Content area
Probability theory and probabilistic algorithms form the fundamental bedrock of modern data science and machine learning. These mathematical frameworks provide essential tools for tackling contemporary data challenges, notably high dimensionality and intricate dependency structures among data points. This thesis investigates three distinct yet interconnected probabilistic problems. The first addresses dimensionality reduction through the lens of generalized t-SNE. The second confronts complex dependencies by exploring Markov Random Fields in conjunction with the Lovász Local Lemma. Finally, the third problem synthesizes challenges of both dimensionality and dependency via Variational Factor Analysis. To ensure accessibility for a broader audience, an introductory chapter will provide requisite background knowledge on these core concepts and their interplay.
