Utility Metrics for Assessment and Subset Selection of Input Variables for Linear Estimation [Tips & Tricks]

This tutorial article introduces the utility metric and its generalizations, which allow for a quick-and-dirty quantitative assessment of the relative importance of the different input variables in a linear estimation model. In particular, we show how these metrics can be cheaply calculated, thereby making them very attractive for model interpretation, online signal quality assessment, or greedy variable selection. The main goal of this article is to provide a transparent and consistent framework that consolidates, unifies, and extends the existing results in this area. In particular, we (1) introduce the basic utility metric and show how it can be calculated at virtually no cost, (2) generalize it toward group-utility and noise-impact metrics, and (3) further extend it to cope with linearly dependent inputs and minimum norm requirements.