2020/03/20 by Rakshith Sharma Srinivasa, Srinivasa, Rakshith S, Mark A. Davenport +3 · 2 citations
Computer Science · Engineering · #Complexity and Algorithms in Graphs #FOS: Computer and information sciences #FOS: Electrical engineering #Information Theory (cs.IT) #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Signal Processing (eess.SP) #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2003.09097
openalex publication_date 2020/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider sketched approximate matrix multiplication and ridge regression in the novel setting of localized sketching, where at any given point, only part of the data matrix is available. This corresponds to a block diagonal structure on the sketching matrix. We show that, under mild conditions, block diagonal sketching matrices require only O(stable rank / ε2) and O( stat. dim. ε) total sample complexity for matrix multiplication and ridge regression, respectively. This matches the state-of-the-art bounds that are obtained using global sketching matrices. The localized nature of sketching considered allows for different parts of the data matrix to be sketched independently and hence is more amenable to computation in distributed and streaming settings and results in a smaller memory and computational footprint.