Fast and Accurate Uncertainty Estimation in Chemical Machine Learning

TL;DR

This paper introduces a fast, cost-effective scheme for estimating uncertainty in chemical machine learning models using resampling and model averaging, enhancing reliability and enabling active learning.

Contribution

It proposes a resampling-based uncertainty estimation method that is computationally inexpensive, adaptable to various models, and improves prediction reliability in chemical applications.

Findings

Reliable uncertainty estimates for molecular energetics

Effective uncertainty estimation for nuclear chemical shieldings

Applicable to energy differences and forces

Abstract

We present a scheme to obtain an inexpensive and reliable estimate of the uncertainty associated with the predictions of a machine-learning model of atomic and molecular properties. The scheme is based on resampling, with multiple models being generated based on sub-sampling of the same training data. The accuracy of the uncertainty prediction can be benchmarked by maximum likelihood estimation, which can also be used to correct for correlations between resampled models, and to improve the performance of the uncertainty estimation by a cross-validation procedure. In the case of sparse Gaussian Process Regression models, this resampled estimator can be evaluated at negligible cost. We demonstrate the reliability of these estimates for the prediction of molecular energetics, and for the estimation of nuclear chemical shieldings in molecular crystals. Extension to estimate the uncertainty in energy differences, forces, or other correlated predictions is straightforward. This method can be easily applied to other machine learning schemes, and will be beneficial to make data-driven predictions more reliable, and to facilitate training-set optimization and active-learning strategies.