On Algorithms in High Dimensions

Explore advanced mathematical concepts in high-dimensional spaces through this 50-minute lecture by Gregory Beylkin from the University of Colorado Boulder. Delve into two key representations of multivariate functions and their associated algorithms that circumvent the "curse of dimensionality." Examine separated representations of functions and operators, their applications in multivariate regression and machine learning, and their connection to parallel factorization and canonical decomposition in statistics. Discover how these representations serve as a nonlinear method for tracking functions in high-dimensional spaces using minimal parameters. Investigate multivariate mixtures, a more generalized class of functions than separated representations, and learn about the corresponding reduction algorithm. Gain insights into the applications of these concepts in both numerical analysis and data science. Recorded on September 26, 2024, this talk is part of IPAM's Analyzing High-dimensional Traces of Intelligent Behavior Workshop at UCLA, offering a deep dive into cutting-edge mathematical approaches for handling complex, high-dimensional data.