2019-05-21: Welcome to the class!Older news »
This is a survey course on numerical methods prominent in modern data analysis and machine learning. Building on basic methods of optimization and numerical linear algebra, the course will explore the role of numerical methods for treating several classes of data analysis problems, including low rank factorizations and completion of matrix data; function approximation by kernel methods; and analysis of data on graphs.
- Optimization basics: gradient descent and SGD, Newton-like, and alternating iterations; building with linear and nonlinear least squares.
- Matrix data and latent factor models: direct methods, iterations, and randomized approximations for SVD and related decomposition methods; non-negative matrix factorization; matrix completion.
- Function approximation: some basic approximation theory; statistical and deterministic interpretations and error analysis for kernel interpolation; methods for scalable kernel inference.
- Numerical methods for graph data: adjacency, Laplacian, and other graph matrices; function interpolation on graphs; spectral clustering and graph partitioning; centrality measures.
See the syllabus for more information on course logistics.