
Estimation in the group action channel
We analyze the problem of estimating a signal from multiple measurements...
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Statistical thresholds for Tensor PCA
We study the statistical limits of testing and estimation for a rank one...
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Tensor estimation with structured priors
We consider rankone symmetric tensor estimation when the tensor is corr...
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Phase transition in random tensors with multiple spikes
Consider a spiked random tensor obtained as a mixture of two components:...
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The AllorNothing Phenomenon in Sparse Linear Regression
We study the problem of recovering a hidden binary ksparse pdimensiona...
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Information theoretic limits of learning a sparse rule
We consider generalized linear models in regimes where the number of non...
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A Unified View of Label Shift Estimation
Label shift describes the setting where although the label distribution ...
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On maximumlikelihood estimation in the allornothing regime
We study the problem of estimating a rank1 additive deformation of a Gaussian tensor according to the maximumlikelihood estimator (MLE). The analysis is carried out in the sparse setting, where the underlying signal has a support that scales sublinearly with the total number of dimensions. We show that for Bernoulli distributed signals, the MLE undergoes an allornothing (AoN) phase transition, already established for the minimum meansquareerror estimator (MMSE) in the same problem. The result follows from two main technical points: (i) the connection established between the MLE and the MMSE, using the first and secondmoment methods in the constrained signal space, (ii) a recovery regime for the MMSE stricter than the simple error vanishing characterization given in the standard AoN, that is here proved as a general result.
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