Fundamental Limits of Low-Rank Matrix Estimation with Diverging Aspect Ratios

Understand

We consider the problem of estimating the factors of a low-rank $n \times d$ matrix, when this is corrupted by additive Gaussian noise.

• A special example of our setting corresponds to clustering mixtures of Gaussians with equal (known) covariances.
• Simple spectral methods do not take into account the distribution of the entries of these factors and are therefore often suboptimal.
• Here, we characterize the asymptotics of the minimum estimation error under the assumption that the distribution of the entries is known to the statistician.