# Detection of Signal in the Spiked Rectangular Models

arXiv: https://arxiv.org/abs/2104.13517 · HTML: https://mlsanity.com/paper/2104.13517/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 29 references that are in the map.
- First posted on arXiv 28 Apr 2021.

## Builds on (most cited first, 7 of 7)

- [Community Detection and Stochastic Block Models](https://mlsanity.com/paper/1703.10146/) (2017)
- [Optimality and Sub-optimality of PCA I: Spiked Random Matrix Models](https://mlsanity.com/paper/1807.00891/) (2018)
- [MMSE of probabilistic low-rank matrix estimation: Universality with respect to the output channel](https://mlsanity.com/paper/1507.03857/) (2015)
- [Fundamental limits of detection in the spiked Wigner model](https://mlsanity.com/paper/1806.09588/) (2018)
- [Detection limits in the high-dimensional spiked rectangular model](https://mlsanity.com/paper/1802.07309/) (2018)
- [Adapting to Unknown Noise Distribution in Matrix Denoising](https://mlsanity.com/paper/1810.02954/) (2018)
- [Weak Detection in the Spiked Wigner Model with General Rank](https://mlsanity.com/paper/2001.05676/) (2020)

## Built on by (most cited first, 4 of 4)

- [SPQR: Controlling Q-ensemble Independence with Spiked Random Model for Reinforcement Learning](https://mlsanity.com/paper/2401.03137/) (2024)
- [Precise Error Rates for Computationally Efficient Testing](https://mlsanity.com/paper/2311.00289/) (2023)
- [Asymptotic Normality of Log Likelihood Ratio and Fundamental Limit of the Weak Detection for Spiked Wigner Matrices](https://mlsanity.com/paper/2203.00821/) (2022)
- [Detection problems in the spiked matrix models](https://mlsanity.com/paper/2301.05331/) (2023)

## Abstract (arXiv)

We consider the problem of detecting signals in the rank-one signal-plus-noise data matrix models that generalize the spiked Wishart matrices. We show that the principal component analysis can be improved by pre-transforming the matrix entries if the noise is non-Gaussian. As an intermediate step, we prove a sharp phase transition of the largest eigenvalues of spiked rectangular matrices, which extends the Baik-Ben Arous-P'ech'e (BBP) transition. We also propose a hypothesis test to detect the presence of signal with low computational complexity, based on the linear spectral statistics, which minimizes the sum of the Type-I and Type-II errors when the noise is Gaussian.