Mastering the Basics: How to Calculate Information Gain in Machine Learning

Mastering the Basics: How to Calculate Information Gain in Machine Learning

Machine learning is becoming an increasingly popular field for businesses and individuals looking to automate various processes. However, to understand the intricacies of machine learning, it is essential to grasp the concept of Information Gain.

Information Gain is a measure that is used in the decision tree algorithm of machine learning to determine the relevance of a feature. It is the difference between the entropy of the parent node and the weighted average of the entropy of the child nodes. The aim of Information Gain is to split a dataset into smaller datasets that contain more information, which is useful for classification, and the algorithm that uses Information Gain is called ‘ID3’.

The formula for calculating Information Gain is:

Information Gain(S, A) = Entropy(S) − Σ(t∈T) |t|/|S|Entropy(t)

Where,

S is the parent dataset.

A is the characteristic/attribute for which Information Gain is being calculated.

T is the set of descendant partitions or child nodes.

|t| is the number of elements in the subset t, and |S| is the number of elements in the parent set S.

Entropy(S) = −p1.log2(p1) − p2.log2(p2)

Where,

p1 and p2 are the proportions of the two classes in the dataset.

To understand Information Gain in detail, let’s take an example. Suppose we have a dataset of 12 emails that are labeled as either ‘spam’ or ‘not spam.’ These emails also have the corresponding features: sender, subject, and message.

Assuming we want to find out the most relevant feature based on Information Gain for email classification, we begin by calculating the entropy of the dataset. Assume 40% of the emails are spam, and 60% are not: Entropy(S)= – (0.4log2(0.4) + 0.6log2(0.6)) = 0.971.

Now, we can choose each feature and calculate its Information Gain. Let’s say we choose the sender feature, and we get two different senders. We calculate the Information Gain as follows:

Information Gain(S, Sender) = Entropy(S) − [(8/12)Entropy(Spam) + (4/12)Entropy(Not Spam)]

Where,

Spam = 2 spam emails from sender A, 2 spam emails from sender B, and 1 spam email from sender C.

Not Spam = 2 not spam emails from sender A and 5 not spam emails from sender B.

Entropy(Spam) = -(2/5)log2(2/5) – (2/5)log2(2/5) – (1/5)log2(1/5) = 1.371.

Entropy(Not Spam) = -(2/7)log2(2/7) – (5/7)log2(5/7) = 0.863.

Information Gain(S, Sender) = 0.971 – [(8/12)*1.371 + (4/12)*0.863] = 0.048.

Now we repeat this process for all other features and select the one with the highest Information Gain value as the most relevant for classification.

In conclusion, Information Gain is a crucial concept in machine learning and plays a vital role in the decision tree algorithm. Understanding Information Gain and how to calculate it can help individuals and businesses create more accurate and relevant models in machine learning. With this article, we hope to have provided you with a clear and concise explanation of Information Gain, its calculation, and its usage.