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 …

We give an overview of random matrix theory (RMT) with the objective of highlighting the
results and concepts that have a growing impact in the formulation and inference of …

We study the first gradient descent step on the first-layer parameters $\boldsymbol {W} $ in a
two-layer neural network: $ f (\boldsymbol {x})=\frac {1}{\sqrt {N}}\boldsymbol {a}^\top\sigma …

We consider the learning of a single-index target function $ f_*:\mathbb {R}^ d\to\mathbb {R}
$ under spiked covariance data: $$ f_*(\boldsymbol {x})=\textstyle\sigma_*(\frac {1}{\sqrt …

How do statistical dependencies in measurement noise influence high-dimensional
inference? To answer this, we study the paradigmatic spiked matrix model of principal …

We perform an analysis of the average generalization dynamics of large neural networks
trained using gradient descent. We study the practically-relevant “high-dimensional” regime …

Single-cell RNA-seq enables the quantitative characterization of cell types based on global
transcriptome profiles. We present single-cell consensus clustering (SC3), a user-friendly …

We study the scaling limits of stochastic gradient descent (SGD) with constant step-size in
the high-dimensional regime. We prove limit theorems for the trajectories of summary …

Recovering low-rank structures via eigenvector perturbation analysis is a common problem
in statistical machine learning, such as in factor analysis, community detection, ranking …

We propose a new method for estimating latent asset pricing factors that fit the time series
and cross-section of expected returns. Our estimator generalizes principal component …