Numerical Algorithms for Machine Learning

Catalog description

An introduction to numerical algorithms that pertain to important problems in machine learning, data science, and artificial intelligence, organized into four modules: 1) Basic topics in numerical analysis, floating point computation, rounding, conditioning, and stability. Numerical solution of equations, curve fitting, and polynomial interpolation with example applications in machine learning. 2) Numerical linear algebra in the context of data science and artificial intelligence, sparse matrix operations, solutions to linear systems, least-squares systems, regularization, linear regression, eigen-decompositions and their relation to dimensionality reduction. Singular value decomposition, non-linear matrix factorization, matrix completion, with applications to recommendation systems and link prediction. Iterative methods for solving linear systems, application of matrix computations in information retrieval and machine learning. 3) Optimization for training machine learning algorithms, duality, convexity, non-linear regression, gradient decent, training of neural networks, back-propagation, stochastic gradient descent, regularization, variance reduction. 4) Graphs and spectral analysis in graph machine learning, graph Laplacian, eigenvalues of a graph, random walks and graph convolution, graph embedding, spectral filters. Offered as CSDS 323 and CSDS 423 . Prereq: Graduate Student standing.