Orthonormal Sketches for Secure Coded Regression

In this work, we propose a method for speeding up linear regression distributively, while ensuring security. We leverage randomized sketching techniques, and improve straggler resilience in asynchronous systems. Specifically, we apply a random orthonormal matrix and then subsample in textitblocks, to simultaneously secure the information and reduce the dimension of the regression problem. In our setup, the transformation corresponds to an encoded encryption in an textitapproximate gradient coding scheme, and the subsampling corresponds to the responses of the non-straggling workers; in a centralized coded computing network. We focus on the special case of the textitSubsampled Randomized Hadamard Transform, which we generalize to block sampling; and discuss how it can be used to secure the data. We illustrate the performance through numerical experiments.