CS 6241

Numerical Methods for Data Science

Location: Zoom
Lecture: TR 2:45-4:00
Discussion: Canvas
Course material: GitHub

Prof: David Bindel
Email: bindel@cornell.edu
OH: Mon 2:00-4:00, Fri 12:30-1:30 and 2:00-3:00, or by appt
Scheduler link


2021-03-15: Project proposal prompt is posted (due March 22).

2021-03-01: Reaction paper prompt is posted (due March 15).

2021-03-01: Office hours for today (March 1) are canceled.

2021-02-25: No class today or OH tomorrow, reaction paper guidelines to be posted before the weekend.

2021-02-18: Office hours for tomorrow (Feb 19) are 11:30-1:30.

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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.