What is the role of information gain in the id3 algorithm?

The ID3 algorithm is one of the basic algorithms in decision tree learning. It selects the best split point by calculating the information gain of each feature to generate a decision tree. Information gain is an important concept in the ID3 algorithm, which is used to measure the contribution of features to the classification task. This article will introduce in detail the concept, calculation method and application of information gain in the ID3 algorithm.

1. The concept of information entropy

Information entropy is a concept in information theory that measures the uncertainty of random variables. For a discrete random variable

Among them, n represents the number of possible values ​​​​of the random variable X, and p(x_i) represents the probability that the random variable X takes the value x_i. The unit of information entropy is bit, which is used to measure the minimum number of bits required to averagely encode a random variable.

The larger the value of information entropy, the more uncertain the random variable is, and vice versa. For example, for a random variable with only two possible values, if the probabilities of the two values ​​are equal, then its information entropy is 1, which means that a coding length of 1 bit is needed to encode it; if the probability of one of the values ​​is is 1, and the probability of another value is 0, then its information entropy is 0, which means that its value can be determined without coding.

2. The concept of conditional entropy

In decision tree learning, we need to calculate the contribution of features to the classification task. In order to measure the classification ability of a feature, we can calculate the uncertainty of classification with the feature given the feature, which is the conditional entropy. Assume that feature A has m values. For each value, we can calculate the probability distribution of the target variable under this value, calculate the corresponding information entropy, and finally find the conditional entropy, which is defined as follows:

H(Y|X)=\sum_{i=1}^{m}\frac{|X_i|}{|X|}H(Y|X=X_i)

Among them, |X| represents the size of the sample set is the information entropy of the target variable Y under the condition of A_i.

3. The concept of information gain

Information gain refers to using A to divide the sample set X under the condition that the feature A is known The amount of reduction in information entropy that can be obtained. The greater the information gain, the greater the information entropy obtained by using feature A to divide the sample set X is reduced, that is, the greater the contribution of feature A to the classification task. The definition of information gain is as follows:

IG(Y,X)=H(Y)-H(Y|X)

Where, H(Y) is the information entropy of the target variable Y, and H(Y|X) is the conditional entropy of the target variable Y under the condition of feature A.

4. Information gain calculation in ID3 algorithm

In the ID3 algorithm, we need to select the best features to divide the sample set X . For each feature A, we can calculate its information gain and select the feature with the largest information gain as the dividing point. Specifically, for each feature A, we can first calculate the number of samples with each value under the feature, then calculate the probability distribution of the target variable with each value under the feature, and calculate the corresponding information entropy . Then, we can calculate the conditional entropy of feature A, and subtract the conditional entropy from the information entropy to get the information gain. Finally, we select the feature with the largest information gain as the dividing point.

In practical applications, in order to prevent overfitting, we usually optimize the information gain, such as using gain ratio to select the best features. The gain ratio is the ratio of information gain to feature entropy, which represents the information gain obtained by using feature A to divide the sample set X relative to the information content of feature A itself. Gain ratio can solve the problem that information gain tends to select features with more values ​​when features have more values.

In short, information gain is a very important concept in the ID3 algorithm, which is used to measure the contribution of a feature to the classification task. In the ID3 algorithm, we select the best split point by calculating the information gain of each feature, thereby generating a decision tree. In practical applications, we can optimize the information gain, such as using gain ratio to select the best features.

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