Code Supplement for "ScreeNOT: Exact MSE-Optimal Singular Value Thresholding in Correlated Noise"

Placeholder Show Content



We derive a formula for optimal hard thresholding of the singular value decomposition in the presence of correlated additive noise; although it nominally involves unobservables, we show how to apply it even where the noise covariance structure is not a-priori known or is not independently estimable.

The proposed method, which we call ScreeNOT, is a mathematically solid alternative to Cattell's ever-popular but vague Scree Plot heuristic from 1966.

ScreeNOT has a surprising oracle property: it typically achieves exactly, in large finite samples, the lowest possible MSE for matrix recovery, on each given problem instance - i.e. the specific threshold it selects gives exactly the smallest achievable MSE loss among all possible threshold choices for that noisy dataset and that unknown underlying true low rank model. The method is computationally efficient and robust against perturbations of the underlying covariance structure.

Our results depend on the assumption that the singular values of the noise have a limiting empirical distribution of compact support; this model, which is standard in random matrix theory, is satisfied by many models exhibiting either cross-row correlation structure or cross-column correlation structure, and also by many situations where there is inter-element correlation structure. Simulations demonstrate the effectiveness of the method even at moderate matrix sizes. The paper is supplemented by ready-to-use software packages implementing the proposed algorithm.


Type of resource software, multimedia
Date created October 2020
Date modified January 10, 2023
Publication date September 29, 2020


Author Donoho, David L.
Author Gavish, Matan
Author Romanov, Elad


Subject Singular value thresholding
Subject Optimal threshold
Subject Scree Plot
Subject Low-rank matrix denoising
Genre Software/code

Bibliographic information

Related item

Access conditions

Use and reproduction
User agrees that, where applicable, content will not be used to identify or to otherwise infringe the privacy or confidentiality rights of individuals. Content distributed via the Stanford Digital Repository may be subject to additional license and use restrictions applied by the depositor.
This work is licensed under a Creative Commons Attribution 4.0 International license (CC BY).

Preferred citation

Preferred citation
Donoho, David L., Gavish, Matan and Romanov, Elad. (2020). Code Supplement for "ScreeNOT: Exact MSE-Optimal Singular Value Thresholding in Correlated Noise". Stanford Digital Repository. Available online at:


Contact information

Also listed in

Loading usage metrics...