Unsupervised Learning Approaches for Large-scale Data

Abstract

Unsupervised learning approaches have gained significant prominence in the field of statistics due to their ability to analyze and interpret complex, unstructured data without the need for labeled datasets. This dissertation primarily focuses on the areas of graphical models and clustering, highlighting both their theoretical foundations and practical applications. For graphical models, inspired by functional magnetic resonance imaging (fMRI) studies, we introduce a novel method for constructing brain connectivity networks with correlated replicates and unmeasured confounders. In fMRI studies, participants are scanned over time, and their mental states, such as being awake or asleep, can vary and are often unmeasurable. To address this, we model the correlation among replicates with a one-lag vector autoregressive model and account for latent effects from unmeasured confounders using a piecewise constant approach. For clustering, traditional methods often fall short in accurately capturing complex relationships within data, particularly when variables can belong to multiple clusters and when clustering structures change over time. In fMRI datasets, regions of interest (ROIs) may contribute to multiple brain functions, and the functions performed by each ROI can vary over time. To address these challenges, we emphasize advanced techniques that account for overlapping clusters and explore the dynamics of these clusters. By applying a latent variable factor model, we estimate time-varying overlapping clusters that can automatically match across different time points. Furthermore, we extend the overlapping clustering method to non-Gaussian data by employing generalized factor models within the clustering structure. This extension broadens the applicability of the clustering methods to a wider range of data types, particularly in fields such as genomics and finance, where non-Gaussian distributions are prevalent.