Skip to main content

Uniqueness of Tensor Decompositions with Applications to Polynomial Identifiability

Author(s): Bhaskara, Aditya; Charikar, Moses; Vijayaraghavan, Aravindan

To refer to this page use:
Abstract: We give a robust version of the celebrated result of Kruskal on the uniqueness of tensor decompositions: given a tensor whose decomposition satisfies a robust form of Kruskal’s rank condition, we prove that it is possible to approximately recover the decomposition if the tensor is known up to a sufficiently small (inverse polynomial) error. Kruskal’s theorem has found many applications in proving the identifiability of parameters for various latent variable models and mixture models such as Hidden Markov models, topic models etc. Our robust version immediately implies identifiability using only polynomially many samples in many of these settings – an essential first step towards efficient learning algorithms. Our methods also apply to the “overcomplete” case, which has proved challenging in many applications. Given the importance of Kruskal’s theorem in the tensor literature, we expect that our robust version will have several applications beyond the settings we explore in this work.
Publication Date: 2014
Citation: Bhaskara, Aditya, Moses Charikar, and Aravindan Vijayaraghavan. "Uniqueness of Tensor Decompositions with Applications to Polynomial Identifiability." In Proceedings of The 27th Conference on Learning Theory, 35 (2014): 742-778.
ISSN: 2640-3498
Pages: 742 - 778
Type of Material: Conference Article
Series/Report no.: Proceedings of Machine Learning Research;
Journal/Proceeding Title: Proceedings of The 27th Conference on Learning Theory
Version: Final published version. This is an open access article.

Items in OAR@Princeton are protected by copyright, with all rights reserved, unless otherwise indicated.