Florent Gérard Krzakala

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Publications associées (66)

Error scaling laws for kernel classification under source and capacity conditions

Florent Gérard Krzakala, Lenka Zdeborová, Bruno Loureiro, Hugo Chao Cui, Bruno Loureiro

In this manuscript we consider the problem of kernel classification. While worst-case bounds on the decay rate of the prediction error with the number of samples are known for some classifiers, they often fail to accurately describe the learning curves of ...

2023

Are Gaussian data all you need? the extents and limits of universality in high-dimensional generalized linear estimation

Florent Gérard Krzakala, Luca Pesce, Ludovic Théo Stephan

In this manuscript we consider the problem of generalized linear estimation on Gaussian mixture data with labels given by a single-index model. Our first result is a sharp asymptotic expression for the test and training errors in the high-dimensional regim ...

PMLR2023

Theoretical characterization of uncertainty in high-dimensional linear classification

Florent Gérard Krzakala, Lenka Zdeborová, Lucas Andry Clarte

Being able to reliably assess not only the accuracy but also the uncertainty of models' predictions is an important endeavor in modern machine learning. Even if the model generating the data and labels is known, computing the intrinsic uncertainty after le ...

IOP Publishing Ltd2023

Generalization error rates in kernel regression: the crossover from the noiseless to noisy regime*

Florent Gérard Krzakala, Lenka Zdeborová, Bruno Loureiro, Hugo Chao Cui

In this manuscript we consider kernel ridge regression (KRR) under the Gaussian design. Exponents for the decay of the excess generalization error of KRR have been reported in various works under the assumption of power-law decay of eigenvalues of the feat ...

2022

Optimal denoising of rotationally invariant rectangular matrices

Florent Gérard Krzakala, Lenka Zdeborová, Emanuele Troiani, Vittorio Erba

In this manuscript we consider denoising of large rectangular matrices: given a noisy observation of a signal matrix, what is the best way of recovering the signal matrix itself? For Gaussian noise and rotationally-invariant signal priors, we completely ch ...

2022

Perturbative construction of mean-field equations in extensive-rank matrix factorization and denoising

Florent Gérard Krzakala, Lenka Zdeborová

Factorization of matrices where the rank of the two factors diverges linearly with their sizes has many applications in diverse areas such as unsupervised representation learning, dictionary learning or sparse coding. We consider a setting where the two fa ...

2022

Asymptotic Errors for Teacher-Student Convex Generalized Linear Models (Or: How to Prove Kabashima’s Replica Formula)

Florent Gérard Krzakala, Alia Abbara

There has been a recent surge of interest in the study of asymptotic reconstruction performance in various cases of generalized linear estimation problems in the teacher-student setting, especially for the case of i.i.d standard normal matrices. Here, we g ...

2022

Multi-layer State Evolution Under Random Convolutional Design

Florent Gérard Krzakala, Lenka Zdeborová

Signal recovery under generative neural network priors has emerged as a promising direction in statistical inference and computational imaging. Theoretical analysis of reconstruction algorithms under generative priors is, however, challenging. For generati ...

2022

Subspace clustering in high-dimensions: Phase transitions & Statistical-to-Computational gap

Florent Gérard Krzakala, Lenka Zdeborová, Luca Pesce, Bruno Loureiro, Bruno Loureiro

A simple model to study subspace clustering is the high-dimensional k -Gaussian mixture model where the cluster means are sparse vectors. Here we provide an exact asymptotic characterization of the statistically optimal reconstruction error in this model i ...

2022

Fluctuations, Bias, Variance & Ensemble of Learners: Exact Asymptotics for Convex Losses in High-Dimension

Florent Gérard Krzakala, Bruno Loureiro

From the sampling of data to the initialisation of parameters, randomness is ubiquitous in modern Machine Learning practice. Understanding the statistical fluctuations engendered by the different sources of randomness in prediction is therefore key to unde ...

JMLR-JOURNAL MACHINE LEARNING RESEARCH2022

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