Uncertainty quantification by direct propagation of shallow ensembles

TL;DR

This paper introduces a practical method called direct propagation of shallow ensembles for uncertainty quantification in machine learning, emphasizing ease of implementation, minimal computational overhead, and effective error propagation in applications like chemistry and materials science.

Contribution

The paper proposes a new uncertainty quantification approach that balances accuracy and simplicity, enabling straightforward integration with existing models and effective error propagation without strong correlation assumptions.

Findings

The method achieves a good trade-off between ease of use and accuracy.

Benchmarks demonstrate reliable uncertainty estimates across datasets.

Application to atomistic machine learning highlights the method's effectiveness.

Abstract

Statistical learning algorithms provide a generally-applicable framework to sidestep time-consuming experiments, or accurate physics-based modeling, but they introduce a further source of error on top of the intrinsic limitations of the experimental or theoretical setup. Uncertainty estimation is essential to quantify this error, and make application of data-centric approaches more trustworthy. To ensure that uncertainty quantification is used widely, one should aim for algorithms that are reasonably accurate, but also easy to implement and apply. In particular, including uncertainty quantification on top of an existing architecture should be straightforward, and add minimal computational overhead. Furthermore, it should be easy to manipulate or combine multiple machine-learning predictions, propagating uncertainty over further modeling steps. We compare several well-established uncertainty quantification frameworks against these requirements, and propose a practical approach, which we dub direct propagation of shallow ensembles, that provides a good compromise between ease of use and accuracy. We present benchmarks for generic datasets, and an in-depth study of applications to the field of atomistic machine learning for chemistry and materials. These examples underscore the importance of using a formulation that allows propagating errors without making strong assumptions on the correlations between different predictions of the model.