4 papers
Minimax Limits of k-Fold Cross-Validation via Majority
Ido Nachum, Rüdiger Urbanke, Thomas Weinberger
We study the mean-squared error of -fold cross-validation as a risk estimator, with particular emphasis on how its accuracy depends on the number of folds . Despite the wides…
The Structure of Cross-Validation Error: Stability, Covariance, and Minimax Limits
Ido Nachum, Rüdiger Urbanke, Thomas Weinberger
Despite ongoing theoretical research on cross-validation (CV), many theoretical questions remain widely open. This motivates our investigation into how properties of algorithm-dist…
Batch Normalization Decomposed
Ido Nachum, Marco Bondaschi, Michael Gastpar +1
\emph{Batch normalization} is a successful building block of neural network architectures. Yet, it is not well understood. A neural network layer with batch normalization comprises…
Which Algorithms Have Tight Generalization Bounds?
Michael Gastpar, Ido Nachum, Jonathan Shafer +1
We study which machine learning algorithms have tight generalization bounds. First, we present conditions that preclude the existence of tight generalization bounds. Specifically,…