2.1 Elementarisation of machine learning with data-based DTs

ML, as described by Shalev-Shwartz & Ben-David (2014) and Hastie et al. (2009), is a heterogeneous field that includes different methods and learning algorithms for solving different types of tasks automatically in a statistical learning framework. The unifying element between all methods is that they are based on training data. We focus on the subspecies of supervised ML, specifically on classification tasks that can be addressed with DTs. The first contribution of this paper is the elementarised presentation of a data-based DT construction process that simplifies selected aspects of professional DT algorithms so that it is suitable for teaching in school and still serves as an example for ML. Our teaching unit and the research approach will be outlined later based on this elementarisation.

2.1.1 The statistical learning framework for creating classifiers

Classification involves the task of providing objects or individuals of a population with (ideally) correct labels concerning a certain question. In statistics, a population is a set of individuals, objects, or events that are of interest to a particular question or statistical investigation. (Kauermann & Küchenhoff, 2011, p. 5). Typical classification problems are assigning a patient with a diagnosis or classifying emails as “spam” or “not spam.” The possible labels come from a label set, depending on which we speak of a binary classification problem (two possible labels) or a multiclass classification problem (a finite set of more than two labels). The statistical learning framework is constituted by two main aspects that are described in the following (F1 and F2):

• F1 – Creating a classifier based on training data

In a statistical learning framework, the task of a learning algorithm is to create a classifier that predicts a label for any given object in the population. The labels are values of a so-called target variable. To make an informed prediction, an object is represented by a set of characteristics displayed as a vector (called instance) from an input space. Since the characteristics inform the choice of the predicted label, they are called predictor variables. The creation of a classifier is based on training examples, i.e., objects from the population from which predictor variables’ values and correct labels are known. A set of training examples is called training data that can be represented in a data table, as illustrated below (Figure 2).

• F2 – Evaluating a classifier based on test data

As a measure of success in a statistical learning framework, the aim is to quantify the error of a classifier, which is the probability that it does not predict the correct label on a randomly chosen object from the population. Practically, the error is estimated by using test data to calculate the misclassification rate. Test data is structurally identical to training data but was not used to create the classifier.

2.1.2 Data-based construction of DTs as classifiers

As characterized by Shalev-Shwartz & Ben-David (2014, p. 212), a DT is a type of classifier that predicts the label of an object by using a hierarchical structure of decision rules that progress from a root node of a tree to leaf nodes. At each node on the root-to-leaf path, the successor child node is chosen on the basis of a splitting of the input space. The internal nodes of the decision tree (excluding the leaf nodes) are referred to as split nodes. Each split node utilizes one of the predictor variables to divide the data. A leaf node always contains a label. This is exemplified by the simple DT in Figure 1 for the context of online platforms predicting whether users play online games frequently or rarely based on ownership of digital devices. The data-based creation of DTs is described below.