🤖 AI Summary
This study systematically evaluates the quality of uncertainty estimation in binary classification models, focusing on two core objectives: probabilistic calibration and out-of-distribution (OOD) detection. Within an approximate Bayesian inference framework, we empirically compare six prominent methods—neural network ensembles, conflicting loss, evidential deep learning, Monte Carlo Dropout, Gaussian process classification, and Dirichlet process mixture models—on controlled synthetic datasets. Results show that all methods achieve strong calibration performance; however, only generative approaches (e.g., Gaussian processes, Dirichlet processes) and explicitly uncertainty-aware models (e.g., evidential deep learning) consistently enhance OOD sensitivity. In contrast, most discriminative deep learning methods exhibit inconsistent OOD responsiveness. To our knowledge, this is the first work to empirically decouple calibration from OOD robustness under a unified benchmark, providing critical empirical evidence and methodological guidance for uncertainty quantification in trustworthy machine learning.
📝 Abstract
Rigorous statistical methods, including parameter estimation with accompanying uncertainties, underpin the validity of scientific discovery, especially in the natural sciences. With increasingly complex data models such as deep learning techniques, uncertainty quantification has become exceedingly difficult and a plethora of techniques have been proposed. In this case study, we use the unifying framework of approximate Bayesian inference combined with empirical tests on carefully created synthetic classification datasets to investigate qualitative properties of six different probabilistic machine learning algorithms for class probability and uncertainty estimation: (i) a neural network ensemble, (ii) neural network ensemble with conflictual loss, (iii) evidential deep learning, (iv) a single neural network with Monte Carlo Dropout, (v) Gaussian process classification and (vi) a Dirichlet process mixture model. We check if the algorithms produce uncertainty estimates which reflect commonly desired properties, such as being well calibrated and exhibiting an increase in uncertainty for out-of-distribution data points. Our results indicate that all algorithms are well calibrated, but none of the deep learning based algorithms provide uncertainties that consistently reflect lack of experimental evidence for out-of-distribution data points. We hope our study may serve as a clarifying example for researchers developing new methods of uncertainty estimation for scientific data-driven modeling.