September 29, 2022
Title: Sharp estimates on random hyperplane tessellations (applied MI-talk)
Speaker: Sjoerd Dirksen
In my talk I will consider the following question. Draw independent random hyperplanes with standard Gaussian directions and uniformly distributed shifts. How many hyperplanes are needed to tessellate a given subset of R^n into uniformly small cells of a given diameter with high probability?
I will first explain two motivating applications for this question: data dimension reduction and signal processing under coarse quantization. I will then present a generally optimal answer to the posed question, which surprisingly deviates from the answer that was conjectured in the literature. If time permits, I will show an extension of this result to a specific structured random tessellation that is designed for computationally fast data dimension reduction.
The talk is based on a recently accepted paper with Shahar Mendelson (ANU Canberra) and Alexander Stollenwerk (UCLouvain).