2014
DOI: 10.48550/arxiv.1411.1076
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A statistical model for tensor PCA

Abstract: We consider the Principal Component Analysis problem for large tensors of arbitrary order k under a single-spike (or rank-one plus noise) model. On the one hand, we use information theory, and recent results in probability theory, to establish necessary and sufficient conditions under which the principal component can be estimated using unbounded computational resources. It turns out that this is possible as soon as the signal-to-noise ratio β becomes larger than C √ k log k (and in particular β can remain bou… Show more

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Cited by 5 publications
(23 citation statements)
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“…Averaging over C is implemented by contracting the black vertices as before. However, as explained under (17), to obtain the maximal power of N, the wavy lines pairing the black vertices should never reconnect any disconnected components of the graph. This means that, at leading order in N, the result is simply a product of the C-averages of each of the two hourglass diagrams, which is the same as…”
Section: Discussionmentioning
confidence: 99%
See 3 more Smart Citations
“…Averaging over C is implemented by contracting the black vertices as before. However, as explained under (17), to obtain the maximal power of N, the wavy lines pairing the black vertices should never reconnect any disconnected components of the graph. This means that, at leading order in N, the result is simply a product of the C-averages of each of the two hourglass diagrams, which is the same as…”
Section: Discussionmentioning
confidence: 99%
“…We remark on some similarity between the questions we address and the spiked tensor model [17,18,21], which deals with tensors of the form…”
Section: The Largest Eigenvalue Of a Tensormentioning
confidence: 99%
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“…The results of [53][54][55] pointed out that that these conclusions are in fact not restricted to the MP law. Investigating the case of a noise materialized by a random tensor considered in the mathematical formalism of the tensorial PCA [61][62][63][64], the authors were able to show that conclusions of statement 1 remain true.…”
Section: Introductionmentioning
confidence: 99%