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.
- Pub Date:
- August 2021
- Mathematics - Statistics Theory;
- Computer Science - Machine Learning;
- Primary: 62G05;
- secondary: 63H30;
- convergence rates, ReLU networks, multiclass classification, conditional class probabilities, margin condition