Nuclear p-norms for large tensor completion


Nov 07, 2017 (modified: Nov 07, 2017) ICLR 2018 Conference Blind Submission readers: everyone Show 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