Inference in Randomized Least Squares and PCA via Normality of Quadratic Forms

arXiv:2404.00912v1 Announce Type: cross
Abstract: Randomized algorithms can be used to speed up the analysis of large datasets. In this paper, we develop a unified methodology for statistical inference via randomized sketching or projections in two of the most fundamental problems in multivariate statistical analysis: least squares and PCA. The methodology applies to fixed datasets -- i.e., is data-conditional -- and the only randomness is due to the randomized algorithm. We propose statistical inference methods for a broad range of …

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