$TCP_\alpha$: Margin-Controlled Confidence estimation for reliable Music Information Retrieval
Deep neural networks are often overconfident, assigning high confidence even to incorrect predictions. Consequently, users lack a reliable signal for deciding when a prediction can be trusted. Post-hoc confidence estimation addresses this by training a lightweight auxiliary head over a frozen classifier. Existing targets, however, suffer from inherent ambiguity: they assign overlapping confidence values to correct and incorrect predictions, while errors near the decision boundary receive confidence scores indistinguishable from correct predictions. In this work, we propose $TCP_\alpha$, a novel confidence target that resolves these limitations by introducing a margin-controlled penalty for misclassified samples. We prove that $TCP_\alpha$ guarantees complete separation between the target values of correct and incorrect predictions, with a separation margin that is independent of the number of classes and increases monotonically with the penalty parameter. Since accurate classifiers naturally produce very few errors, learning these targets results in a severely imbalanced regression problem. We therefore present a systematic study of training strategies for learning under this imbalance and identify an effective training configuration through extensive ablation studies. We evaluate the proposed approach on r\=aga identification, investigate its robustness under domain shift, and further validate it on frame-wise ornamentation detection without modifying the selected configuration. Across all settings, $TCP_\alpha$ consistently outperforms existing confidence targets for failure prediction. Rejecting only the least-confident 8\% of predictions improves the base model's macro-F1 from 0.89 to 0.98, while fine-tuning the confidence head with only 5\% labeled samples from a new corpus effectively restores performance under domain shift.