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.Older news »
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.