Hierarchical Time Series Modeling with Business and Audio Applications

Abstract

Hierarchical structure in data naturally occurs in many settings, especially in problems in business forecasting and audio modeling. For example, in retail demand data, there is often a hierarchy of product information, such as items, sub-categories and categories. In audio modeling, commonly used data representations, both from deep modeling and signal processing perspectives, represent complex audio information in a hierarchical manner. Leveraging this structure in the data via hierarchical modeling leads to several advantages, from both a statistical and an application perspective. Hierarchical models are often more interpretable in context if the structure of the model matches the hierarchical structure of the data. Additionally, utilizing hierarchical modeling often improves predictions and forecasts. These predictive gains with hierarchical models are often possible with relatively simple models, without needing to resort to large, complex multivariate models that less explicitly consider the structure of the problem. In this dissertation, we develop new classes of hierarchical models motivated by - and applied to - problems arising in business forecasting and audio applications. Our models and methods address challenges shared by many domains, such as utilizing aggregate information to improve forecasts of sparse, noisy, heterogeneous data. In general, we are interested in probabilistic, interpretable, computationally efficient models that utilize the structure in the data, making (Bayesian) hierarchical models a natural choice. We apply hierarchical multi-scale models in the business domain to personalized forecasting of item purchases by individual households and enterprise-wide revenue forecasts for groups of stores and categories for a large grocery chain. In the audio domain, hierarchical models are used to explore systematic differences between performance styles of various orchestras and as a backbone of a general methodology to explore deep audio features in the context of hand-crafted, application-meaningful features. Overall, the main result of this dissertation is that utilizing hierarchical structure in data can improve predictions and interpretation across many application areas.