# Mismatched Estimation of rank-one symmetric matrices under Gaussian noise

arXiv: https://arxiv.org/abs/2107.08927 · HTML: https://mlsanity.com/paper/2107.08927/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jul 2021.

## Built on by (most cited first, 2 of 2)

- [Statistical limits of dictionary learning: random matrix theory and the spectral replica method](https://mlsanity.com/paper/2109.06610/) (2021)
- [The price of ignorance: how much does it cost to forget noise structure in low-rank matrix estimation?](https://mlsanity.com/paper/2205.10009/) (2022)

## Abstract (arXiv)

We consider the estimation of an n-dimensional vector s from the noisy element-wise measurements of ssT, a generic problem that arises in statistics and machine learning. We study a mismatched Bayesian inference setting, where some of the parameters are not known to the statistician. We derive the full exact analytic expression of the asymptotic mean squared error (MSE) in the large system size limit for the particular case of Gaussian priors and additive noise. From our formulas, we see that estimation is still possible in the mismatched case; and also that the minimum MSE (MMSE) can be achieved if the statistician chooses suitable parameters. Our technique relies on the asymptotics of the spherical integrals and can be applied as long as the statistician chooses a rotationally invariant prior.