Decision Tree (DT) Model

A Decision Tree (DT) Model is a prediction model that follows a decision tree pattern (composed of if-then nodes and edges with decision choices at the decision tree leaf nodes).

• Context:
  • It can be induced by a Decision Tree Training System (that implements a decision tree training algorithm).
  • It can range from being a Abstract Decision Tree Pattern to being a Decision Tree Data Structure (such as a trained decision tree based on PMML).
  • It can range from being a Categorical Value Decision Tree to being a Ordinal Value Decision Tree to being an Numeric Value Decision Tree.
  • It can range from being a Binary-Splits Decision Tree to being an n'ary-Splits Decision Tree, depending on the branching factor.
  • It can be applied to a Decision Tree Training System (that implements a decision tree training algorithm).
  • It can be a component of an Decision Tree Ensemble.
  • It can support Test Tuples with Missing Values.
• Example(s):
  • A Trained Classification Tree, such as:
    IF A/4 THEN
      (IF B=0 THEN yes/76%:no/24% ELSE no/63%:no/37%)
ELSE yes/81%:no/19%
• Counter-Example(s):
  • a Rule List.
  • a Support Vector-based Predictive Model.
  • a Trained Linear Function.
  • a Artificial Neural Network Model.
• See: Decision Tree Type, Classification, Decision Tree Ensemble, Model Tree, Decision List, Decision Stump, Unprunned Tree.

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References

2017a

• (Furnkranz, 2017) ⇒ Johannes Fürnkranz, (2017). "Decision Tree". In Encyclopedia of Machine Learning and Data Mining pp 330-335.
  • ABSTRACT: The induction of decision trees is one of the oldest and most popular techniques for learning discriminatory models, which has been developed independently in the statistical (Breiman et al. 1984; Kass 1980 ) and machine learning (Hunt et al. 1966 ; Quinlan 1983, 1986) communities. A decision tree is a tree-structured classification model, which is easy to understand, even by non-expert users, and can be efficiently induced from data. An extensive survey of decision-tree learning can be found in Murthy (1998).
  • QUOTE: Decision trees are also often used as components in Ensemble Methods such as random forests (Breiman 2001 ) or AdaBoost (Freund and Schapire 1996). They can also be modified for predicting numerical target variables, in which case they are known as regression trees. One can also put more complex prediction models into the leaves of a tree, resulting in Model Trees.

2017b

• (Scikit-Learn, 2017) ⇒ "1.10. Decision Trees" http://scikit-learn.org/stable/modules/tree.html Retrieved on 2017-10-15
  • QUOTE: 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 features.

    For instance, in the example below, decision trees learn from data to approximate a sine curve with a set of if-then-else decision rules. The deeper the tree, the more complex the decision rules and the fitter the model.

    Figure:Decision Tree Regression

Some advantages of decision trees are:

• Simple to understand and to interpret. Trees can be visualised.
• Requires little data preparation. Other techniques often require data normalisation, dummy variables need to be created and blank values to be removed. Note however that this module does not support missing values.
• The cost of using the tree (i.e., predicting data) is logarithmic in the number of data points used to train the tree.
• Able to handle both numerical and categorical data. Other techniques are usually specialised in analysing datasets that have only one type of variable. See algorithms for more information.
• Able to handle multi-output problems.
• Uses a white box model. If a given situation is observable in a model, the explanation for the condition is easily explained by boolean logic. By contrast, in a black box model (e.g., in an artificial neural network), results may be more difficult to interpret.
• Possible to validate a model using statistical tests. That makes it possible to account for the reliability of the model.
• Performs well even if its assumptions are somewhat violated by the true model from which the data were generated.

