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In operations research, specifically in decision analysis, a decision tree (or tree diagram) is a decision support tool that uses a graph or model of decisions and their possible consequences, including chance event outcomes, resource costs, and utility. Operations Research (OR in North America South Africa and Australia and Operational Research in Europe is an interdisciplinary branch of applied Mathematics and Decision Analysis (DA is the Discipline comprising the Philosophy, Theory, Methodology, and Professional practice necessary to address In Graph theory, a tree is a graph in which any two vertices are connected by exactly one path. A diagram is a 2D geometric symbolic Representation of Information according to some Visualization technique A causal model is an abstract model that uses cause and effect logic to describe the behaviour of a System. In Economics, utility is a measure of the relative satisfaction from or desirability of Consumption of various Goods and services. A decision tree is used to identify the strategy most likely to reach a goal. A goal or objective consists of a projected state of affairs which a Person or a System plans or intends to achieve or bring about — a personal or Another use of trees is as a descriptive means for calculating conditional probabilities. Conditional probability is the Probability of some event A, given the occurrence of some other event B.

In data mining and machine learning, a decision tree is a predictive model; that is, a mapping from observations about an item to conclusions about its target value. Data mining is the process of Sorting through large amounts of data and picking out relevant information Machine learning is a subfield of Artificial intelligence that is concerned with the design and development of Algorithms and techniques that allow computers to "learn" More descriptive names for such tree models are classification tree (discrete outcome) or regression tree (continuous outcome). In these tree structures, leaves represent classifications and branches represent conjunctions of features that lead to those classifications. The machine learning technique for inducing a decision tree from data is called decision tree learning, or (colloquially) decision trees. Decision tree learning, used in Data mining and Machine learning, uses a Decision tree as a predictive model which maps observations about an

Contents

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. Decision Analysis (DA is the Discipline comprising the Philosophy, Theory, Methodology, and Professional practice necessary to address An influence diagram (ID (also called a decision network) is a compact graphical and mathematical representation of a decision situation In Economics, Game theory, and Decision theory the expected utility theorem or expected utility hypothesis predicts that the "betting preferences"

For example a factory makes product B. The manager has to decide to invest in development for a new product - product A or product C. (She cannot do both due to budget constraints. ) Product A is estimated to require two million dollars of R&D investment, but only has a 50% chance of the research being successful and a product being obtained. It will have a 30% chance of selling $5M profit, a 40% chance of selling $10M profit, and a 30% chance of no sales. Product C, 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. In this case either Product A or Product C are expected to turn a profit but product C has the higher expected value of $2 million:

Image:dtree2.png

The same example again, this time taking account of the time value of money by discounting to Net Present Values, for this scenario it can be seen that Product C is clearly the winning choice with a payout of $0. Net present value ( NPV) or net present worth ( NPW) is defined as the total Present value (PV of a Time series of Cash flows 36 million. Product A is not expected to turn a profit.

Image:dtreenpva2.png

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"). Preference (also called " taste " or "penchant" is a concept used in the Social sciences particularly Economics. In Economics, utility is a measure of the relative satisfaction from or desirability of Consumption of various Goods and services.

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

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. An influence diagram (ID (also called a decision network) is a compact graphical and mathematical representation of a decision situation Decision Analysis (DA is the Discipline comprising the Philosophy, Theory, Methodology, and Professional practice necessary to address Operations Research (OR in North America South Africa and Australia and Operational Research in Europe is an interdisciplinary branch of applied Mathematics and Management science (MS, is the discipline of using Mathematical modeling and other analytical methods to help make better business Management decisions

Creation of decision nodes

Three popular rules are applied in the automatic creation of classification trees. The Gini rule splits off a single group of as large a size as possible, whereas the entropy and twoing rules find multiple groups comprising as close to half the samples as possible. Both algorithms proceed recursively down the tree until stopping criteria are met.

Advantages

Amongst decision support tools, decision trees (and influence diagrams) have several advantages:

Decision trees:

Image:Investment Decision Occam s Tree.gif

Image:Project Investment Portfolio Occam s Tree.gif

See also

References

External links

Dictionary

decision tree

-noun

  1. A visualization of a complex decision making situation in which the possible decisions and their likely outcomes are organized in the form of a graph that resembles a tree.
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