Subsampled Randomized Hadamard Transform for Regression of Dynamic Graphs

A well-known problem in data science and machine learning is linear regression, which is recently extended to dynamic graphs. Existing exact algorithms for updating solutions of dynamic graph regression require at least a linear time (in terms of n: the number of nodes of the graph). However, this time complexity might be intractable in practice. In this paper, we utilize subsampled randomized Hadamard transform to propose a randomized algorithm for dynamic graphs. Suppose that we are given an nxm matrix embedding M of the graph, where m ⇐ n. Let r be the number of samples required for a guaranteed approximation error, which is a sublinear function of n. After an edge insertion or an edge deletion in the graph, our algorithm updates the approximate solution in O(rm) time.