The disadvantages of decision trees include:

• Decision-tree learners can create over-complex trees that do not generalise the data well. This is called overfitting. Mechanisms such as pruning (not currently supported), setting the minimum number of samples required at a leaf node or setting the maximum depth of the tree are necessary to avoid this problem.
• Decision trees can be unstable because small variations in the data might result in a completely different tree being generated. This problem is mitigated by using decision trees within an ensemble.
• The problem of learning an optimal decision tree is known to be NP-complete under several aspects of optimality and even for simple concepts. Consequently, practical decision-tree learning algorithms are based on heuristic algorithms such as the greedy algorithm where locally optimal decisions are made at each node. Such algorithms cannot guarantee to return the globally optimal decision tree. This can be mitigated by training multiple trees in an ensemble learner, where the features and samples are randomly sampled with replacement.
• There are concepts that are hard to learn because decision trees do not express them easily, such as XOR, parity or multiplexer problems.
• Decision tree learners create biased trees if some classes dominate. It is therefore recommended to balance the dataset prior to fitting with the decision tree.

2017c

• (Wikipedia, 2017) ⇒ https://en.wikipedia.org/wiki/Decision_tree_learning Retrieved:2017-10-15.
  • Decision tree learning uses a decision tree (as a predictive model) to go from observations about an item (represented in the branches) to conclusions about the item's target value (represented in the leaves). It is one of the predictive modelling approaches used in statistics, data mining and machine learning. Tree models where the target variable can take a discrete set of values are called classification trees ; in these tree structures, leaves represent class labels and branches represent conjunctions of features that lead to those class labels. Decision trees where the target variable can take continuous values (typically real numbers) are called regression trees.

    In decision analysis, a decision tree can be used to visually and explicitly represent decisions and decision making. In data mining, a decision tree describes data (but the resulting classification tree can be an input for decision making). This page deals with decision trees in data mining.

2010

• http://www.dmg.org/v4-0-1/TreeModel.html
  • QUOTE: The TreeModel in PMML allows for defining either a classification or prediction structure. Each Node holds a logical predicate expression that defines the rule for choosing the Node or any of the branching Nodes.

2009

• (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/C4.5_algorithm
  • The decision trees generated by C4.5 can be used for classification, and for this reason, C4.5 is often referred to as a statistical classifier.

2009

• http://www.stat.cmu.edu/~cshalizi/350/lectures/22/lecture-22.pdf
  • Having built up increasingly complicated models for regression, I'll now switch gears and introduce a class of nonlinear predictive model which at first seems too simple to possible work, namely prediction trees. These have two varieties, regression trees and classification trees.

2006

• (Shalizi, 2006) ⇒ Cosma Shalizi. (2006). “Lecture 10: Regression Trees." 36-350: Data Mining, October 11, 2006.
  • The next three lectures are going to be about a particular kind of nonlinear predictive model, namely prediction trees. These have two varieties, regression trees, which we’ll start with today, and classification trees, the subject of the next lecture.

2003

• (Palchak et al., 2003) ⇒ Michael J. Palchak, James F. Holmes, Cheryl W. Vance, Rebecca E. Gelber, Bobbie A. Schauer, Mathew J. Harrison, Jason Willis-Shore, Sandra L. Wootton-Gorges, Robert W. Derlet, and Nathan Kuppermann. (2003). “A Decision Rule for Identifying Children at Low Risk for Brain Injuries After Blunt Head Trauma.” In: Annals of Emergency Medicine, 42(4).
  • We internally validated the decision trees developed in the main analyses by using 10-fold cross-validation. … The decision tree for traumatic brain injury identified on CT scan included the same 4 predictor variables as in the main analysis, although the order of the variables in the resulting tree was different (Figure 4).

1995

• ([[McCarthy & Lehnert, 1995) ⇒ Joseph F. McCarthy, and Wendy G. Lehnert. (1995). “Using Decision Trees for Coreference Resolution.” In: Proceedings of the 14th International Joint Conference on Artificial Intelligence (IJCAI 1995)

1984

• (Breiman et al., 1984) ⇒ Leo Breiman, Jerome H. Friedman, Charles J. Stone, and R. A. Olshen. (1984). “Classification and Regression Trees." Chapman & Hall/CRC. ISBN:0412048418

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