2020/06/23 by Vivek F. Farias, Farias, Vivek F., Andrew A. Li +3
Computer Science · Decision Sciences · Medicine · #Advanced Statistical Process Monitoring #Anomaly Detection Techniques and Applications #Data-Driven Disease Surveillance #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML)
paper · pdf · doi:10.48550/arxiv.2006.13126
openalex publication_date 2020/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Inaccurate records of inventory occur frequently, and by some measures cost retailers approximately 4% in annual sales. Detecting inventory inaccuracies manually is cost-prohibitive, and existing algorithmic solutions rely almost exclusively on learning from longitudinal data, which is insufficient in the dynamic environment induced by modern retail operations. Instead, we propose a solution based on cross-sectional data over stores and SKUs, observing that detecting inventory inaccuracies can be viewed as a problem of identifying anomalies in a (low-rank) Poisson matrix. State-of-the-art approaches to anomaly detection in low-rank matrices apparently fall short. Specifically, from a theoretical perspective, recovery guarantees for these approaches require that non-anomalous entries be observed with vanishingly small noise (which is not the case in our problem, and indeed in many applications). So motivated, we propose a conceptually simple entry-wise approach to anomaly detection in low-rank Poisson matrices. Our approach accommodates a general class of probabilistic anomaly models. We show that the cost incurred by our algorithm approaches that of an optimal algorithm at a min-max optimal rate. Using synthetic data and real data from a consumer goods retailer, we show that our approach provides up to a 10x cost reduction over incumbent approaches to anomaly detection. Along the way, we build on recent work that seeks entry-wise error guarantees for matrix completion, establishing such guarantees for sub-exponential matrices, a result of independent interest.