CS 6241

News

2023-09-12: The reaction paper (due 10/3) and project proposal (due 10/17) prompts are posted.

2023-08-16: Welcome to CS 6241!

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Overview

In this class, we treat numerical methods underlying a variety of modern machine learning and data analysis techniques. The course consists of six units of roughly two weeks each:

• Least squares and regression: direct and iterative linear and nonlinear least squares solvers; direct randomized approximations and preconditioning; Newton, Gauss-Newton, and IRLS methods for nonlinear problems; regularization; robust regression.
• Matrix and tensor data decompositions: direct methods, iterations, and randomized approximations for SVD and related decomposition methods; nonlinear dimensionality reduction; non-negative matrix factorization; tensor decompositions.
• Low-dimensional structure in function approximation: active subspace / sloppy model approaches to identifying the most relevant parameters in high-dimensional input spaces and model reduction approaches to identifying low-dimensional structure in high-dimensional output spaces.
• Kernel interpolation and Gaussian processes: statistical and deterministic interpretations and error analysis for kernel interpolation; methods for dealing with ill-conditioned kernel systems; and methods for scalable inference and kernel hyper-parameter learning.
• Numerical methods for graph data: implication of different graph structures for linear solvers; graph-based coordinate embedding methods; analysis methods based on matrix functions; computation of centrality measures; and spectral methods for graph partitioning and clustering.
• Learning models of dynamics: system identification and auto-regressive model fitting; Koopman theory; dynamic mode decomposition.

See the syllabus for more information on course logistics.