Feature Relevancy, Necessity and Usefulness: Complexity and Algorithms

TL;DR

This paper advances techniques for identifying relevant, necessary, and useful features in complex models like neural networks, providing efficient algorithms and a new global usefulness measure with practical experiments.

Contribution

It introduces improved algorithms for detecting feature relevance and necessity, and proposes a novel global usefulness measure applicable to various models.

Findings

Necessity detection is efficient even in neural networks.

New algorithms successfully identify relevant and necessary features.

The usefulness measure correlates with model behavior across datasets.

Abstract

Given a classification model and a prediction for some input, there are heuristic strategies for ranking features according to their importance in regard to the prediction. One common approach to this task is rooted in propositional logic and the notion of \textit{sufficient reason}. Through this concept, the categories of relevant and necessary features were proposed in order to identify the crucial aspects of the input. This paper improves the existing techniques and algorithms for deciding which are the relevant and/or necessary features, showing in particular that necessity can be detected efficiently in complex models such as neural networks. We also generalize the notion of relevancy and study associated problems. Moreover, we present a new global notion (i.e. that intends to explain whether a feature is important for the behavior of the model in general, not depending on a particular input) of \textit{usefulness} and prove that it is related to relevancy and necessity. Furthermore, we develop efficient algorithms for detecting it in decision trees and other more complex models, and experiment on three datasets to analyze its practical utility.