Sparse Super Symmetric Tensor Factorization

2008 ◽  
pp. 781-790 ◽  
Author(s):  
Andrzej Cichocki ◽  
Marko Jankovic ◽  
Rafal Zdunek ◽  
Shun-ichi Amari
Keyword(s):  
Symmetric Tensor ◽  
Tensor Factorization

scholarly journals Mutual information for low-rank even-order symmetric tensor estimation

2020 ◽  
Author(s):  
Clément Luneau ◽  
Jean Barbier ◽  
Nicolas Macris
Keyword(s):  
Mutual Information ◽  
Finite Rank ◽  
Interpolation Method ◽  
Symmetric Tensor ◽  
Low Rank ◽  
Tensor Factorization ◽  
Adaptive Interpolation ◽  
Odd Order ◽  
Rank One ◽  
Even Order

Abstract We consider a statistical model for finite-rank symmetric tensor factorization and prove a single-letter variational expression for its asymptotic mutual information when the tensor is of even order. The proof applies the adaptive interpolation method originally invented for rank-one factorization. Here we show how to extend the adaptive interpolation to finite-rank and even-order tensors. This requires new non-trivial ideas with respect to the current analysis in the literature. We also underline where the proof falls short when dealing with odd-order tensors.

Mitigating the Effect of Out-of-Vocabulary Entity Pairs in Matrix Factorization for KB Inference

2018 ◽  
Author(s):  
Prachi Jain ◽  
Shikhar Murty ◽  
Mausam . ◽  
Soumen Chakrabarti
Keyword(s):  
Knowledge Base ◽  
Hybrid Model ◽  
Matrix Factorization ◽  
Relation Extraction ◽  
Tensor Factorization ◽  
Evaluation Protocol

This paper analyzes the varied performance of Matrix Factorization (MF) on the related tasks of relation extraction and knowledge-base completion, which have been unified recently into a single framework of knowledge-base inference (KBI) [Toutanova et al., 2015]. We first propose a new evaluation protocol that makes comparisons between MF and Tensor Factorization (TF) models fair. We find that this results in a steep drop in MF performance. Our analysis attributes this to the high out-of-vocabulary (OOV) rate of entity pairs in test folds of commonly-used datasets. To alleviate this issue, we propose three extensions to MF. Our best model is a TF-augmented MF model. This hybrid model is robust and obtains strong results across various KBI datasets.

scholarly journals CONSTRUCTIVE NONCOMMMUTATIVE INVARIANT THEORY

2021 ◽  
Author(s):  
MÁTYÁS DOMOKOS ◽  
VESSELIN DRENSKY
Keyword(s):  
Lie Algebra ◽  
Associative Algebra ◽  
Invariant Theory ◽  
Reductive Group ◽  
Symmetric Tensor ◽  
Free Associative Algebra ◽  
Tensor Algebra ◽  
Enveloping Algebra ◽  
Finite Dimensional ◽  
Degree Bounds

AbstractThe problem of finding generators of the subalgebra of invariants under the action of a group of automorphisms of a finite-dimensional Lie algebra on its universal enveloping algebra is reduced to finding homogeneous generators of the same group acting on the symmetric tensor algebra of the Lie algebra. This process is applied to prove a constructive Hilbert–Nagata Theorem (including degree bounds) for the algebra of invariants in a Lie nilpotent relatively free associative algebra endowed with an action induced by a representation of a reductive group.

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