2022/08/12 by Fengnan Gao, Tengyao Wang, Gao, Fengnan +1
Biochemistry, Genetics and Molecular Biology · Mathematics · #62J05 #62M10 #FOS: Computer and information sciences #FOS: Mathematics #Gene expression and cancer classification #Methodology (stat.ME) #Single-cell and spatial transcriptomics #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2208.06326
openalex publication_date 2022/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a new methodology 'charcoal' for estimating the location of sparse changes in high-dimensional linear regression coefficients, without assuming that those coefficients are individually sparse. The procedure works by constructing different sketches (projections) of the design matrix at each time point, where consecutive projection matrices differ in sign in exactly one column. The sequence of sketched design matrices is then compared against a single sketched response vector to form a sequence of test statistics whose behaviour shows a surprising link to the well-known CUSUM statistics of univariate changepoint analysis. The procedure is computationally attractive, and strong theoretical guarantees are derived for its estimation accuracy. Simulations confirm that our methods perform well in extensive settings, and a real-world application to a large single-cell RNA sequencing dataset showcases the practical relevance.