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. Prior work has shown that sketching is effective in the dense case, but the prior approach cannot be applied to the sparse case because a fast Johnson-Lindenstrauss transform (e.g., using a fast Fourier transform) must be applied in each mode, causing the sparse tensor to become dense. Instead, we perform sketching through leverage score sampling, crucially relying on the fact that the structure of the Khatri-Rao product allows sampling from overestimates of the leverage scores without forming the full product or the corresponding probabilities.
After 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 of the solution accuracy. We randomly sample rows proportional to leverage score upper bounds that can be efficiently computed using the special Khatri-Rao product allows sampling from overestimates of the leverage scores without forming the full product or the corresponding probabilities.