Leveraging Neural Autoregressive Distribution Estimators (NADE) for Retail Demand Forecasting

Abstract

Currently, the challenge of accurately predicting customer demand in retail is an important problem in the field of supply chain management, and even a small increase in the accuracy of prediction can lead to significant cost savings and improvements in customer satisfaction. The traditional statistical methods like ARIMA and exponential smoothing have been widely used in the industry for some time now, but come with some limitations, particularly in accounting for the complex and non-linear nature of temporal relationships and multivariate interactions. This has led to the use of deep learning alternatives. This paper presents a novel approach using Neural Autoregressive Distribution Estimators (NADE) to handle the probabilistic retail demand forecasting problem, overcoming the gap between point-estimate and full distributional inference approaches. The proposed NADE-based model aims to estimate the joint probability distribution over future demand sequences, which is approached here by breaking the multivariate distribution into conditionals, allowing for quantifying uncertainty as well as point predictions. The architecture combines the spatial Graph Neural Network (GNN) layers to model inter-product relational dependency, which is a key requirement in the retail basket context, and an autoregressive decoder to generate sequential demands. Two benchmark retail datasets were used for experimental evaluation: the M5 Forecasting Competition dataset and the Kaggle Walmart Sales dataset. For experimental evaluation, two benchmark retail datasets have been taken: The M5 Forecasting Competition dataset with 42,840 SKUs in 10 stores across 1,913 days and the dataset of Walmart Sales from the Kaggle website. The results indicate that the proposed NADE-GNN hybrid has a Mean Absolute Percentage Error (MAPE) of 8.43%, a Root Mean Square Error (RMSE) of 12.17, and a Continuous Ranked Probability Score (CRPS) of 0.094, achieving improvements of 27.3%, 17.4%, and 14.0%, respectively, over baseline models such as LSTM, Transformer, and N-BEATS. In the ablation study, the GNN spatial encoding yields an additional 6.2% MAPE improvement, and autoregressive conditioning yields another 4.1% improvement. It is realized with Python, PyTorch, and DGL, and hyperparameter optimization is done by grid search. The results show that NADE is a strong, uncertainty-aware foundation for retail demand forecasting in dynamic, high-SKU retail stores.