Sublinear update time randomized algorithms for dynamic graph regression

A well-known problem in data science and machine learning is linear regression, which recently extended to dynamic graphs. Existing exact algorithms for updating the solution of graph regression require at least a time (in terms n: size graph). However, this complexity might be intractable practice. In current paper, we utilize subsampled randomized Hadamard transformand CountSketchto propose first sublinear update general Suppose that are given n×d matrix embedding M graph, where d≪n has certain properties. Let r number samples required by transform 1±ϵ approximation, n. Our algorithm supports edge insertion deletion updates approximate O(rd) time. second based on CountSketchand insertion, deletion, node deletion. It O(qd) time, q=O(d2ϵ2log6(d/ϵ)).