Tensor train completion: local recovery guarantees via Riemannian optimization

Abstract

In this work, we estimate the number of randomly selected elements of a tensor that with high probability guarantees local convergence of Riemannian gradient descent for tensor train completion. We derive a new bound for the orthogonal projections onto the tangent spaces based on the harmonic mean of the unfoldings' singular values and introduce a notion of core coherence for tensor trains. We also extend the results to tensor train completion with auxiliary subspace information and obtain the corresponding local convergence guarantees.

arXiv comment1 figure added; Accepted version

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Cited by in corpus (3)

• Entrywise tensor-train approximation of large tensors via random embeddings
• Quasioptimal alternating projections and their use in low-rank approximation of matrices and tensors
• Variational Bayesian inference for CP tensor completion with side information