[Paper Review] Improving Sales Forecasting Accuracy: A Tensor Factorization Approach with Demand Awareness

Xuan Bi, Gediminas Adomavičius+2 more|arXiv (Cornell University)|Nov 6, 2020

Recommender Systems and Techniques97 references4 citations

TL;DR

This paper proposes ATLAS, a tensor factorization approach that improves sales forecasting accuracy by modeling demand dynamics across stores and products using a regularized CPD framework. By integrating temporal patterns via SARIMA and LSTM models, ATLAS achieves significant accuracy gains—especially in sparse data scenarios—demonstrated across eight IRI grocery datasets with over 165 million transactions.

ABSTRACT

Due to accessible big data collections from consumers, products, and stores, advanced sales forecasting capabilities have drawn great attention from many companies especially in the retail business because of its importance in decision making. Improvement of the forecasting accuracy, even by a small percentage, may have a substantial impact on companies' production and financial planning, marketing strategies, inventory controls, supply chain management, and eventually stock prices. Specifically, our research goal is to forecast the sales of each product in each store in the near future. Motivated by tensor factorization methodologies for personalized context-aware recommender systems, we propose a novel approach called the Advanced Temporal Latent-factor Approach to Sales forecasting (ATLAS), which achieves accurate and individualized prediction for sales by building a single tensor-factorization model across multiple stores and products. Our contribution is a combination of: tensor framework (to leverage information across stores and products), a new regularization function (to incorporate demand dynamics), and extrapolation of tensor into future time periods using state-of-the-art statistical (seasonal auto-regressive integrated moving-average models) and machine-learning (recurrent neural networks) models. The advantages of ATLAS are demonstrated on eight product category datasets collected by the Information Resource, Inc., where a total of 165 million weekly sales transactions from more than 1,500 grocery stores over 15,560 products are analyzed.

Motivation & Objective

• Improve sales forecasting accuracy in retail by leveraging collaborative information across stores and products.
• Address the challenge of sparse historical sales data for specific store-product combinations through collaborative modeling.
• Incorporate dynamic consumer demand patterns into forecasting to reflect competitive interactions between stores and products.
• Develop a scalable, unified framework that generalizes across multiple product categories and time periods.
• Enable forward-looking predictions using hybrid statistical and deep learning methods for extrapolating tensor factorizations into future time periods.

Proposed method

• Formulate sales data as a 3D tensor with modes: store, product, and time, enabling multi-way decomposition.
• Apply Canonical Polyadic Decomposition (CPD) to extract low-rank latent factors representing store, product, and temporal patterns.
• Introduce a novel demand-aware regularization term based on local consumer demand dynamics, modeled as a covariance matrix of sales across nearby stores.
• Integrate state-of-the-art time series models—SARIMA and LSTM—into the tensor framework to extrapolate future sales from learned latent factors.
• Optimize the regularized tensor decomposition using an alternating least squares algorithm with convergence guarantees.
• Use a hybrid modeling strategy: train CPD on historical data, then apply SARIMA/LSTM to forecast future time slices based on learned components.

Experimental results

Research questions

• RQ1 Can a unified tensor factorization model improve sales forecasting accuracy across multiple stores and products compared to standard collaborative filtering methods?
• RQ2 How does incorporating demand dynamics—modeled as inter-store sales correlations—enhance forecasting performance, especially in low-data regimes?
• RQ3 To what extent do hybrid time series models (SARIMA and LSTM) improve extrapolation accuracy when combined with tensor decomposition?
• RQ4 How does ATLAS perform relative to baseline methods (e.g., BPTF, TRMF, CPD) across diverse product categories with varying data sparsity?
• RQ5 What is the impact of demand-aware regularization on model generalization and robustness in real-world retail datasets?

Key findings

• ATLAS significantly improves forecasting accuracy across all eight product categories in the IRI dataset, outperforming baseline methods including BPTF, TRMF, and CPD.
• The model achieves the lowest mean absolute scaled error (MASE) in all categories, with improvements ranging from 5% to over 20% relative to state-of-the-art baselines.
• Incorporating demand-aware regularization leads to a measurable reduction in forecasting error, particularly in sparse data scenarios where collaborative signal is critical.
• The hybrid use of SARIMA and LSTM for time-series extrapolation enhances future prediction accuracy, with LSTM showing stronger performance on long-horizon forecasts.
• Computational efficiency is maintained: ATLAS runs in 1.83 hours on the frozen pizza dataset and 0.81 hours on the toothpaste dataset, outperforming SARIMA (28.07 and 18.49 hours) and approaching the speed of simpler models like CPD and BPTF.
• The model demonstrates robustness across diverse product categories, indicating broad applicability in real-world retail forecasting settings.