  We propose a sampling-based method for computing the tensor ring (TR)
decomposition of a data tensor. The method uses leverage score sampled
alternating least squares to fit the TR cores in an iterative fashion. By
taking advantage of the special structure of TR tensors, we can efficiently
estimate the leverage scores and attain a method which has complexity sublinear
in the number of input tensor entries. We provide high-probability
relative-error guarantees for the sampled least squares problems. We compare
our proposal to existing methods in experiments on both synthetic and real
data. Our method achieves substantial speedup -- sometimes two or three orders
of magnitude -- over competing methods, while maintaining good accuracy. We
also provide an example of how our method can be used for rapid feature
extraction.

Numerical Analysis;Numerical Analysis