Ultra Marginal Feature Importance

Scientists frequently prioritize learning from data rather than training the best possible model; however, research in machine learning often prioritizes the latter. The development of marginal feature importance methods, such as marginal contribution feature importance, attempts to break this trend by providing a useful framework for explaining relationships in data in an interpretable fashion. In this work, we generalize the framework of marginal contribution feature importance to improve performance with regards to detecting correlated interactions and reducing runtime. To do so, we consider "information subsets" of the set of features $F$ and show that our importance metric can be computed directly after applying fair representation learning methods from the AI fairness literature. The methods of optimal transport and linear regression are considered and explored experimentally for removing all the information of our feature of interest $f$ from the feature set $F$. Given these implementations, we show on real and simulated data that ultra marginal feature importance performs at least as well as marginal contribution feature importance, with substantially faster computation time and better performance in the presence of correlated interactions and unrelated features.