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Generalization Error Rates in Kernel Regression: The Crossover from the Noiseless to Noisy Regime
Hugo Cui, Bruno Loureiro, Florent Krzakala +1
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 vari…
Learning curves of generic features maps for realistic datasets with a teacher-student model
Bruno Loureiro, Cédric Gerbelot, Hugo Cui +4
Teacher-student models provide a framework in which the typical-case performance of high-dimensional supervised learning can be described in closed form. The assumptions of Gaussia…
The Gaussian equivalence of generative models for learning with shallow neural networks
Sebastian Goldt, Bruno Loureiro, Galen Reeves +3
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 explici…
Generalization error in high-dimensional perceptrons: Approaching Bayes error with convex optimization
Benjamin Aubin, Florent Krzakala, Yue M. Lu +1
We consider a commonly studied supervised classification of a synthetic dataset whose labels are generated by feeding a one-layer neural network with random iid inputs. We study th…
The role of regularization in classification of high-dimensional noisy Gaussian mixture
Francesca Mignacco, Florent Krzakala, Yue M. Lu +1
We consider a high-dimensional mixture of two Gaussians in the noisy regime where even an oracle knowing the centers of the clusters misclassifies a small but finite fraction of th…
Dense Limit of the Dawid-Skene Model for Crowdsourcing and Regions of Sub-optimality of Message Passing Algorithms
Christian Schmidt, Lenka Zdeborová
Crowdsourcing is a strategy to categorize data through the contribution of many individuals. A wide range of theoretical and algorithmic contributions are based on the model of Daw…