Document Type
Dissertation - Open Access
Award Date
2026
Degree Name
Doctor of Philosophy (PhD)
Department / School
Mathematics and Statistics
First Advisor
Semhar Michael
Abstract
A class of problems in statistical pattern recognition exists in which there is high-dimensional data with few realizations per class, commonly referred to as few-shot learning. Data that arises in forensic source identification, which deals with providing a probabilistic value of evidence with regard to the source of some object, falls into this class of problems. Namely, the data is sampled from a hierarchical sampling process, lives in a high-dimensional space, the number of sources (or classes) tends towards infinity, and there are few observations per source. This can be thought of as a few-shot learning problem. Because of these properties, many current methods rely on normality assumptions and shared covariance matrices across classes. In reality, subpopulation structures and more complex distributions often exist, and failing to account for this complexity can lead to misleading results, especially in forensic source identification problems. The aim of this dissertation is to loosen these assumptions at various points in the hierarchical sampling process by introducing novel methods, namely finite mixture models, and studying their properties through Monte Carlo simulations, real-data analysis, and theoretical foundations. This is done by modeling subpopulations that exist between sources, within sources, and in situations where the subpopulations we wish to find are the distributions of the sources themselves. Furthermore, a generalization is proposed that enables the rapid implementation and testing of a class of models for modeling subpopulations, performing classification, and density estimation, and that also extends to applications and models beyond this dissertation to cover a wide breadth of literature in model-base clustering and classification.
Publisher
South Dakota State University
Recommended Citation
Simpson, Andrew, "Detecting and Characterizing Latent Subpopulations of Classes via Mixture Models" (2026). Electronic Theses and Dissertations. 2171.
https://openprairie.sdstate.edu/etd2/2171
Rights Statement
