidence driving the predictions. In contrast, while faithfulness-oriented methods explicitly verify model behavior, they are almost exclusively designed for post-hoc classification tasks. To bridge this gap, we propose IB-Forecast, an inherently interpretable multivariate time-series forecasting framework. It decomposes forecasting into a learned periodic component and a residual component computed with explainable masks over input tokens. With a budget-constrained information bottleneck, end-to-end optimization enables users to directly control explanation sparsity. With a rigorous faithfulness evaluation protocol, extensive experiments demonstrate that IB-Forecast matches the forecasting error of leading black-box models while providing faithful explanations at no additional inference cost. Furthermore, under a matched sparsity budget, these native explanations consistently surpass gradient-based, occlusion-based, and optimization-based baselines across all evaluated datasets. Ultimately, whereas the native explanations of existing interpretable forecasters exhibit poor faithfulness, IB-Forecast guarantees high explanation fidelity, requiring only 14-20% of the observations to deliver low-error predictions.

Xu Zheng, Wei Cheng, Zhuomin Chen +3

Florida International University, Miami, FL, USA · NEC Laboratories America, Princeton, NJ, USA · University of Houston, Houston, TX, USA +1

Multivariate Time Series Forecasting Explainable Time Series Forecasting Interpretable ML Time Series Forecasting Information Bottleneck

Ask PDF

Mar 4, 2026

PatchDecomp: Interpretable Patch-Based Time Series Forecasting

Time series forecasting, which predicts future values from past observations, plays a central role in many domains and has driven the development of highly accurate neural network models. However, the complexity of these models often limits human understanding of the rationale behind their predictions. We propose PatchDecomp, a neural network-based time series forecasting method that achieves both high accuracy and interpretability. PatchDecomp divides input time series into subsequences (patches) and generates predictions by aggregating the contributions of each patch. This enables clear attribution of each patch, including those from exogenous variables, to the final prediction. Experiments on multiple benchmark datasets demonstrate that PatchDecomp provides predictive performance comparable to recent forecasting methods. Furthermore, we show that the model's explanations not only influence predicted values quantitatively but also offer qualitative interpretability through visualization of patch-wise contributions.

Hiroki Tomioka, Genta Yoshimura

Mitsubishi Electric Corporation, Japan

Time Series Forecasting Explainable Time Series Forecasting

Ask PDF

Abstract

Explainable Time Series Forecasting

Explore similar work

NVExplain: Explaining Time Series Forecasting with Latent Trajectory Analysis and Structure-Preserving Surrogates

Information Bottleneck Learning for Faithful Time Series Forecasting Explanations

PatchDecomp: Interpretable Patch-Based Time Series Forecasting