Bruno Loureiro

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Related publications (23)

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

Learning curves for the multi-class teacher-student perceptron

Lenka Zdeborová, Bruno Loureiro, Elisabetta Cornacchia, Bruno Loureiro, Francesca Mignacco

One of the most classical results in high-dimensional learning theory provides a closed-form expression for the generalisation error of binary classification with a single-layer teacher-student perceptron on i.i.d. Gaussian inputs. Both Bayes-optimal (BO) ...

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

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

Secure Coding via Gaussian Random Fields

Florent Gérard Krzakala, Bruno Loureiro

Inverse probability problems whose generative models are given by strictly nonlinear Gaussian random fields show the all-or-nothing behavior: There exists a critical rate at which Bayesian inference exhibits a phase transition. Below this rate, the optimal ...

IEEE2022

Phase diagram of Stochastic Gradient Descent in high-dimensional two-layer neural networks

Florent Gérard Krzakala, Lenka Zdeborová, Bruno Loureiro, Bruno Loureiro, Ludovic Théo Stephan

Despite the non-convex optimization landscape, over-parametrized shallow networks are able to achieve global convergence under gradient descent. The picture can be radically different for narrow net-works, which tend to get stuck in badly-generalizing loca ...

2022

The Gaussian equivalence of generative models for learning with shallow neural networks

Florent Gérard Krzakala, Lenka Zdeborová, Bruno Loureiro

Understanding the impact of data structure on the computational tractability of learning is a key challenge for the theory of neural networks. Many theoretical works do not explicitly model training data, or assume that inputs are drawn component-wise inde ...

2021

Learning Gaussian Mixtures with Generalized Linear Models: Precise Asymptotics in High-dimensions

Florent Gérard Krzakala, Lenka Zdeborová, Bruno Loureiro, Gabriele Sicuro

Generalised linear models for multi-class classification problems are one of the fundamental building blocks of modern machine learning tasks. In this manuscript, we characterise the learning of a mixture of K Gaussians with generic means and covariances v ...

2021

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 ...

2021

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