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⊗C^6⊗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.
One example of general unidentifiable tensors / Luca Chiantini; Giorgio Ottaviani; Massimiliano Mella. - In: JOURNAL OF ALGEBRAIC STATISTICS. - ISSN 1309-3452. - STAMPA. - 5:(2014), pp. 64-71. [http://dx.doi.org/10.18409/jas.v5i1.25]
One example of general unidentifiable tensors
OTTAVIANI, GIORGIO MARIA;
2014
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⊗C^6⊗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.
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