Fitting an ellipsoid to random points: predictions using the replica method
A Maillard, D Kunisky - IEEE Transactions on Information …, 2024 - ieeexplore.ieee.org
We consider the problem of fitting a centered ellipsoid to n standard Gaussian random
vectors in R d, as n, d→∞ with n/d 2→ α> 0. It has been conjectured that this problem is, with …
vectors in R d, as n, d→∞ with n/d 2→ α> 0. It has been conjectured that this problem is, with …
Exact threshold for approximate ellipsoid fitting of random points
A Maillard, AS Bandeira - arXiv preprint arXiv:2310.05787, 2023 - arxiv.org
We consider the problem $(\rm P) $ of exactly fitting an ellipsoid (centered at $0 $) to $ n $
standard Gaussian random vectors in $\mathbb {R}^ d $, as $ n, d\to\infty $ with $ n/d …
standard Gaussian random vectors in $\mathbb {R}^ d $, as $ n, d\to\infty $ with $ n/d …
Ellipsoid fitting up to constant via empirical covariance estimation
M Tulsiani, J Wu - arXiv preprint arXiv:2307.10941, 2023 - arxiv.org
The ellipsoid fitting conjecture of Saunderson, Chandrasekaran, Parrilo and Wilsky
considers the maximum number $ n $ random Gaussian points in $\mathbb {R}^ d $, such …
considers the maximum number $ n $ random Gaussian points in $\mathbb {R}^ d $, such …
Universality of kernel random matrices and kernel regression in the quadratic regime
Kernel ridge regression (KRR) is a popular class of machine learning models that has
become an important tool for understanding deep learning. Much of the focus has been on …
become an important tool for understanding deep learning. Much of the focus has been on …
Generalized Ellipsoids
AA Ahmadi, A Chaudhry, C Dibek - arXiv preprint arXiv:2407.20362, 2024 - arxiv.org
We introduce a family of symmetric convex bodies called generalized ellipsoids of degree $
d $(GE-$ d $ s), with ellipsoids corresponding to the case of $ d= 0$. Generalized ellipsoids …
d $(GE-$ d $ s), with ellipsoids corresponding to the case of $ d= 0$. Generalized ellipsoids …