Decision tree

This article is about decision trees in decision analysis. For the use of the term in machine learning, see Decision tree learning.

File:Manual decision tree.jpg

Traditionally, decision trees have been created manually.

A decision tree is a decision support tool that uses a tree-like graph or model of decisions and their possible consequences, including chance event outcomes, resource costs, and utility. It is one way to display an algorithm.

Decision trees are commonly used in operations research, specifically in decision analysis, to help identify a strategy most likely to reach a goal, but are also a popular tool in machine learning.

Overview

A decision tree is a flowchart-like structure in which each internal node represents a "test" on an attribute (e.g. whether a coin flip comes up heads or tails), each branch represents the outcome of the test and each leaf node represents a class label (decision taken after computing all attributes). The paths from root to leaf represents classification rules.

In decision analysis a decision tree and the closely related influence diagram are used as a visual and analytical decision support tool, where the expected values (or expected utility) of competing alternatives are calculated.

A decision tree consists of 3 types of nodes:

1. Decision nodes - commonly represented by squares
2. Chance nodes - represented by circles
3. End nodes - represented by triangles

Decision trees are commonly used in operations research and operations management. If in practice decisions have to be taken online with no recall under incomplete knowledge, a decision tree should be paralleled by a probability model as a best choice model or online selection model algorithm. Another use of decision trees is as a descriptive means for calculating conditional probabilities.

Decision trees, influence diagrams, utility functions, and other decision analysis tools and methods are taught to undergraduate students in schools of business, health economics, and public health, and are examples of operations research or management science methods.

Decision tree building blocks

Decision tree elements

File:Decision-Tree-Elements.png

Drawn from left to right, a decision tree has only burst nodes (splitting paths) but no sink nodes (converging paths). Therefore, used manually, they can grow very big and are then often hard to draw fully by hand. Traditionally, decision trees have been created manually - as the aside example shows - although increasingly, specialized software is employed.

Decision rules

The decision tree can be linearized into decision rules, where the outcome is the contents of the leaf node, and the conditions along the path form a conjunction in the if clause. In general, the rules have the form:

if condition1 and condition2 and condition3 then outcome.

Decision rules can also be generated by constructing association rules with the target variable on the right.

Decision tree using flowchart symbols

Commonly a decision tree is drawn using flowchart symbols as it is easier for many to read and understand.

File:DecisionCalcs.jpg

Analysis example

Analysis can take into account the decision maker's (e.g., the company's) preference or utility function, for example:

File:RiskPrefSensitivity2Threshold.png

The basic interpretation in this situation is that the company prefers B's risk and payoffs under realistic risk preference coefficients (greater than $400K—in that range of risk aversion, the company would need to model a third strategy, "Neither A nor B").

Influence diagram

Much of the information in a decision tree can be represented more compactly as an influence diagram, focusing attention on the issues and relationships between events.

The squares represent decisions, the ovals represent action, and the diamond represents results.

Association rule induction

Decision trees can also be seen as generative models of induction rules from empirical data. An optimal decision tree is then defined as a tree that accounts for most of the data, while minimizing the number of levels (or "questions"). Several algorithms to generate such optimal trees have been devised, such as ID3/4/5, CLS, ASSISTANT, CART.

Advantages and disadvantages

Among decision support tools, decision trees (and influence diagrams) have several advantages. Decision trees:

• Are simple to understand and interpret. People are able to understand decision tree models after a brief explanation.
• Have value even with little hard data. Important insights can be generated based on experts describing a situation (its alternatives, probabilities, and costs) and their preferences for outcomes.
• Allow the addition of new possible scenarios
• Help determine worst, best and expected values for different scenarios
• Use a white box model. If a given result is provided by a model.
• Can be combined with other decision techniques.

Disadvantages of decision trees:

• For data including categorical variables with different number of levels, information gain in decision trees are biased in favor of those attributes with more levels.
• Calculations can get very complex particularly if many values are uncertain and/or if many outcomes are linked.

See also

• Behavior tree (artificial intelligence, robotics and control)
• Boosting (machine learning)
• Decision cycle
• Decision tables
• Decision tree model of computation
• DRAKON
• Expectiminimax tree
• Influence diagram
• Markov chain
• Morphological analysis
• Random forest
• Odds algorithm
• Operations research
• Topological combinatorics
• Truth table

External links

• SilverDecisions: a free and open source decision tree software
• Decision Tree Analysis mindtools.com
• Decision Analysis open course at George Mason University
• Extensive Decision Tree tutorials and examples