Fast Prediction of New Feature Utility

We study the new feature utility prediction problem: statistically testing whether adding a new feature to the data representation can improve predictive accuracy on a supervised learning task. In many applications, identifying new informative features is the primary pathway for improving performance. However, evaluating every potential feature by re-training the predictor with it can be costly. The paper describes an efficient, learner-independent technique for estimating new feature utility without re-training based on the current predictor's outputs. The method is obtained by deriving a connection between loss reduction potential and the new feature's correlation with the loss gradient of the current predictor. This leads to a simple yet powerful hypothesis testing procedure, for which we prove consistency. Our theoretical analysis is accompanied by empirical evaluation on standard benchmarks and a large-scale industrial dataset.