# Decision tree

(Redirected from Decision trees)
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.

## 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, specifically in decision analysis, to help identify a strategy most likely to reach a goal. 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

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,[1] 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.

### Analysis example

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

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").

### Another example

Decision trees can be used to optimize an investment portfolio. The following example shows a portfolio of 7 investment options (projects). The organization has \$10,000,000 available for the total investment. Bold lines mark the best selection 1, 3, 5, 6, and 7, which will cost \$9,750,000 and create a payoff of 16,175,000. All other combinations would either exceed the budget or yield a lower payoff.[2]

### 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.

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.