One example of general unidentifiable tensors
Algebraic Geometry
2013-04-26 v3
Abstract
The identifiability of parameters in a probabilistic model is a crucial notion in statistical inference. We prove that a general tensor of rank 8 in C^3\otimes C^6\otimes C^6 has at least 6 decompositions as sum of simple tensors, so it is not 8-identifiable. This is the highest known example of balanced tensors of dimension 3, which are not k-identifiable, when k is smaller than the generic rank.
Keywords
Cite
@article{arxiv.1303.6914,
title = {One example of general unidentifiable tensors},
author = {Luca Chiantini and Massimiliano Mella and Giorgio Ottaviani},
journal= {arXiv preprint arXiv:1303.6914},
year = {2013}
}
Comments
7 pages, one Macaulay2 script as ancillary file, two references added