[CS] Ryan Robinett Candidacy Exam/Apr 21, 2025

[via cs]

This is an announcement of Ryan Robinett's Candidacy Exam.
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Candidate: Ryan Robinett

Date: Monday, April 21, 2025

Time: 10 am CST

Remote Location: https://uchicago.zoom.us/j/4175248751?pwd=akZlcjhzM292MDJiN25Tc0ZWQ1g0UT09&omn=93290424400 Meeting ID: 417 524 8751 Passcode: 102991

Title: Novel computational and geometric frameworks for manifold learning, Riemannian optimization, and feature selection

Abstract: In machine learning, Riemannian manifolds offer a useful abstraction for approximating commonly encountered, non-Euclidean empirical data distributions and optimization state spaces. While Euclidean machine learning algorithms have been adapted to Riemannian manifolds, these adaptations rely on computationally intensive differential-geometric primitives, such as exponential maps and parallel transports. In this talk, we present a framework for efficiently approximating differential-geometric primitives on arbitrary manifolds via construction of an atlas graph representation, which leverages the canonical characterization of a manifold as a finite collection, or atlas, of overlapping coordinate charts. To demonstrate the utility of this approach, we first construct an atlas graph encoding of Carlsson’s space of natural image patches that preserves homology groups, pairwise geodesic distances, and intrinsic dimensionality, and scalar curvature. We then demonstrate that the learned atlas graph enables the computation of differential-geometric primitives pointwise, allowing us to perform the Riemannian principal boundary algorithm—a Riemannian-geometric generalization of the support vector machine—on the learned representation. To investigate the utility of the atlas graph framework in exploratory data analysis, we also construct local coordinate charts in the boundary of the 2-Wasserstein manifold over the Euclidean hypercube and demonstrate how morphological variation in wings of Drosophila melanogaster, both within and between strains, can be quantified as low-dimensional vector bundles over this manifold. Lastly, we use information theory to reframe the problem of feature selection as a simultaneous optimization over two separate coordinate charts with different Riemannian metrics. This framework is discussed in the context of leveraging quantum computing to perform feature selection in cancer data for improving clinical decisionmaking.

Advisor: Lorenzo Orecchia, Samantha J. Riesenfeld

Committee Members: Samantha J. Riesenfeld, Lorenzo Orecchia, Shmuel Weinberger, & Fred Chong