Presented by Zuofu Huang
Ph.D. Candidate in Biostatistics
Ph.D. Adviser: Dr. Julian Wolfson

The widespread collection of data from mobile and wearable devices has created unprecedented opportunities to study human behavior at fine temporal resolution. One common structure for such data is categorical sequences—ordered, multinomial observations across many time points. These sequences present unique statistical challenges due to their high dimensionality and complex short- and long-term temporal dependence. The goal of this thesis is to further develop statistical tools motivated by real-world questions on such categorical sequences. We begin by addressing the problem of synthesizing sequential categorical data. The ability to synthesize realistic data in a parametrizable way is valuable for a number of reasons, including privacy, missing data imputation, and evaluating the performance of statistical and computational methods. We propose the paired Markov Chain (paired-MC) method, a flexible framework that produces sequences that closely mimic real data while providing a straightforward mechanism for modifying characteristics of the synthesized sequences. Next, we aim to develop and evaluate approaches to identifying “key” sequence positions which distinguish sequence types. We frame this challenge as a regression problem and introduce a variety of regularization techniques that could be applied to achieve interpretable dimension reduction. Finally, we consider prediction tasks arising in settings such as online prediction, where only partially observed categorical sequences are available and the goal is to infer behavior in the unobserved portion of the sequence. In this work, prediction tasks in categorical sequences are framed from a missing-data perspective and addressed through sequence synthesis. This perspective allows both time-point and structural prediction tasks to be handled within a common framework while naturally incorporating uncertainty through repeated synthesis.