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1. (15 pts) From exercise 18.6 in the book: Consider the following data set com...

May 8, 2024

To construct a decision tree using the decision tree learning algorithm with information gain, we need to calculate the information gain for each attribute and choose the one with the highest gain to split at each node. Here's how to approach this problem:

Step-by-step Instruction

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Calculate the entropy of each attribute (A1, A2, A3)

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Calculate the information gain for each attribute

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Choose the attribute with the highest information gain for the root node

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Split the dataset based on the chosen attribute and repeat the process for each subset

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Stop splitting when all instances in a subset have the same output value or when there are no more attributes to split on

Now, let's write the Python code to calculate the information gain:

python

The main function and use cases for testing the information gain calculation would look like this:

python

Explanation

The code defines functions to calculate entropy, class probabilities, information gain, and to group the dataset by an attribute. It also includes a placeholder function for building the decision tree, which will be implemented later.

Time Complexity

The time complexity for calculating information gain is O(n), where n is the number of instances in the dataset, as it requires iterating over all instances to group them and calculate entropies.

Space Complexity

The space complexity is O(n), as it requires storing the grouped data, which in the worst case can be as large as the original dataset.