Theoretical guarantees on the performance of the proposed divergence-based empirical risk functions compared to traditional approaches in the presence of label noise or distribution shift can be analyzed based on the properties of the chosen divergences. For instance, f-divergences and α-Rényi divergences have specific characteristics that make them suitable for handling noisy labels and distribution shifts.
Robustness to Noisy Labels: The divergence-based empirical risk functions are designed to be more robust to noisy pseudo-labels, where the pseudo-labels may differ from the true labels of the unlabeled data samples. The theoretical guarantees stem from the properties of f-divergences and α-Rényi divergences, which enable the models to learn from noisy data more effectively.
Upper Bounds on True Risk: By providing an upper bound on the true risk of the empirical risk functions under certain conditions, the theoretical guarantees ensure that the models trained using these divergence-based approaches have a performance ceiling that is quantifiable. This can help in understanding the limitations and capabilities of the models in semi-supervised learning scenarios.
Comparison with Traditional Approaches: The theoretical analysis can demonstrate the superiority of the divergence-based empirical risk functions over traditional self-training methods in terms of robustness, convergence properties, and generalization performance. These guarantees provide insights into the effectiveness of the proposed approaches in challenging learning scenarios.