1 citations · 1 across the 6 of their papers we have counts for
8 papers
Stability of the Markov-Krein Transform Under Classical Convolutions
Pierre Mergny
We prove that, for every , the image of the generalized Markov-Krein transform on probability measures with finite logarithmic moment is closed under classical additive convol…
Spectral phase transitions in Gaussian multi-index models
Florent Krzakala, Pierre Mergny, Vanessa Piccolo
Recovering a low-dimensional latent subspace from nonlinear observations of Gaussian covariates in high dimensions is a fundamental problem in feature learning. Here, we consider G…
Spectral Thresholds in Correlated Spiked Models and Fundamental Limits of Partial Least Squares
Pierre Mergny, Lenka Zdeborová
We provide a rigorous random matrix theory analysis of spiked cross-covariance models where the signals across two high-dimensional data channels are partially aligned. These model…
Computational Thresholds in Multi-Modal Learning via the Spiked Matrix-Tensor Model
Hugo Tabanelli, Pierre Mergny, Lenka Zdeborova +1
We study the recovery of multiple high-dimensional signals from two noisy, correlated modalities: a spiked matrix and a spiked tensor sharing a common low-rank structure. This sett…
Optimal Spectral Transitions in High-Dimensional Multi-Index Models
Leonardo Defilippis, Yatin Dandi, Pierre Mergny +2
We consider the problem of how many samples from a Gaussian multi-index model are required to weakly reconstruct the relevant index subspace. Despite its increasing popularity as a…
Fundamental limits of Non-Linear Low-Rank Matrix Estimation
Pierre Mergny, Justin Ko, Florent Krzakala +1
We consider the task of estimating a low-rank matrix from non-linear and noisy observations. We prove a strong universality result showing that Bayes-optimal performances are chara…
Spectral Phase Transition and Optimal PCA in Block-Structured Spiked models
Pierre Mergny, Justin Ko, Florent Krzakala
We discuss the inhomogeneous spiked Wigner model, a theoretical framework recently introduced to study structured noise in various learning scenarios, through the prism of random m…
Spectral Phase Transitions in Non-Linear Wigner Spiked Models
Alice Guionnet, Justin Ko, Florent Krzakala +2
We study the asymptotic behavior of the spectrum of a random matrix where a non-linearity is applied entry-wise to a Wigner matrix perturbed by a rank-one spike with independent an…