BBP phase transition
A phenomenon in random matrix theory describing an abrupt change in the degree to which sample eigenvectors align with the true signal, introduced by Baik, Ben Arous and Péché.
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In the spiked Wigner model, when λ is below the BBP phase transition threshold λ_c=1, the sample eigenvector is completely orthogonal to the true signal and spectral methods fail; above the threshold, the squared direction cosine between the eigenvector and the signal is approximately 1-λ^{-2}.
The doubly sparse model simultaneously parametrizes the nonzero support of the signal and the nonzero structure of the noise, examining how the BBP-type phase transition moves with the two types of sparsity.
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In the spiked Wigner model, when λ is below the BBP phase transition threshold λ_c=1, the sample eigenvector is completely orthogonal to the true signal and spectral methods fail; above the threshold, the squared direction cosine between the eigenvector and the signal is approximately 1-λ^{-2}.
50%UnverifiedThe doubly sparse model simultaneously parametrizes the nonzero support of the signal and the nonzero structure of the noise, examining how the BBP-type phase transition moves with the two types of sparsity.
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