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Latent Variable ModelsExplores latent variable models, EM algorithm, and Jensen's inequality in statistical modeling.
Replica and Symmetry BreakingExplores the Nobel Prize-winning discovery of replica and cavity methods in complex systems, focusing on the random energy model and the application of probability theory.
Large Deviations PrincipleExplores the Large Deviations Principle, focusing on exponential tail decay and Laplace transform analysis.
Advanced ProbabilityDelves into advanced probability theory, covering inequalities, trials, distributions, and calculations for probabilities and expectations.
Convergence in ProbabilityExplores convergence in probability, concentration inequalities, laws of large numbers, and properties of distributions.