Understanding of Non-linear Parametric Regression and Classification Models: A Taylor Series based Approach

Abstract

Machine learning methods like classification and regression models are specific solutions for pattern recognition problems. Subsequently, the patterns ’found’ by these methods can be used either in an exploration manner or the model converts the patterns into discriminative values or regression predictions. In both application scenarios it is important to visualize the data-basis of the model, because this unravels the patterns. In case of linear classifiers or linear regression models the task is straight forward, because the model is characterized by a vector which acts as variable weighting and can be visualized. For non-linear models the visualization task is not solved yet and therefore these models act as ’black box’ systems. In this contribution we present a framework, which approximates a given trained parametric model (either classification or regression model) by a series of polynomial models derived from a Taylor expansion of the original non-linear model’s output function. These polynomial models can be visualized until the second order and subsequently interpreted. This visualization opens the ways to understand the data basis of a trained non-linear model and it allows estimating the degree of its non-linearity. By doing so the framework helps to understand non-linear models used for pattern recognition tasks and unravel patterns these methods were using for their predictions.