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From Wikipedia, the free encyclopedia

Traditionally, decision trees have been created manually.
Traditionally, decision trees have been created manually.

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

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.

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  • ✪ Decision Tree Tutorial in 7 minutes with Decision Tree Analysis & Decision Tree Example (Basic)
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  • ✪ StatQuest: Decision Trees

Transcription

Decision Tree Tutorial in 7 minutes with Decision Tree Analysis & Decision Tree Example (Basic) Hello! Welcome back again to www.MBAbullshit.com. The topic for this video is Decision Tree Analysis and this is the basic video on this topic. Remember, you can always go back to www.MBAbullshit.com. This video completely explains the very basic Decision Tree concept. After this, you’ll be ready for my next video on Decision Tree Exam Training to help you pass or get high grades. Let’s start with a story. Let’s say you can choose between two business projects either a candy shop or a lemonade stand. Let’s say the candy shop can earn up to one hundred dollars and the lemonade stand can earn up to ninety dollars. Which one should you do? Of course, the answer is quite easy and obvious; you should choose the candy shop in this simple situation. But what if, let’s make the story a step further. What if the candy shop had a fifty percent chance of success and also had a fifty percent of failure? If your candy shop is a success, you would earn one hundred dollars. If it was a failure, you would lose thirty dollars; it’s a negative sign there, a negative thirty. On the other hand, if you have a lemonade stand, you also have a fifty percent success and a fifty percent chance of failure. If it’s a success, you would probably earn ninety dollars and if it’s a failure, you would probably lose ten dollars. Which one do you choose now? So now it’s not so simple. Actually it’s very simple; you would use a simple formula like this. Okay? And it would look like this: fifty percent times one hundred dollars plus fifty percent multiplied by negative thirty and we would get a figure here which we call an “Expected Value.” I’m going to explain that a little bit more in a while so just be patient. Where do we get this fifty percent over here? It’s the same as the fifty percent over here. Where do we get the one hundred dollars over here? It’s the same as the one hundred dollars over here. Plus fifty percent over here, corresponds the fifty percent over here chance of failure, multiplied by negative thirty or loss of thirty. Where do we get that? It corresponds the negative thirty dollars over here. Now we come up with these thirty five dollars. Then we do the same thing for the lemonade stand. Fifty percent chance of success, ninety dollars that you would earn if it is a success plus fifty percent chance of failure multiplied by the loss of ten dollars which you would have if lemonade stands become a failure. We end up with this formula over here and this figure over here: fifty percent times ninety plus fifty percent multiplied by negative ten percent equals forty dollars. So now, which one would you choose? Obviously, would you choose the thirty five dollars? Or would you choose the forty dollars? Obviously, you would choose the forty dollars. These forty dollars is what we call the “Expected Value” of the Lemonade project. The “Expected Value” of the Candy project is thirty five dollars. Since we are choosing a business, we choose the bigger one, the one with the bigger expected value. I promise you I speak more about expected value. What do you mean by this? Well, does this mean that if you do the Lemonade project, you will earn forty dollars? Forty dollars over here. Does this mean you will earn forty dollars? No! It means that if you did identical Lemonade projects very many times in exactly the same situation as you have here. If you did it very many times in exactly the same situation then your average earnings will probably be forty dollars per time on the average. So it does not mean, you’ll earn forty dollars each time and it certainly does not mean you will earn forty dollars this time. It just means that your average earning is forty dollars if in some strange world, you had the chance to replicate or duplicate exactly the same situation many, many times. Make sure that’s what you mean by that. You understand that’s what we mean by Expected Value. It’s different from everyday street language. If you say, “Oh, I expect my friend to give me five dollars today.” that means he probably will give you exactly five dollars. But in MBA bullshit language, it means what I just explained right now, your average earning in certain situation if you could replicate that same situation very many times. Right. So that’s how simple it is. Okay? Now you’re ready for my next video. This video that we watched right now was a very simple example, not enough to pass an exam or to get high marks or high grades but still you should have completely understood at least the concept of this video. Remember to share it if you like it. On twitter, simply @MBAbullshit, www.facebook.com/MBAbullshit is the place to go to find out the latest update from me and the latest videos. Please do forward our YouTube videos links on your email. Have a great day! Goodbye! debbierojonan Page 1

