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Dataset sky airtemp humidity wind water forecast enjoysport sunny warm normal strong warm same yes sunny warm high strong warm same yes rainy cold high strong warm change no sunny warm high strong cool change yes

A Decision Tree is a hierarchical breakdown of a dataset from the root node to the leaf node based on the governing attributes to solve a classification or regression problem. Decision Trees (DTs) are a non-parametric supervised learning algorithm that predicts the value of a target variable by learning rules inferred from the data features.

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Now, as we know the terminologies, it will be easier to follow the theory. To get better hands-on, let's take a very popular dataset of PlayTennis and follow the formation of a flowchart. Here the objective of this flowchart would be to decide whether tennis play will happen or not based on the outlook, temperature, humidity, and wind conditions.

A decision tree is a visualization of attributes governing the decision hierarchically. Consider the dataset above. Fig.1 shows one of the possible decision trees for the given dataset. If we notice carefully, some attributes (such as temperature) in the dataset are redundant, i.e., the decision is independent of that particular attribute.

In our loss function's blog, we learned about this term. Let's quickly revise it here. The Entropy of a dataset is the average amount of information needed to classify any observation in the data. It is termed Uncertainty. If Entropy is higher, the confidence in classifying any observation into any class is lower and vice-versa.

For an equally balanced categorical value, the Entropy is equal to 1. A real-world dataset may not necessarily be balanced. In the given example, the output cases (yes & no) are imbalanced, i.e. [9 'yes' and 5' no'], so the Entropy is not equal to 1.

Any attribute chosen to partition a tree will result in a loss of Entropy. This means that on choosing any attribute to form a tree, the balancedness of the dataset will reduce. Information gain is the measure of the effectiveness of an attribute in retaining the Entropy. The attribute with the highest information gain is chosen as the next node (first in the case of "root node") in the tree.

Let's take the example of an ID3 Decision tree and build it from scratch. ID3 stands for Iterative (iteratively) Dichotomizes (divides) the dataset into two or more sub-groups. It is inherently a greedy approach, which means it always selects the best attribute to perform the splitting.

First, we check the Entropy of the dataset using (1). There are two different classes in the output, so c = 2. Next, among the 14 samples of the dataset, 9 are 'yes' and 5 are 'no'. Thus:

Now concerning each attribute of outlook (['sunny',' overcast',' rainy']), the information gain is to be computed for all the remaining attributes of the dataset (['humidity', 'temp', 'windy']), provided the Entropy of the dataset is not zero. Please remember that every attribute can appear only once in the tree. Now let's further grow the tree.

Now, with respect to 'overcast', the Entropy of the dataset is 0. This means that all the observations with respect to this attribute have the same class ('yes' in our case). Thus, the output can be labeled 'yes' for the 'overcast' attribute of 'outlook'. Thus, the tree further grows as:

As the Entropy of the above dataset is 0 thus, the output can be labeled as the only class present in the dataset ('no') for the attribute 'TRUE' of 'windy' along the tree. Thus, the final tree can be drawn as: ff782bc1db