# ScreeNOT: Exact MSE-Optimal Singular Value Thresholding in Correlated Noise

arXiv: https://arxiv.org/abs/2009.12297 · HTML: https://mlsanity.com/paper/2009.12297/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Sep 2020.

## Built on by (most cited first, 15 of 15)

- [Model Editing as a Robust and Denoised variant of DPO: A Case Study on Toxicity](https://mlsanity.com/paper/2405.13967/) (2024)
- [Uncovering hidden geometry in Transformers via disentangling position and context](https://mlsanity.com/paper/2310.04861/) (2023)
- [Is your data alignable? Principled and interpretable alignability testing and integration of single-cell data](https://mlsanity.com/paper/2308.01839/) (2023)
- [Matrix Denoising with Doubly Heteroscedastic Noise: Fundamental Limits and Optimal Spectral Methods](https://mlsanity.com/paper/2405.13912/) (2024)
- [LEARNER: A Transfer Learning Method for Low-Rank Matrix Estimation](https://mlsanity.com/paper/2412.20605/) (2024)
- [Sailing in high-dimensional spaces: Low-dimensional embeddings through angle preservation](https://mlsanity.com/paper/2406.09876/) (2024)
- [Design a Metric Robust to Complicated High Dimensional Noise for Efficient Manifold Denoising](https://mlsanity.com/paper/2401.03921/) (2024)
- [Signed Diverse Multiplex Networks: Clustering and Inference](https://mlsanity.com/paper/2402.10242/) (2024)
- [Inference for Similarity and Alignability between Noisy High-Dimensional Datasets](https://mlsanity.com/paper/2511.21074/) (2025)
- [Spectral Transformation for Layer-wise Global Rank Discovery in Federated LoRA for Vision Transformers](https://mlsanity.com/paper/2607.21074/) (2026)
- [Factorized Fusion Shrinkage for Dynamic Relational Data](https://mlsanity.com/paper/2210.00091/) (2022)
- [On the Noise Sensitivity of the Randomized SVD](https://mlsanity.com/paper/2305.17435/) (2023)
- [Federated One-Shot Ensemble Clustering](https://mlsanity.com/paper/2409.08396/) (2024)
- [Unsupervised Attributed Dynamic Network Embedding with Stability Guarantees](https://mlsanity.com/paper/2503.02859/) (2025)
- [Enhancing Spectral Embedding through Robust and Flexible Knowledge Transfer in Electronic Health Records](https://mlsanity.com/paper/2606.11570/) (2026)

## Abstract (arXiv)

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: package ScreeNOT in Python (via PyPI) and R (via CRAN).