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Nuclear p-norms for large tensor completion
Nov 07, 2017 (modified: Nov 07, 2017)ICLR 2018 Conference Blind Submissionreaders: everyoneShow Bibtex
Abstract:We present algorithms for tensor completion using regularizers based
on tensor nuclear p-norms. For the particular case of the nuclear
infinity-norm, we generalize to higher-order tensors the theoretical
guarantees of the max-norm for matrix completion. From a practical perspective,
we present two algorithms based on stochastic gradients to regularize the canonical
decomposition of tensors, and show on large-scale benchmark datasets
for knowledge base completion that (a) contrary to what suggested prior results in the literature, the canonical decomposition of tensors can achieve state-of-the-art level performance on FB15K and WN, and (b) our new regularizations reach or outperform the state-of-the-art on task where the canonical decomposition alone is not reaching it. In particular, we provide evidence that the nuclear 3-norm can replace the structures and/or regularization terms of existing link prediction models, and
leads to better performance.
TL;DR:Efficient regularizers for tensor completion applied to large scale link prediction in knowledge bases.
Keywords:tensor completion, knowledge base completion, relational learning, tensor norms
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