Spike Estimation from Heteroscedastic Noise via Random Splitting
Abstract
In this paper, we consider a spiked Wigner type matrix with a heteroscedastic and unknown variance profile. It is well known that in the supercritical regime of the BBP transition, strong spikes can create outliers in the spectrum. Unfortunately, in the heteroscedastic case, in general it is not possible to estimate the spike strength from these observed outlier consistently, as the latter is a solution to a Dyson equation with unknown parameters from the variance profile. In this paper, inspired by the work on sparse matrix completion \citep{BordenaveCosteNadakuditi2023}, we introduce an asymmetrized model by randomly splitting the spiked matrix into two parts, which transforms the noisy Wigner type matrix into a non Hermitian random matrix, while preserving the Hermitian spikes at the cost of a dilution. We establish a BBP type transition for the asymmetrized model, from which we can estimate the strength of the spikes precisely, even without knowing the variance profile of the noise part. We then further apply our approach to study the correlation between two correlated spiked models, where the spike/signal parts of the two models are correlated, and the noise parts are independent but may both be heteroscedastic. By applying our asymmetrization approach to the two models separately and also jointly, we are able to obtain a precise estimate of the correlation between the signal parts of the two models.
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BibTeX
@misc{bao2026spike,
title = {{Spike Estimation from Heteroscedastic Noise via Random Splitting}},
author = {Zhigang Bao and Kha Man Cheong and Yuji Li and Jiaxin Qiu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11169},
eprint = {2609.11169},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11169},
note = {CC0},
}
RIS
TY - UNPB
TI - Spike Estimation from Heteroscedastic Noise via Random Splitting
AU - Zhigang Bao
AU - Kha Man Cheong
AU - Yuji Li
AU - Jiaxin Qiu
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11169
UR - https://arxiv.org/abs/2609.11169
AB - In this paper, we consider a spiked Wigner type matrix with a heteroscedastic and unknown variance profile. It is well known that in the supercritical regime of the BBP transition, strong spikes can create outliers in the spectrum. Unfortunately, in the heteroscedastic case, in general it is not possible to estimate the spike strength from these observed outlier consistently, as the latter is a solution to a Dyson equation with unknown parameters from the variance profile. In this paper, inspired by the work on sparse matrix completion \citep{BordenaveCosteNadakuditi2023}, we introduce an asymmetrized model by randomly splitting the spiked matrix into two parts, which transforms the noisy Wigner type matrix into a non Hermitian random matrix, while preserving the Hermitian spikes at the cost of a dilution. We establish a BBP type transition for the asymmetrized model, from which we can estimate the strength of the spikes precisely, even without knowing the variance profile of the noise part. We then further apply our approach to study the correlation between two correlated spiked models, where the spike/signal parts of the two models are correlated, and the noise parts are independent but may both be heteroscedastic. By applying our asymmetrization approach to the two models separately and also jointly, we are able to obtain a precise estimate of the correlation between the signal parts of the two models.
ER -