As machine learning systems become increasingly integrated into real-world applications, accurately representing uncertainty is crucial for enhancing their safety, robustness, and reliability. Training neural networks to fit high-dimensional probability distributions via maximum likelihood has become an effective method for uncertainty quantification. However, such models often exhibit poor calibration, leading to overconfident predictions. Traditional metrics like Expected Calibration Error (ECE) and Negative Log Likelihood (NLL) have limitations, including biases and parametric assumptions. This paper proposes a new approach using conditional kernel mean embeddings to measure calibration discrepancies without these biases and assumptions. Preliminary experiments on synthetic data demonstrate the method's potential, with future work planned for more complex applications.
Young et al. (Mon,) studied this question.