Co-Occuring Directions Sketching for Approximate Matrix Multiply
Youssef Mroueh, Etienne Marcheret, Vaibhava Goel

TL;DR
This paper presents a deterministic co-occurring directions sketching algorithm for approximate matrix multiplication that achieves better error bounds and low-rank approximation accuracy than existing methods, validated through empirical experiments.
Contribution
Introduction of a novel deterministic co-occurring directions algorithm for AMM with improved error bounds and empirical performance.
Findings
Achieves a $1 + \\epsilon$ approximation of the optimal low-rank matrix product.
Outperforms existing randomized and deterministic methods in experiments.
Validated theoretical error bounds with empirical results.
Abstract
We introduce co-occurring directions sketching, a deterministic algorithm for approximate matrix product (AMM), in the streaming model. We show that co-occuring directions achieves a better error bound for AMM than other randomized and deterministic approaches for AMM. Co-occurring directions gives a -approximation of the optimal low rank approximation of a matrix product. Empirically our algorithm outperforms competing methods for AMM, for a small sketch size. We validate empirically our theoretical findings and algorithms
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Taxonomy
TopicsStochastic Gradient Optimization Techniques · Sparse and Compressive Sensing Techniques · Complexity and Algorithms in Graphs
