The Ultimate Guide: How to Calculate Information Gain for Machine Learning

If you are familiar with the world of machine learning, then you know how important it is to have the right data to build an accurate model. The information gain is a numerical value that helps you understand which feature is the most relevant when building a model. In this article, we’ll delve into the topic of information gain and share a step-by-step guide to calculating it.

What is Information Gain?

Information gain is a statistical measure that helps you to quantify how much information a particular feature provides in a dataset. It helps to reduce the entropy (uncertainty) in the classification process. The technique is widely used in decision tree algorithms, where it’s vital to identify features that are most relevant or provide the most information.

How to Calculate Information Gain Step-by-Step

Calculating information gain is a straightforward process; it can be broken down into a few steps:

1. Calculate the entropy of the dataset before the split
2. Calculate the entropy of the dataset after the split
3. Calculate the weight of each subset of data after the split
4. Calculate the information gain as the difference between before and after the split entropy values

Step 1: Calculate the Entropy of the Dataset Before the Split

Entropy is essentially a measurement of the amount of disorder or randomness in a given set of data. The entropy value is calculated using the following formula:

Entropy(S) = -p1*log2(p1) – p2*log2(p2) -…- pn*log2(pn)

Where p1, p2, …, pn are the proportions of the positive and negative instances in the dataset. To calculate the entropy before the split, you should use the entire dataset.

Step 2: Calculate the Entropy of the Dataset After the Split

To calculate the entropy after the split, you need to divide your dataset into subsets based on a specific attribute. Then you calculate the entropy value for each subset using the same formula used in step 1.

Step 3: Calculate the Weight of Each Subset of Data After the Split

The weight of each subset of data is equal to the proportion of the dataset that belongs to that subset. This proportion is then multiplied by the entropy value of that subset, giving you the weighted entropy value.

Step 4: Calculate the Information Gain as the Difference Between Before and After the Split Entropy Values

To calculate the information gain, you simply subtract the entropy value after the split from the entropy value before the split. The result is the information gain of the attribute that was used to make the split.

Examples of Information Gain Calculation

Suppose we have a dataset of 10 instances, as shown below:

We want to know which attribute provides the most information gain when deciding whether the person buys a pet.

Step 1: Calculate the Entropy of the Dataset Before the Split

Entropy = -0.5*log2(0.5) – 0.5*log2(0.5) = 1

Step 2: Calculate the Entropy of the Dataset After the Split

Suppose we split the dataset by the Age attribute.

Subset 1: (Youth, High, Single, No), (Youth, High, Married, No), (Youth, Medium, Single, No), (Youth, Low, Single, Yes)
Subset 2: (Middle-aged, High, Single, Yes), (Middle-aged, Low, Married, Yes)
Subset 3: (Senior, Medium, Single, Yes), (Senior, Low, Single, Yes), (Senior, Low, Married, No), (Senior, Medium, Married, Yes)

Entropy_Subset_1 = -0.75*log2(0.75) – 0.25*log2(0.25) = 0.81
Entropy_Subset_2 = -0.5*log2(0.5) – 0.5*log2(0.5) = 1
Entropy_Subset_3 = -0.5*log2(0.5) – 0.5*log2(0.5) = 1

Step 3: Calculate the Weight of Each Subset of Data After the Split

Subset 1: 4/10 = 0.4
Subset 2: 2/10 = 0.2
Subset 3: 4/10 = 0.4

Weighted_Entropy_Subset_1 = 0.4*0.81 = 0.324
Weighted_Entropy_Subset_2 = 0.2*1 = 0.2
Weighted_Entropy_Subset_3 = 0.4*1 = 0.4

Step 4: Calculate the Information Gain as the Difference Between Before and After the Split Entropy Values

Information_Gain_Age = 1 – (0.324 + 0.2 + 0.4) = 0.076

We can repeat the same process for the other attributes in the dataset and select the attribute with the highest information gain.

Conclusion

In summary, information gain is a useful technique used in machine learning to identify the most informative feature in a dataset. Calculating information gain can help improve the performance of machine learning models, as it helps you select the best features for the model’s purpose. When calculating information gain, you should follow a simple four-step process that involves calculating the entropy of the dataset before and after the split, calculating the weight of each subset after the split, and finally, calculating the information gain.

We hope this guide has helped you understand how to calculate information gain in machine learning. Happy coding!