The decimation scheme for symmetric matrix factorization
Matrix factorization is an inference problem that has acquired importance due to its vast
range of applications that go from dictionary learning to recommendation systems and …
range of applications that go from dictionary learning to recommendation systems and …
Matrix inference in growing rank regimes
The inference of a large symmetric signal-matrix S∈ RN× N corrupted by additive Gaussian
noise, is considered for two regimes of growth of the rank M as a function of N. For sub-linear …
noise, is considered for two regimes of growth of the rank M as a function of N. For sub-linear …
Rectangular rotational invariant estimator for general additive noise matrices
F Pourkamali, N Macris - 2023 IEEE International Symposium …, 2023 - ieeexplore.ieee.org
We propose a rectangular rotational invariant estimator to recover a real matrix from noisy
matrix observations coming from an arbitrary additive rotational invariant perturbation, in the …
matrix observations coming from an arbitrary additive rotational invariant perturbation, in the …
Bayesian extensive-rank matrix factorization with rotational invariant priors
F Pourkamali, N Macris - Advances in Neural Information …, 2024 - proceedings.neurips.cc
We consider a statistical model for matrix factorization in a regime where the rank of the two
hidden matrix factors grows linearly with their dimension and their product is corrupted by …
hidden matrix factors grows linearly with their dimension and their product is corrupted by …
Matrix denoising: Bayes-optimal estimators via low-degree polynomials
G Semerjian - arXiv preprint arXiv:2402.16719, 2024 - arxiv.org
We consider the additive version of the matrix denoising problem, where a random
symmetric matrix $ S $ of size $ n $ has to be inferred from the observation of $ Y= S+ Z …
symmetric matrix $ S $ of size $ n $ has to be inferred from the observation of $ Y= S+ Z …
Gradient flow on extensive-rank positive semi-definite matrix denoising
In this work, we present a new approach to analyze the gradient flow for a positive semi-
definite matrix denoising problem in an extensive-rank and high-dimensional regime. We …
definite matrix denoising problem in an extensive-rank and high-dimensional regime. We …
Under-parameterized double descent for ridge regularized least squares denoising of data on a line
R Sonthalia, X Li, B Gu - arXiv preprint arXiv:2305.14689, 2023 - arxiv.org
The relationship between the number of training data points, the number of parameters in a
statistical model, and the generalization capabilities of the model has been widely studied …
statistical model, and the generalization capabilities of the model has been widely studied …
Spherical integrals of sublinear rank
J Husson, J Ko - arXiv preprint arXiv:2208.03642, 2022 - arxiv.org
We consider the asymptotics of $ k $-dimensional spherical integrals when $ k= o (N) $. We
prove that the $ o (N) $-dimensional spherical integrals are approximately the products of $1 …
prove that the $ o (N) $-dimensional spherical integrals are approximately the products of $1 …
Singular vectors of sums of rectangular random matrices and optimal estimation of high-rank signals: The extensive spike model
Across many disciplines spanning from neuroscience and genomics to machine learning,
atmospheric science, and finance, the problems of denoising large data matrices to recover …
atmospheric science, and finance, the problems of denoising large data matrices to recover …
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 …