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Intelligent Decision Support Systems – CSE 435 Fall 2012 Giulio Finestrali

Show a counter-example proving that using information gain does not necessarily produce an optimal decision tree. Intelligent Decision Support Systems – CSE 435 Fall 2012 Giulio Finestrali. Consider the following table. Gain(Container Type). Gain(Drink Type). Gain(Temperature).

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Intelligent Decision Support Systems – CSE 435 Fall 2012 Giulio Finestrali

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  1. Show a counter-example proving that using information gain does not necessarily produce an optimal decision tree Intelligent Decision Support Systems – CSE 435 Fall 2012 Giulio Finestrali

  2. Consider the following table

  3. Gain(Container Type)

  4. Gain(Drink Type)

  5. Gain(Temperature)

  6. So we pick Container Type! When Container Type = Glass, we can already output No. For Container Type = Cup, we are left with sample 1, 3, and 4. We have to run the algorithm again.

  7. Comparison Obviously they have the same Information Gain. Skipping… the result is Gain(Drink Type) = Gain(Temperature) = 0.251 We decide to pick Drink Type.

  8. Resulting Decision Tree

  9. Alternative What if at the beginning we pick Temperature (the worst information gain attribute) as the root for our decision tree? Turns out we can build a shorter tree this way.

  10. Resulting Decision Tree

  11. Why? Just ideas: Not much data to work with. The table is short. Also, the table is not complete (a lot of missing combinations)

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