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Found 10 papers, 3 papers with code
Permutation recovery of spikes in noisy high-dimensional tensor estimation
We determine the sample complexity required for gradient flow to efficiently recover all spikes, without imposing any assumptions on the separation of the signal-to-noise ratios (SNRs).
Stochastic gradient descent in high dimensions for multi-spiked tensor PCA
The order in which correlations become macroscopic depends on their initial values and the corresponding SNRs, leading to either exact recovery or recovery of a permutation of the spikes.
Langevin dynamics for high-dimensional optimization: the case of multi-spiked tensor PCA
We study nonconvex optimization in high dimensions through Langevin dynamics, focusing on the multi-spiked tensor PCA problem.
Applying statistical learning theory to deep learning
Although statistical learning theory provides a robust framework to understand supervised learning, many theoretical aspects of deep learning remain unclear, in particular how different architectures may lead to inductive bias when trained using gradient based methods.
Learning curves for the multi-class teacher-student perceptron
For Gaussian teacher weights, we investigate the performance of ERM with both cross-entropy and square losses, and explore the role of ridge regularisation in approaching Bayes-optimality.
Fluctuations, Bias, Variance & Ensemble of Learners: Exact Asymptotics for Convex Losses in High-Dimension
From the sampling of data to the initialisation of parameters, randomness is ubiquitous in modern Machine Learning practice.
Graph-based Approximate Message Passing Iterations
Approximate-message passing (AMP) algorithms have become an important element of high-dimensional statistical inference, mostly due to their adaptability and concentration properties, the state evolution (SE) equations.
Learning Gaussian Mixtures with Generalised Linear Models: Precise Asymptotics in High-dimensions
Generalised linear models for multi-class classification problems are one of the fundamental building blocks of modern machine learning tasks.
Multi-class Classification
Vocal Bursts Intensity Prediction
Learning curves of generic features maps for realistic datasets with a teacher-student model
While still solvable in a closed form, this generalization is able to capture the learning curves for a broad range of realistic data sets, thus redeeming the potential of the teacher-student framework.
Asymptotic errors for convex penalized linear regression beyond Gaussian matrices
We consider the problem of learning a coefficient vector $x_{0}$ in $R^{N}$ from noisy linear observations $y=Fx_{0}+w$ in $R^{M}$ in the high dimensional limit $M, N$ to infinity with $\alpha=M/N$ fixed.
