3.0

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Doctoral-level topics course on dimension reduction and manifold learning for subsequent statistical inference tasks, with applications to current research and open problems in hypothesis testing, network analysis, and large language models. Topics include estimation and information tests for multinomial distributions and random graphs with latent positions on an unknown manifold; asymptotic properties of spectral embeddings and multidimensional scaling; and convergence of shortest path distances to Riemannian distances. Encompasses a wide range of material from statistics, graph theory, matrix analysis, functional analysis, and differential geometry. Though course is self contained, strong background in mathematics is recommended for exploration of specific research directions at the intersection of manifold learning and statistics.