Implications on Feature Detection when using the Benefit-Cost Ratio

TL;DR

This paper investigates how using the benefit-cost ratio in feature selection affects the ability to identify relevant features, revealing potential pitfalls when cost differences are large or effect sizes are small.

Contribution

It provides a simulation-based analysis of the implications of the benefit-cost ratio in feature detection, highlighting risks and proposing mitigation strategies.

Findings

Large cost differences reduce relevant feature detection

Benefit-cost ratio can favor noise features over relevant ones

Rescaling costs or using hyperparameters can mitigate issues

Abstract

In many practical machine learning applications, there are two objectives: one is to maximize predictive accuracy and the other is to minimize costs of the resulting model. These costs of individual features may be financial costs, but can also refer to other aspects, like for example evaluation time. Feature selection addresses both objectives, as it reduces the number of features and can improve the generalization ability of the model. If costs differ between features, the feature selection needs to trade-off the individual benefit and cost of each feature. A popular trade-off choice is the ratio of both, the BCR (benefit-cost ratio). In this paper we analyze implications of using this measure with special focus to the ability to distinguish relevant features from noise. We perform a simulation study for different cost and data settings and obtain detection rates of relevant features and empirical distributions of the trade-off ratio. Our simulation study exposed a clear impact of the cost setting on the detection rate. In situations with large cost differences and small effect sizes, the BCR missed relevant features and preferred cheap noise features. We conclude that a trade-off between predictive performance and costs without a controlling hyperparameter can easily overemphasize very cheap noise features. While the simple benefit-cost ratio offers an easy solution to incorporate costs, it is important to be aware of its risks. Avoiding costs close to 0, rescaling large cost differences, or using a hyperparameter trade-off are ways to counteract the adverse effects exposed in this paper.