Convergence rates of deep ReLU networks for multiclass classification
| Autor: | Bos, Thijs, Schmidt-Hieber, Johannes |
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| Přispěvatelé: | Mathematics of Operations Research, Digital Society Institute |
| Rok vydání: | 2022 |
| Předmět: |
FOS: Computer and information sciences
Statistics and Probability Computer Science - Machine Learning conditional class probabilities Mathematics - Statistics Theory Statistics Theory (math.ST) Convergence rates multiclass classification Machine Learning (cs.LG) FOS: Mathematics Primary: 62G05 secondary: 63H30 68T07 ReLu networks margin condition Statistics Probability and Uncertainty |
| Zdroj: | Electronic Journal of Statistics, 16(1), 2724-2773. Institute of Mathematical Statistics |
| ISSN: | 1935-7524 |
| DOI: | 10.1214/22-ejs2011 |
| Popis: | 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. Comment: convergence rates, ReLU networks, multiclass classification, conditional class probabilities, margin condition |
| Databáze: | OpenAIRE |
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