  Inductive Logic Programming (ILP) is a form of machine learning (ML) which in
contrast to many other state of the art ML methods typically produces highly
interpretable and reusable models. However, many ILP systems lack the ability
to naturally learn from any noisy or partially misclassified training data. We
introduce the relaxed learning from failures approach to ILP, a noise handling
modification of the previously introduced learning from failures (LFF) approach
which is incapable of handling noise. We additionally introduce the novel Noisy
Popper ILP system which implements this relaxed approach and is a modification
of the existing Popper system. Like Popper, Noisy Popper takes a
generate-test-constrain loop to search its hypothesis space wherein failed
hypotheses are used to construct hypothesis constraints. These constraints are
used to prune the hypothesis space, making the hypothesis search more
efficient. However, in the relaxed setting, constraints are generated in a more
lax fashion as to avoid allowing noisy training data to lead to hypothesis
constraints which prune optimal hypotheses. Constraints unique to the relaxed
setting are generated via hypothesis comparison. Additional constraints are
generated by weighing the accuracy of hypotheses against their sizes to avoid
overfitting through an application of the minimum description length. We
support this new setting through theoretical proofs as well as experimental
results which suggest that Noisy Popper improves the noise handling
capabilities of Popper but at the cost of overall runtime efficiency.
