
Allornothing statistical and computational phase transitions in sparse spiked matrix estimation
We determine statistical and computational limits for estimation of a ra...
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Optimal Correlators for Detection and Estimation in Optical Receivers
Motivated by modern applications of light detection and ranging (LIDAR),...
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Phase transition in the spiked random tensor with Rademacher prior
We consider the problem of detecting a deformation from a symmetric Gaus...
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Estimation in the Spiked Wigner Model: A Short Proof of the Replica Formula
We consider the problem of estimating the rankone perturbation of a Wig...
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Statistical properties of large data sets with linear latent features
Analytical understanding of how lowdimensional latent features reveal t...
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01 phase transitions in sparse spiked matrix estimation
We consider statistical models of estimation of a rankone matrix (the s...
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Multiple Output Regression with Latent Noise
In highdimensional data, structured noise caused by observed and unobse...
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Tensor estimation with structured priors
We consider rankone symmetric tensor estimation when the tensor is corrupted by Gaussian noise and the spike forming the tensor is a structured signal coming from a generalized linear model. The latter is a mathematically tractable model of a nontrivial hidden lowerdimensional latent structure in a signal. We work in a large dimensional regime with fixed ratio of signaltolatent space dimensions. Remarkably, in this asymptotic regime, the mutual information between the spike and the observations can be expressed as a finitedimensional variational problem, and it is possible to deduce the minimummeansquareerror from its solution. We discuss, on examples, properties of the phase transitions as a function of the signaltonoise ratio. Typically, the critical signaltonoise ratio decreases with increasing signaltolatent space dimensions. We discuss the limit of vanishing ratio of signaltolatent space dimensions and determine the limiting tensor estimation problem. We also point out similarities and differences with the case of matrices.
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