Scalable Bayesian Inference for Interpretable Time-Series Models

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From healthcare to retail, from governments to education, we are collecting and storing data. These data sources provide unprecedented opportunities: healthcare data stores, originally collected for billing purposes, can be mined to better understand diseases and improve treatments; government data stores, originally collected for reporting purposes, can be mined to improve national welfare and security; retail data stores, originally collected for accounting purposes, can be used to detect complex fraud and improve the customer experience. In particular, these large data stores allow us to understand the patterns of patients, customers, citizens, and students over time. Probabilistic models for time-series analysis can recover patterns such as disease trajectories and purchasing needs. However, using these data to better understand these patterns---generally collected and stored for other purposes---is challenging for several reasons. These data are typically stored in standard relational databases and subject to complex security protections. They are also often biased and incomplete; one can use them to discover interesting patterns but the results must be used with caution. This proposal makes steps toward addressing these core problems. In particular, we propose to create methods for analyzing time-series that can run efficiently on existing data management architectures and provide interpretable results that can be vetted by a domain expert for accuracy. We apply these approaches to understanding disease progression in diabetes and psychiatric diseases through the analysis of electronic health records. From a technical point of view, this work focuses on a particular probabilistic time-series model, the Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM). Inference in this model is typically performed in a numerical computing environment using Markov Chain Monte Carlo (MCMC). The first part of our work involves adapting the MCMC steps so that they can be run efficiently with a traditional database architectures. Specifically, we will develop methods that do not require the data to be removed from the database by splitting the inference into computations that operate directly on the data---to be performed within the database---and computations that operate on derived statistics---to be performed in a numerical computing environment. The second part of our work involves making models learned from sparse, high-dimensional data more interpretable. Here we will leverage the fact that while these data stores are typically high-dimensional (tens of thousands of dimensions), these dimensions are not all independent; in fact, in most real applications there exists knowledge about how these data are structured. We will apply these knowledge bases to create sparse models that are easier for domain experts to interpret. While we focus on our healthcare application for this work, these techniques are relevant to a variety of applications involving time-series with high-dimensional, sparsely sampled data.