  Scientists frequently prioritize learning from data rather than training the
best possible model; however, research in machine learning often prioritizes
the latter. Marginal contribution feature importance (MCI) was developed to
break this trend by providing a useful framework for quantifying the
relationships in data. In this work, we aim to improve upon the theoretical
properties, performance, and runtime of MCI by introducing ultra-marginal
feature importance (UMFI), which uses dependence removal techniques from the AI
fairness literature as its foundation. We first propose axioms for feature
importance methods that seek to explain the causal and associative
relationships in data, and we prove that UMFI satisfies these axioms under
basic assumptions. We then show on real and simulated data that UMFI performs
better than MCI, especially in the presence of correlated interactions and
unrelated features, while partially learning the structure of the causal graph
and reducing the exponential runtime of MCI to super-linear.
