Approximate Weighted C R Coded Matrix Multiplication

Abstract

One of the most common operations in signal processing is matrix multiplication. However, it presents a major computational bottleneck when the matrix dimension is high, as can occur for large data size or feature dimension. Two different approaches to overcoming this bottleneck are: 1) low rank approximation of the matrix product; and 2) distributed computation. We propose a scheme that combines these two approaches. To enable distributed low rank approximation, we generalize the approximate matrix CR-multiplication to accommodate weighted block sampling, and we introduce a weighted coded matrix multiplication method. This results in novel approximate weighted CR coded matrix multiplication schemes, which achieve improved performance for distributed matrix multiplication and are robust to stragglers.