Uncertainty in Equation Learning

2022

Conference Paper

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Equation learning is a deep learning framework for explainable machine learning in regression settings, with applications in engineering and the natural sciences. Equation learners typically do not capture uncertainty about the model or its predictions, although uncertainty is often highly structured and particularly relevant for these kinds of applications. We show how simple, yet effective, forms of Bayesian deep learning can be used to build structure and explainable uncertainty over a set of found equations. Specifically, we use a mixture of Laplace approximations, where each mixture component captures a different equation structure, and the local Laplace approximations capture parametric uncertainty within one family of equations. We present results on both synthetic and real world examples.

@inproceedings{Werner2022:UncertaintyEQL,
  title = {Uncertainty in Equation Learning},
  author = {Werner, Matthias and Junginger, Andrej and Hennig, Philipp and Martius, Georg},
  booktitle = {Proceedings of the Genetic and Evolutionary Computation Conference Companion (GECCO)},
  pages = {2298-2305},
  publisher = {Association for Computing Machinery},
  year = {2022},
  doi = {10.1145/3520304.3533964}
}