Binary recursive partitioning process continues until none of the nodes can split or stopping rule of tree growth is reached. Binary recursive partitioning process splits each node of tree into only two nodes, but some of tree algorithms can generate multiway splits [20]. Quest classification tree algorithm is developed by Loh and Shih in 1997, and this model generates binary splits [32]. This method, unlike other classification algorithms such as CART and THAID, does not use exhaustive search algorithm (because these algorithms suffer from variable selection bias) and so improves computational cost and variable selection bias.

A crucial step in creating a decision tree is to find the best split of the data into two subsets. This is also used in the scikit-learn library from Python, which is often used in practice to build a Decision Tree. It’s important to keep in mind the limitations of decision trees, of which the most prominent one is the tendency to overfit.

Classification tree labels records and assigns them to discrete classes. Classification tree can also provide the measure of confidence that the classification is correct. XLMiner uses the Gini index as the splitting criterion, which is a commonly used measure of inequality. A Gini index of 0 indicates that all records in the node belong to the same category. A Gini index of 1 indicates that each record in the node belongs to a different category. For a complete discussion of this index, please see Leo Breiman’s and Richard Friedman’s book, Classification and Regression Trees (3).

These approaches unlike classic tree approaches generate several trees that this advantage makes researchers to select the best tree based on study aim. Because in some studies, sensitivity is important for researcher and what is classification tree method in other studies, specificity is important. Some of tree-based methods such as CART, QUEST, C4.5, and CHAID fit a constant model in the nodes of tree, thus a large tree is generated, and this tree has hard interpretation.

## Classification and regression trees

Decision Trees (DTs) are a non-parametric supervised learning method used

for classification and regression. The goal is to create a model that predicts the value of a

target variable by learning simple decision rules inferred from the data

## Lesson 11: Tree-based Methods

features. Figure 3 shows the relative frequency at which factors occur in trained decision trees (i.e., feature importance). In accordance with the logistic regression analysis, the most important factors are age, age of onset of depression, HAMD score at intake, number of past depressive episodes, and months since the last depressive episode.

Our results indicate that decision trees can improve upon HAMD-based relapse prediction in terms of better accuracy and specificity. Gradient boosting techniques can further improve prediction performance by combining multiple trees into an ensemble. Boosted trees and logistic regression classifiers that used the same factors had comparable levels of accuracy, specificity, and sensitivity. The stopping criterion of simulation chain in OML’S Bayesian classification trees approach has two steps. The first step includes the plot of iterations against accuracy measures (false and positive negative rate and misclassification rate), log posterior, log likelihood, and tree size.

## Classification Tree Method

The CTM is a black-box testing method and supports any type of system under test. This includes (but is not limited to) hardware systems, integrated hardware-software systems, plain software systems, including embedded software, user interfaces, operating systems, parsers, and others (or subsystems of mentioned systems). Because it can take a set of training data and construct a decision tree, Classification Tree Analysis is a form of machine learning, like a neural network. However, unlike a neural network such as the Multi-Layer Perceptron (MLP) in TerrSet, CTA produces a white box solution rather than a black box because the nature of the learned decision process is explicitly output. The structure of the tree gives us information about the decision process.

The tree grows by recursively splitting data at each internode into new internodes containing progressively more homogeneous sets of training pixels. A newly grown internode may become a leaf when it contains training pixels from only one class, or pixels from one class dominate the population of pixels in that internode, and the dominance is at an acceptable level specified by the user. When there are no more internodes to split, the final classification tree rules are formed. OML and Hu in 2011 compared the performance of Bayesian classification trees with the CART of Breiman et al., and they concluded that the Bayesian approach has higher sensitivity and specificity in comparison to CART. They also investigated overfitting of the Bayesian approach by using cross-validation method, and this approach did not show any evidence of overfitting [98]. In this simulation algorithm, q(

T

,

T

∗

) generates

T

- The stopping rule of simulation algorithm for regression tree like classification tree includes two steps.
- Also, despite some advantages for Bayesian tree approaches in comparison with classic tree models, the number of published articles based on using Bayesian tree approaches for data analysis is low.
- We start with the entire space and recursively divide it into smaller regions.
- The basic idea of the classification tree method is to separate the input data characteristics of the system under test into different classes that directly reflect the relevant test scenarios (classifications).
- Exhaustive CHAID algorithm is proposed by Biggs et al. in 1991 and this algorithm is an improved CHAID method.

∗

from T by randomly selecting among four steps.

The third section presents several alternatives to the algorithms used by CART. We begin with a look at one class of algorithms – including QUEST, CRUISE, and GUIDE– which is designed to reduce potential bias toward variables with large numbers of available splitting values. Next, we explore C4.5, another program popular in the artificial-intelligence and machine-learning communities. C4.5 offers the added functionality of converting any tree to a series of decision rules, providing an alternative means of viewing and interpreting its results. Finally, we discuss chi-square automatic interaction detection (CHAID), an early classification-tree construction algorithm used with categorical predictors. The section concludes with a brief comparison of the characteristics of CART and each of these alternative algorithms.

In this approach, prior distributions are defined over the splitting node (S), splitting variable (V), splitting rule (R), tree size (𝒦), and parameters of data distribution in terminal nodes (

ѱ

). Classic tree approaches use only observations for data analysis, but Bayesian approaches combine prior information with observations. Classification trees have been positioned as a key technique in classification problem due to their unique and easy-to-interpret visualization of the fitted model.