D Paul, A Aue - Journal of Statistical Planning and Inference, 2014 - Elsevier
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 …
J Ba, MA Erdogdu, T Suzuki… - Advances in Neural …, 2024 - proceedings.neurips.cc
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 …
M Lettau, M Pelger - The Review of Financial Studies, 2020 - academic.oup.com
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 …