Interpretable transformed ANOVA approximation on the example of the prevention of forest fires

TL;DR

This paper introduces an interpretable ANOVA-based approximation method using a transformed orthonormal basis tailored for normally distributed data, demonstrated on forest fire prediction data.

Contribution

It develops a novel transformation-based orthonormal system in L2 space for explainable ANOVA approximation with Z-score data, enhancing interpretability in machine learning.

Findings

Attribute ranking identifies key variables for fire detection.

Method effectively applies to forest fire dataset from UCI.

Provides insights into variable importance for fire prediction.

Abstract

The distribution of data points is a key component in machine learning. In most cases, one uses min-max normalization to obtain nodes in $[0,1]$ or Z-score normalization for standard normal distributed data. In this paper, we apply transformation ideas in order to design a complete orthonormal system in the $\mathrm{L}_2$ space of functions with the standard normal distribution as integration weight. Subsequently, we are able to apply the explainable ANOVA approximation for this basis and use Z-score transformed data in the method. We demonstrate the applicability of this procedure on the well-known forest fires data set from the UCI machine learning repository. The attribute ranking obtained from the ANOVA approximation provides us with crucial information about which variables in the data set are the most important for the detection of fires.