Title: Generalized t-SNE and Beyond: Probabilistic Methods for Dimensionality Reduction, Combinatorial Optimization, and Machine Learning
Abstract: 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. In my defense, we will go through three distinct yet in-terconnected 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 Lov ́asz 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 introduction will be provided related requisite background knowledge on these core concepts and their interplay.