Decision tree

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[edit] Note on terminology

In operations research, and decision analysis specifically, a decision tree is an idea generation tool that generally refers to a graph or model of decisions and their possible consequences, including chance event outcomes, resource costs, and utility. A decision tree is a decision support tool, used to identify the strategy most likely to reach a goal. Another use of trees is as a descriptive means for calculating conditional probabilities.

In data mining, on the other hand, a decision tree is a predictive model; that is, a mapping of observations about an item to conclusions about the item's target value. More descriptive names for such tree models are classification tree or reduction tree. In these tree structures, leaves represent classifications and branches represent conjunctions of features that lead to those classifications [1]. The machine learning technique for inducing a decision tree from data is called decision tree learning, or (colloquially) decision trees.

[edit] General

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

For example a factory manager has to decide to invest in product A or product B (she cannot do both due to budget constrants). Product A is estimated to require two million pounds (or dollars if you like) of R&D investment, but only has a 50% chance of the research being successful and a product being obtained. It will then have a 30% chance of selling $5M profit, a 40% chance of selling $10M profit, and a 30% chance of no sales. Product B, on the other hand, will also cost $2M in R&D but has an 80% chance of selling $5M profit and a 20% chance of no sales. $1M is the manufacturing cost for either product.

If the company has a policy of maximising expected values, which is the preferred strategy? The alternatives, probabilities, payoffs, and resulting expected value calculations are shown in the example tree below. Product B is preferred, with a significantly higher expected value:

Image:factory2.png

(Although the example does not appear to take into account discounting to Net Present Values, the assumption might be that the cost and sales inputs have already been discounted.)

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

Image: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").

[edit] Influence diagram

A decision tree can be represented more compactly as an influence diagram, focusing attention on the issues and relationships between events.

Image:Factory2_InfluenceDiagram.png

[edit] Uses in teaching

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.

[edit] Decision tree advantages

Amongst 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.
  • use a white box model. If a given result is provided by a model, the explanation for the result is easily replicated by simple math. (An example of a black box model is an artificial neural network since the explanation for the results can be excessively complex for a decision maker to comprehend.)

[edit] See also

[edit] Software

[edit] External links

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