Hierarchical time-series forecasting (HTSF) is an important problem for many real-world business applications where the goal is to simultaneously forecast multiple time-series that are related to each other via a hierarchical relation. Recent works, however, do not address two important challenges that are typically observed in many demand forecasting applications at large companies. First, many time-series at lower levels of the hierarchy have high sparsity i.e., they have a significant number of zeros. Most HTSF methods do not address this varying sparsity across the hierarchy. Further, they do not scale well to the large size of the real-world hierarchy typically unseen in benchmarks used in literature. We resolve both these challenges by proposing HAILS, a novel probabilistic hierarchical model that enables accurate and calibrated probabilistic forecasts across the hierarchy by adaptively modeling sparse and dense time-series with different distributional assumptions and reconciling them to adhere to hierarchical constraints. We show the scalability and effectiveness of our methods by evaluating them against real-world demand forecasting datasets. We deploy HAILS at a large chemical manufacturing company for a product demand forecasting application with over ten thousand products and observe a significant 8.5\% improvement in forecast accuracy and 23% better improvement for sparse time-series. The enhanced accuracy and scalability make HAILS a valuable tool for improved business planning and customer experience.

Within the academic and professional auditing communities, there has been growing concern about how to accurately assess the various risks associated with performing an audit. These risks are difficult to conceptualize in terms of numeric estimates.

Within the academic and professional auditing communities, there has been growing concern about how to accurately assess the various risks associated with performing an audit. These risks are difficult to conceptualize in terms of numeric estimates. This article discusses the development of a prototype computational model (computer program) that assesses one of the major audit risks -- inherent risk. This program bases most of its inferencing activities on a qualitative model of a typical business enterprise.