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204.3.6 The Decision Tree Algorithm

Step by step.

Link to the previous post : https://statinfer.com/204-3-5-information-gain-in-decision-tree-split/

 

In this post we will understand the decision tree algorithm step by step, how the split criterion and stop criterion are decided.

The Decision tree Algorithm

  • The major step is to identify the best split variables and best split criteria.
  • Once we have the split then we have to go to segment level and drill down further.

Until stopped:

  1. Select a leaf node
  2. Find the best splitting attribute
  3. Spilt the node using the attribute
  4. Go to each child node and repeat step 2 & 3

Stopping criteria:

  • Each leaf-node contains examples of one type
  • Algorithm ran out of attributes
  • No further significant information gain

The Decision tree Algorithm – Demo

Entropy([4+,10-]) Ovearll = 86.3% (Impurity)

  • Entropy([7+,1-]) Male= 54.3%
  • Entropy([3+,3-]) Female = 100%
  • Information Gain for Gender=86.3-((8/14)54.3+(6/14)100) =12.4

Entropy([4+,10-]) Ovearll = 86.3% (Impurity)

  • Entropy([0+,9-]) Married = 0%
  • Entropy([4+,1-]) Un Married= 72.1%
  • Information Gain for Marital Status=86.3-((9/14)0+(5/14)72.1)=60.5
  • The information gain for Marital Status is high, so it has to be the first variable for segmentation
  • Now we consider the segment “Married” and repeat the same process of looking for the best splitting variable for this sub segment ### The Decision tree Algorithm

Until stopped:

  1. Select a leaf node
  2. Find the best splitting attribute
  3. Spilt the node using the attribute
  4. Go to each child node and repeat step 2 & 3 Stopping criteria:
  5. Each leaf-node contains examples of one type
  6. Algorithm ran out of attributes
  7. No further significant information gain

Many Splits for a Single Variable

  • Sometimes we may find multiple values taken by a variable
    • which will lead to multiple split options for a single variable
    • that will give us multiple information gain values for a single variable

What is the information gain for income?


  • What is the information gain for income?
  • There are multiple options to calculate Information gain.
  • For income, we will consider all possible scenarios and calculate the information gain for each scenario.
  • The best split is the one with highest information gain.
  • Within income, out of all the options, the split with best information gain is considered.
  • So, node partitioning for multi class attributes need to be included in the decision tree algorithm.
  • We need find best splitting attribute along with best split rule.

The next post is about building a decision tree in python.

Link to the next post : https://statinfer.com/204-3-7-building-a-decision-tree-in-python/

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