[HTML][HTML] Log-concavity and strong log-concavity: a review
We review and formulate results concerning log-concavity and strong-log-concavity in both
discrete and continuous settings. We show how preservation of log-concavity and strongly …
discrete and continuous settings. We show how preservation of log-concavity and strongly …
Introduction to the non-asymptotic analysis of random matrices
R Vershynin - arxiv preprint arxiv:1011.3027, 2010 - arxiv.org
This is a tutorial on some basic non-asymptotic methods and concepts in random matrix
theory. The reader will learn several tools for the analysis of the extreme singular values of …
theory. The reader will learn several tools for the analysis of the extreme singular values of …
Concentration inequalities
Concentration inequalities deal with deviations of functions of independent random
variables from their expectation. In the last decade new tools have been introduced making …
variables from their expectation. In the last decade new tools have been introduced making …
Algorithmic regularization in over-parameterized matrix sensing and neural networks with quadratic activations
We show that the gradient descent algorithm provides an implicit regularization effect in the
learning of over-parameterized matrix factorization models and one-hidden-layer neural …
learning of over-parameterized matrix factorization models and one-hidden-layer neural …
[BOOK][B] Upper and lower bounds for stochastic processes
M Talagrand - 2014 - Springer
This book had a previous edition [132]. The changes between the two editions are not only
cosmetic or pedagogical, and the degree of improvement in the mathematics themselves is …
cosmetic or pedagogical, and the degree of improvement in the mathematics themselves is …
Statistical, robustness, and computational guarantees for sliced wasserstein distances
Sliced Wasserstein distances preserve properties of classic Wasserstein distances while
being more scalable for computation and estimation in high dimensions. The goal of this …
being more scalable for computation and estimation in high dimensions. The goal of this …
Beyond ntk with vanilla gradient descent: A mean-field analysis of neural networks with polynomial width, samples, and time
Despite recent theoretical progress on the non-convex optimization of two-layer neural
networks, it is still an open question whether gradient descent on neural networks without …
networks, it is still an open question whether gradient descent on neural networks without …
[BOOK][B] Geometry of isotropic convex bodies
The study of high-dimensional convex bodies from a geometric and analytic point of view,
with an emphasis on the dependence of various parameters on the dimension stands at the …
with an emphasis on the dependence of various parameters on the dimension stands at the …
[BOOK][B] Eigenvalue distribution of large random matrices
LA Pastur, M Shcherbina - 2011 - books.google.com
Random matrix theory is a wide and growing field with a variety of concepts, results, and
techniques and a vast range of applications in mathematics and the related sciences. The …
techniques and a vast range of applications in mathematics and the related sciences. The …
Non-asymptotic theory of random matrices: extreme singular values
M Rudelson, R Vershynin - … of Mathematicians 2010 (ICM 2010) (In …, 2010 - World Scientific
The classical random matrix theory is mostly focused on asymptotic spectral properties of
random matrices as their dimensions grow to infinity. At the same time many recent …
random matrices as their dimensions grow to infinity. At the same time many recent …