Mastering the Art of Calculating Information Gain

Mastering the Art of Calculating Information Gain

Have you ever wondered how data scientists select the most important features for a given problem? One technique they use is called Information Gain, a popular approach in the field of Machine Learning.

Simply put, Information Gain measures the decrease in uncertainty caused by a feature. In other words, it tells us how much we know about the target variable after taking into consideration a particular attribute.

In this article, we’ll take an in-depth look at Information Gain and how to calculate it effectively.

The Math behind Information Gain

Information Gain is based on the concept of Entropy, which measures the impurity of a set of labels. The more homogeneous the set is, the lower its Entropy. Conversely, a more diverse set will have a higher Entropy value.

Here’s the formula for Entropy:

H(T) = -∑ p(i) log2(p(i))

Where H(T) is the Entropy of the set, p(i) denotes the probability of each label, and log2 is the binary logarithm.

To understand this formula, let’s take an example. Suppose we have a set of patients, and we want to predict the outcome of their treatment, which can be either Successful or Failed. If all patients have recovered, then the Entropy is zero since there’s no uncertainty. If half of them have recovered and half have not, the Entropy is one, which means we have no information about the outcome. If the majority of patients have recovered, say 80%, then the Entropy would be 0.722, implying that we have some information about the outcome, but not enough to be confident.

Now that we know how to calculate Entropy, let’s move on to Information Gain.

Information Gain is defined as the difference between the Entropy of the original data set and the weighted average of the Entropy of its subsets after splitting on a particular attribute.

Here’s the formula for Information Gain:

IG(T, A) = H(T) – ∑ (|S| / |T|) * H(S)

Where IG(T, A) is the Information Gain of attribute A on data set T, |S| is the number of instances in subset S, and |T| is the total number of instances in the original set.

To put it simply, Information Gain tells us how much we’ll learn about the target variable if we split the data on a particular feature.

For instance, if we have a data set with three attributes, A, B, and C, and we split the data on attribute A, we can calculate the Information Gain of A as follows:

IG(T, A) = H(T) – [(|S1| / |T|) * H(S1) + (|S2| / |T|) * H(S2)]

Where S1 and S2 are the subsets resulting from the split using attribute A.

Applications of Information Gain

Information Gain is a widely-used technique in Machine Learning for feature selection. By calculating the Information Gain of each attribute, we can decide which ones are more relevant to the problem at hand.

For example, if we’re trying to predict the price of a house based on features such as location, size, and age, we can use Information Gain to determine which feature has the most impact on the price. Suppose we calculate the Information Gain of each attribute and find that location has the highest value. This means that if we know the location of a house, we’ll be able to predict its price more accurately.

Information Gain is also useful for building decision trees, a popular algorithm that uses a series of questions to classify instances. Decision trees work by selecting the attribute with the highest Information Gain at each step and splitting the data accordingly.

Conclusion

Information Gain is a powerful technique for selecting relevant features in Machine Learning. By measuring the decrease in uncertainty caused by each attribute, we can identify those that have the most impact on the target variable.

In this article, we’ve learned how to calculate Information Gain using Entropy and the formula for weighted average. We’ve also seen some applications of Information Gain in feature selection and decision tree construction.

As you explore the world of Machine Learning, keep in mind that mastering the art of calculating Information Gain is a crucial step towards building accurate and efficient models.