adaptiveHardThresholding {ScreeNOT}

Adaptive hard thresholding

Description

Performs optimal adaptive hard thresholding on the input matrix Y.

Usage

adaptiveHardThresholding(Y, k, strategy = "i")

Arguments

Y

A data matrix, on whose singular values thresholding should be performed.

k

An upper bound (potentially loose) on the latent signal rank. That is, the procedure assumes that there are AT MOST k informative principal components of Y.

strategy

Method for reconstructing the noise bulk (optional). Can be one of the following: '0': tranpsort to zero; 'w': winsorization; 'i': imputation (default option).

Value

Xest

An estimate of the low-rank signal. That is: the matrix obtained by thresholding the singular values of Y.

Topt

The hard threshold computed by the procedure. To wit, the procedure retains the i-th PC of Y if and only if the corresponding singular value, y_i, satisfies y_i > Topt.

r

The number of "relevant" components: r = rank(Xest).

Author(s)

Elad Romanov

References

David L. Donoho, Matan Gavish and Elad Romanov. "ScreeNOT: Exact MSE-optimal singular value thresholding in correlated noise." Annals of Statistics (2023). https://github.com/eladromanov/ScreeNOT

Examples

   Y <- matrix(rnorm(1e6)/sqrt(1e3),nrow=1e3)
        # Y is a 1000x1000 i.i.d. Gaussian matrix
   val <- ScreeNOT::adaptiveHardThresholding(Y, 10)
        # Runs the ScreeNOT procedure, with an upper bound k=10
   cat('Computed threshold: ', val$Topt)
        # The adaptively computed threshold
   cat('Known optimal threshold: ', 4/sqrt(3))
        # The known optimal threshold for this noise bulk