The Gamma Test

Abstract

The Gamma Test is a non-linear modelling analysis tool that allows us to quantify the extent to which a numerical input/output data set can be expressed as a smooth relationship. In essence, it allows us to efficiently calculate that part of the variance of the output that cannot be accounted for by the existence of any smooth model based on the inputs, even though this model is unknown. A key aspect of this tool is its speed: the Gamma Test has time complexity O(Mlog M), where M is the number of datapoints. For data sets consisting of a few thousand points and a reasonable number of attributes, a single run of the Gamma Test typically takes a few seconds. In this chapter we will show how the Gamma Test can be used in the construction of predictive models and classifiers for numerical data. In doing so, we will demonstrate the use of this technique for feature selection, and for the selection of embedding dimension when dealing with a time-series.