  We show how to develop sampling-based alternating least squares (ALS)
algorithms for decomposition of tensors into any tensor network (TN) format.
Provided the TN format satisfies certain mild assumptions, resulting algorithms
will have input sublinear per-iteration cost. Unlike most previous works on
sampling-based ALS methods for tensor decomposition, the sampling in our
framework is done according to the exact leverage score distribution of the
design matrices in the ALS subproblems. We implement and test two tensor
decomposition algorithms that use our sampling framework in a feature
extraction experiment where we compare them against a number of other
decomposition algorithms.
