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Least squares regression on sparse grids

Presented by: 
Bastian Bohn
Friday 22nd February 2019 - 09:40 to 10:15
INI Seminar Room 1
In this talk, we first recapitulate the framework of least squares regression on certain sparse grid and hyperbolic cross spaces. The underlying numerical problem can be solved quite efficiently with state-of-the-art algorithms. Analyzing its stability and convergence properties, we can derive the optimal coupling between the number of necessary data samples and the degrees of freedom in the ansatz space.Our analysis is based on the assumption that the least-squares solution employs some kind of Sobolev regularity of dominating mixed smoothness, which is seldomly encountered for real-world applications. Therefore, we present possible extensions of the basic sparse grid least squares algorithm by introducing suitable a-priori data transformations in the second part of the talk. These are tailored such that the resulting transformed problem suits the sparse grid structure.

Co-authors: Michael Griebel (University of Bonn), Jens Oettershagen (University of Bonn), Christian Rieger (University of Bonn)
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons