A Deep Learning Framework for Quantile Demand Forecasting in E-commerce with Doubly Censored Data

Ziwen Ye; Jiawen Wei; Teng Song; Chen Chen; Guangrui Ma

cs.LGOct 29, 2026

A Deep Learning Framework for Quantile Demand Forecasting in E-commerce with Doubly Censored Data

Authors: Ziwen Ye, Jiawen Wei, Teng Song, Chen Chen, Guangrui Ma

Organizations: Meituan, Beijing, China

Abstract

In recent years, a growing number of online retail companies have embraced deep learning models for demand forecasting, leveraging their scalability in processing large-scale datasets. Accurate demand forecasts enable improved planning and allow operational flexibility to adjust sales accordingly. Moreover, quantile estimation has gained widespread application as it offers valuable uncertainty quantification, thereby enhancing the robustness of decision-making processes. However, limited research has addressed the effective quantification of uncertainty when target labels are ambiguous. In retail, actual sales can be capped by stock and boosted by temporary promotions, whereas the target is underlying demand. Such scenarios are characterized by double censoring and no deep-learning pipeline yet exists for such data. In this paper, we introduce a straightforward framework for learning quantiles from doubly-censored observations and propose a tailored evaluation metric. Our approach is supported by theoretical guarantees, and we empirically demonstrate that our metric correlates well with the oracle calibration measure. Experimental results show that our estimator surpasses existing baselines. Finally, inventory simulations and real-world applications confirm the practical utility of our method in retail operations.

Figures & tables

Figure 2. The illustration of re-weighting strategy.

Metrics	Kendall’s $\tau$	Spearman’s $\rho$
ECE	$-0.220^{**}$	$-0.262^{**}$
D-Calibration	$0.327^{**}$	$0.414^{**}$
ECE-uncensored	$0.486^{**}$	$0.597^{**}$
Ext. D-Calibration	0.740	0.842

Table 1. Performance comparison of calibration metrics.

{}^{**}(p<0.01)

(WSR vs Ext. D-Calibration).

Model	Extended D-Calibration	Oracle Calibration	Sharpness	Real CRPS
Excl. Censor	0.154 ⋆ ⋆	0.492 ⋆ ⋆	8.646	$0.093^{\star\star}$
LogNorm	$0.832^{\star\star}$	$1.761^{\star\star}$	12.101	$0.164^{\star\star}$
CQRNN	$0.293^{\star\star}$	$0.585^{\star\star}$	9 .039	$0.114^{\star\star}$
S-CRPS	$0.189^{\star\star}$	$0.513^{\star\star}$	9.296	0.092 ⋆ ⋆
DPE (Our Method)	0.086	0.486	11.218	0.086

Table 2. Performance metrics for different survival methods. Bold = best; u nderline = runner-up;

{}^{\star}p<0.05

{}^{\star\star}p<0.01

vs DPE (WSR, except Sharpness).

Dataset	Youxuan		Maicai
Metrics	Extended D-Calibration	Sharpness	Extended D-Calibration	Sharpness
Excl. censor	0.049	7 6.72	0.17	9.82
LogNorm	0.039	107.96	0.14	10.8
S-CRPS	0.045	77.54	0.13	11.67
CQRNN	0.042	77.67	0 .07	10.45
DPE	0 .040	76.4	0.05	1 0.3

Table 3. Calibration and sharpness comparison (lower is better).

Uncertainty Quantification

Uncertainty quantification estimates how reliable predictions and scientific inferences are, and how uncertainty propagates into decisions.

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Jul 14, 2026J/K move · Enter open · S save

Learning-based Probabilistic Load Forecasting with Post-hoc and In-model Uncertainty

Sarah Al-Shareeda, Gulcihan Ozdemir, Heung Seok Jeon

aComputer System and Technology Department, Faculty of Computer Science and Information Technology, University of Malaya, Malaysia · bInformatics Institute, Istanbul Technical University, Turkey · cComputer Engineering Department Konkuk University South Korea

Quantile Regression Time Series Forecasting Probabilistic Forecasting Electricity Load Forecasting Uncertainty Calibration Probabilistic Time Series Forecasting

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Smart-building load forecasters are often trained offline on dense, multivariate, high-frequency data, but deployment may provide only hourly, feature-limited inputs. Missing features must then be reconstructed, and their errors can propagate through the model. If this input uncertainty is not reflected, prediction intervals may become miscalibrated, affecting demand-response scheduling. Our work examines where uncertainty should be placed once inference inputs are reconstructed. We develop a unified one-day-ahead probabilistic forecasting framework that aligns temporal resolution, reconstructs the unavailable inputs, and derives causal features, and we compare a modular post-hoc residual-quantile scheme with an integrated in-model quantile-learning scheme. The comparison uses three mid-scale Deep Learning (DL) backbones: recurrent, hybrid recurrent, and attention-based Temporal Fusion Transformer (TFT) models, under identical inputs, forecasting horizon, preprocessing rules, and training budgets. Results show that uncertainty placement is backbone-dependent. Integrated quantile learning is most reliable with the TFT, yielding 2.2-3.6% MAPE and 28-83W RMSE on the labeled test window, while producing intervals about 5x narrower than the modular intervals at the closest-to-nominal coverage level. Diebold-Mariano tests support the TFT ranking and the mixed behavior of the recurrent backbones. A reconstruction-sensitivity test shows that reconstructed inputs increase the Quantile Score (QS) by 106% while interval width remains nearly unchanged, indicating that the model does not automatically absorb reconstruction-induced uncertainty. Robustness checks against non-DL baselines and seasonal hold-out weeks support this ranking. Our results expose the limits of post-hoc residual quantiles when inference depends on reconstructed inputs.

Abstract

Uncertainty Quantification

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