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Convex Tensor Decomposition via Structured Schatten Norm Regularization
Ryota Tomioka · Taiji Suzuki

Thu Dec 05 07:00 PM -- 11:59 PM (PST) @ Harrah's Special Events Center, 2nd Floor

We propose a new class of structured Schatten norms for tensors that includes two recently proposed norms ("overlapped'' and "latent'') for convex-optimization-based tensor decomposition. Based on the properties of the structured Schatten norms, we mathematically analyze the performance of "latent'' approach for tensor decomposition, which was empirically found to perform better than the "overlapped'' approach in some settings. We show theoretically that this is indeed the case. In particular, when the unknown true tensor is low-rank in a specific mode, this approach performs as well as knowing the mode with the smallest rank. Along the way, we show a novel duality result for structures Schatten norms, which is also interesting in the general context of structured sparsity. We confirm through numerical simulations that our theory can precisely predict the scaling behaviour of the mean squared error.

Author Information

Ryota Tomioka (Microsoft Research AI4Science)
Taiji Suzuki (The University of Tokyo/RIKEN-AIP)

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