[Colloquium] Ryan Robinett MS Presentation/Jun 8, 2022

[Megan Woodward]

This is an announcement of Ryan Robinett's MS Presentation
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Candidate: Ryan Robinett

Date: Wednesday, June 08, 2022

Time: 12 pm CST

Location: JCL 390

M.S. Paper Title: Manifold learning, Riemannian optimization, and their implications for the analysis of single-cell RNA-sequencing data

Abstract: The fundamental goal of dimensionality reduction is to create a lower dimensional representation of data that avoids either diminishing features intrinsic to the data or artificially generating features that are not intrinsic to the data. It has been established that, given points sampled uniformly from simulated manifolds, where ground-truth topology and metric information are known, common dimensionality reduction methods impose both hazards. This is particularly problematic for the analysis of single-cell RNA-sequencing data, which is increasingly relied upon for biological discovery. For a random variable generating the data, topological and metric information are, in principle, completely captured by a probability measure with support over a manifold M in Rn. Here we give an overview of topological, differentiable, and Riemannian manifolds from a theoretical standpoint. We highlight recent findings in manifold learning, applications in single-cell transcriptomic analysis, and implications for the future of manifold learning. We lastly present a data structure that can be learned from point cloud data that is amenable to Riemannian optimization techniques.

Advisors: Lorenzo Orecchia

Committee Members: Lorenzo Orecchia, Rebecca Willett, and Samantha Riesenfeld