For classification problems, trained deep neural networks return probabilities of class memberships. In this work we study convergence of the learned probabilities to the true conditional class probabilities. More specifically we consider sparse deep ReLU network reconstructions minimizing cross-entropy loss in the multiclass classification setup. Interesting phenomena occur when the class membership probabilities are close to zero. Convergence rates are derived that depend on the near-zero behaviour via a margin-type condition.
The research has been supported by the NWO/STAR grant 613.009.034b and the NWO Vidi grant VI.Vidi.192.021.
We thank the two referees and the editor for many helpful suggestions.
"Convergence rates of deep ReLU networks for multiclass classification." Electron. J. Statist. 16 (1) 2724 - 2773, 2022. https://doi.org/10.1214/22-EJS2011