Contents

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 represent 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 three types of nodes:[1]

  1. Decision nodes – typically represented by squares
  2. Chance nodes – typically represented by circles
  3. End nodes – typically 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

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,[2] 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 be generated by constructing association rules with the target variable on the right. They can also denote temporal or causal relations.[3]

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, commonly used in operations research courses, is the distribution of lifeguards on beaches (a.k.a. the "Life's a Beach" example).[4] The example describes two beaches with lifeguards to be distributed on each beach. There is maximum budget B that can be distributed among the two beaches (in total), and using a marginal returns table, analysts can decide how many lifeguards to allocate to each beach.

Lifeguards on each beach Drownings prevented in total, beach #1 Drownings prevented in total, beach #2
1 1 3
2 4 0

In this example, a decision tree can be drawn to illustrate the principles of diminishing returns on beach #2.

Beach Decision Tree
Beach Decision Tree

The decision tree illustrates that when sequentially distributing lifeguards, placing a first lifeguard on beach #1 would be optimal if there is only the budget for 1 lifeguard. But if there is a budget for two guards, then placing both on beach #2 would prevent more overall drownings.

Lifeguards
Lifeguards

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 rectangle on the left represents a decision, the ovals represent actions, and the diamond represents results.
The rectangle on the left represents a decision, the ovals represent actions, 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").[5] Several algorithms to generate such optimal trees have been devised, such as ID3/4/5,[6] CLS, ASSISTANT, and 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.
  • 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:

  • They are unstable, meaning that a small change in the data can lead to a large change in the structure of the optimal decision tree.
  • They are often relatively inaccurate. Many other predictors perform better with similar data. This can be remedied by replacing a single decision tree with a random forest of decision trees, but a random forest is not as easy to interpret as a single decision tree.
  • For data including categorical variables with different number of levels, information gain in decision trees is biased in favor of those attributes with more levels.[7]
  • Calculations can get very complex, particularly if many values are uncertain and/or if many outcomes are linked.

See also

References

  1. ^ Kamiński, B.; Jakubczyk, M.; Szufel, P. (2017). "A framework for sensitivity analysis of decision trees". Central European Journal of Operations Research. 26 (1): 135–159. doi:10.1007/s10100-017-0479-6. PMC 5767274. PMID 29375266.
  2. ^ Quinlan, J. R. (1987). "Simplifying decision trees". International Journal of Man-Machine Studies. 27 (3): 221–234. CiteSeerX 10.1.1.18.4267. doi:10.1016/S0020-7373(87)80053-6.
  3. ^ K. Karimi and H.J. Hamilton (2011), "Generation and Interpretation of Temporal Decision Rules", International Journal of Computer Information Systems and Industrial Management Applications, Volume 3
  4. ^ Wagner, Harvey M. (1975-09-01). Principles of Operations Research: With Applications to Managerial Decisions (2nd ed.). Englewood Cliffs, NJ: Prentice Hall. ISBN 9780137095926.
  5. ^ R. Quinlan, "Learning efficient classification procedures", Machine Learning: an artificial intelligence approach, Michalski, Carbonell & Mitchell (eds.), Morgan Kaufmann, 1983, p. 463-482. doi:10.1007/978-3-662-12405-5_15
  6. ^ Utgoff, P. E. (1989). Incremental induction of decision trees. Machine learning, 4(2), 161-186. doi:10.1023/A:1022699900025
  7. ^ Deng,H.; Runger, G.; Tuv, E. (2011). Bias of importance measures for multi-valued attributes and solutions (PDF). Proceedings of the 21st International Conference on Artificial Neural Networks (ICANN).

External links

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