Course description: Matrices are a popular way to model data (e.g., term-document data, people-SNP data, social network data, machine learning kernels, and so on), but the size-scale, noise properties, and diversity of modern data presents serious challenges for many traditional deterministic matrix algorithms. The course will cover the theory and practice of randomized algorithms for large-scale matrix problems arising in modern massive data set analysis (i.e., Randomized Numerical Linear Algebra). Topics to be covered include: underlying theory, including the Johnson-Lindenstrauss lemma, random sampling and projection algorithms, and connections between representative problems such as matrix multiplication, least-squares regression, least-absolute deviations regression, low-rank matrix approximation, etc.; numerical and computational issues that arise in practice in implementing algorithms in different computational environments; machine learning and statistical issues, as they arise in modern large-scale data applications; and extensions/connections to related problems as well as recent work that builds on the basic methods. Appropriate for advanced graduate students in computer science, statistics, and mathematics, as well as computationally-inclined students from application domains.
Prerequisites: General mathematical sophistication; and a solid understanding of Algorithms, Linear Algebra, and Probability Theory, at the advanced undergraduate or beginning graduate level, or equivalent.
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