Before revision:  In this work, we present an application of randomized numerical linear algebra to fitting the CP decomposition of sparse tensors, solving a significantly smaller sampled least squares problem at each iteration with probabilistic guarantees on the approximation errors.
After revision:  In this work, we present an application of randomized numerical linear algebra to fitting the CP decomposition of sparse tensors, we propose sketching each subproblem using leverage scores to select a subset of the rows, with probabilistic guarantees on the approximation errors.