Convergence rates of deep ReLU networks for multiclass classification
Abstract
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 crossentropy 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 nearzero behaviour via a margintype condition.
 Publication:

arXiv eprints
 Pub Date:
 August 2021
 arXiv:
 arXiv:2108.00969
 Bibcode:
 2021arXiv210800969B
 Keywords:

 Mathematics  Statistics Theory;
 Computer Science  Machine Learning;
 Primary: 62G05;
 secondary: 63H30;
 68T07
 EPrint:
 convergence rates, ReLU networks, multiclass classification, conditional class probabilities, margin condition