Aurora Grefsrud: Convergence properties of probability and uncertainty estimates in non-deterministic machine learning classification

Abstract

Conditional class probability estimation is a difficult, but important task in data-driven modeling. Uncertainty quantification (UQ) aims to capture the fidelity of such estimates but is often not comparable across models due to vastly different theoretical frameworks, making it difficult to evaluate their usefulness. By employing a uniting theoretical, statistical framework for UQ based on Monte Carlo estimates, we empirically compare the performance of 6 different machine learning algorithms for class probability estimation: (i) a Neural Network (NN) ensemble, (ii) NN ensemble with conflictual loss, (iii) evidential deep learning, (iv) NN with Monte Carlo Dropout, (v) Gaussian Process classification and (vi) a Dirichlet Process Mixture Model. The models are trained on continuous data with known conditional class probability distributions, which introduces a varying source of irreducible uncertainty over the input feature space. We evaluate performance using an extensive set of metrics, including comparisons to the known distribution of the data, and show that all the algorithms have some bias for out-of-distribution probability and uncertainty estimates. These properties are critical to know about when training, evaluating and using the models. We provide this framework for UQ, model comparison and asymptotic investigations to further understanding of the strengths and limitations of machine learning classification algorithms when trained on non-deterministic data.