4 papers · 1 filter
Semi-Supervised Learning on Graphs using Graph Neural Networks
Juntong Chen, Claire Donnat, Olga Klopp +1
Graph neural networks (GNNs) work remarkably well in semi-supervised node regression, yet a rigorous theory explaining when and why they succeed remains lacking. To address this ga…
Statistical Guarantees for High-Dimensional Stochastic Gradient Descent
Jiaqi Li, Zhipeng Lou, Johannes Schmidt-Hieber +1
Stochastic Gradient Descent (SGD) and its Ruppert-Polyak averaged variant (ASGD) lie at the heart of modern large-scale learning, yet their theoretical properties in high-dimension…
On the expressivity of deep Heaviside networks
Insung Kong, Juntong Chen, Sophie Langer +1
We show that deep Heaviside networks (DHNs) have limited expressiveness but that this can be overcome by including either skip connections or neurons with linear activation. We pro…
Asymptotics of Stochastic Gradient Descent with Dropout Regularization in Linear Models
Jiaqi Li, Johannes Schmidt-Hieber, Wei Biao Wu
This paper proposes an asymptotic theory for online inference of the stochastic gradient descent (SGD) iterates with dropout regularization in linear regression. Specifically, we e…