On the Relationship between Feature Selection Metrics and Accuracy

Feature selection metrics are commonly used in the machine learning pipeline to rank and select features before creating a predictive model. While many different metrics have been proposed for feature selection, final models are often evaluated by accuracy. In this paper, we consider the relationship between common feature selection metrics and accuracy. In particular, we focus on misorderings: cases where a feature selection metric may rank features differently than accuracy would. We analytically investigate the frequency of misordering for a variety of feature selection metrics as a function of parameters that represent how a feature partitions the data. Our analysis reveals that different metrics have systematic differences in how likely they are to misorder features which can happen over a wide range of partition parameters. We then perform an empirical evaluation with different feature selection metrics on several real-world datasets to measure misordering. Our empirical results generally match our analytical results, illustrating that misordering features happens in practice and can provide some insight into the performance of feature selection metrics.