This review covers recent results concerning the estimation of large covariance matrices
using tools from Random Matrix Theory (RMT). We introduce several RMT methods and …

Interpolators—estimators that achieve zero training error—have attracted growing attention
in machine learning, mainly because state-of-the art neural networks appear to be models of …

We propose a patch-based singular value shrinkage method for diffusion magnetic
resonance image estimation targeted at low signal to noise ratio and accelerated …

We provide a unified analysis of the predictive risk of ridge regression and regularized
discriminant analysis in a dense random effects model. We work in a high-dimensional …

We study the statistical properties of the iterates generated by gradient descent, applied to
the fundamental problem of least squares regression. We take a continuous-time view, ie …

The spiked covariance model has gained increasing popularity in high-dimensional data
analysis. A fundamental problem is determination of the number of spiked eigenvalues, K …

Factor analysis and principal component analysis are used in many application areas. The
first step, choosing the number of components, remains a serious challenge. Our work …

Nonparametric Bayesian posterior contraction rates for discretely observed scalar diffusions
Page 1 The Annals of Statistics 2017, Vol. 45, No. 4, 1664–1693 DOI: 10.1214/16-AOS1504 © …

In our “big data” age, the size and complexity of data is steadily increasing. Methods for
dimension reduction are ever more popular and useful. Two distinct types of dimension …

We take a random matrix theory approach to random sketching and show an asymptotic first-
order equivalence of the regularized sketched pseudoinverse of a positive semidefinite …