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math.ST2025
A novel statistical approach to analyze image classification
Juntong Chen, Sophie Langer, Johannes Schmidt-Hieber
The recent statistical theory of neural networks focuses on nonparametric denoising problems that treat randomness as additive noise. Variability in image classification datasets d…
math.ST2024
Statistical theory for image classification using deep convolutional neural networks with cross-entropy loss under the hierarchical max-pooling model
Michael Kohler, Sophie Langer
Convolutional neural networks (CNNs) trained with cross-entropy loss have proven to be extremely successful in classifying images. In recent years, much work has been done to also…
math.ST2024
Dropout Regularization Versus -Penalization in the Linear Model
Gabriel Clara, Sophie Langer, Johannes Schmidt-Hieber
We investigate the statistical behavior of gradient descent iterates with dropout in the linear regression model. In particular, non-asymptotic bounds for the convergence of expect…