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Abstract:
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Experimental design is one of the fundamental contributions statisticians made to the society. It has led to major advances in science and engineering. Given the enormous success of experimental design in the past, it is imperative for statisticians to think how to best utilize this thinking in the Big Data era. Data with massive sample size and/or high dimensionality appear in observations, physical or simulation experiments, digital engineering, and many other sources. This work is motivated by the increasing need of subsampling a Hadamard matrix in statistical analysis methods as varied as compressed sensing, leverage score subsampling and matrix completion. The current solution to this problem, which randomly takes a subsample from a Hadamard matrix, suffers from high variability and large coherence. In this talk, we will discuss an experimental design framework to exploit substructures with low coherence in Hadamard matrices to accelerate large-scale statistical analysis. The effectiveness of the proposed framework will be corroborated by theoretical results and illustrated with examples from compressed sensing.
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