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Therefore, we have everything we need to calculate the information gain.In this case, information gain can be calculated as:gain = s_entropy – (8/20 * s1_entropy + 12/20 * s2_entropy)Tying this all together, the complete example is listed below.# calculate the entropy for the split in the dataset# calculate the entropy for the split in the dataset return -(class0 * log2(class0) + class1 * log2(class1))gain = s_entropy – (8/20 * s1_entropy + 12/20 * s2_entropy)First, the entropy of the dataset is calculated at just under 1 bit. Information Gain is also known as Mutual Information. Read the beginning of my Before we get to Information Gain, we have to first talk about Here’s how we calculate Information Entropy for a dataset with The easiest way to understand this is with an example. Technically, they calculate the same quantity if applied to the same data.We can understand the relationship between the two as the more the difference in the joint and marginal probability distributions (mutual information), the larger the gain in information (information gain).This section provides more resources on the topic if you are looking to go deeper.In this post, you discovered information gain and mutual information in machine learning. two classes in the case of a binary classification dataset.One interpretation of entropy from information theory is that it specifies the minimum number of bits of information needed to encode the classification of an arbitrary member of S (i.e., a member of S drawn at random with uniform probability).For example, in a binary classification problem (two classes), we can calculate the entropy of the data sample as follows:A dataset with a 50/50 split of samples for the two classes would have a maximum entropy (maximum surprise) of 1 bit, whereas an imbalanced dataset with a split of 10/90 would have a smaller entropy as there would be less surprise for a randomly drawn example from the dataset.We can demonstrate this with an example of calculating the entropy for this imbalanced dataset in Python. Before we get to Information Gain, we have to first talk about Information Entropy. The reason behind this is simple: by observing such a value one gains additional information about the behavior of a random variable. The In this context of feature selection, information gain may be referred to as “A quantity called mutual information measures the amount of information one can obtain from one random variable given another.The mutual information between two random variables It measures the average reduction in uncertainty about x that results from learning the value of y; or vice versa, the average amount of information that x conveys about y.Kullback-Leibler, or KL, divergence is a measure that calculates the difference between two probability distributions.The mutual information can also be calculated as the KL divergence between the joint probability distribution and the product of the marginal probabilities for each variable.If the variables are not independent, we can gain some idea of whether they are ‘close’ to being independent by considering the Kullback-Leibler divergence between the joint distribution and the product of the marginals […] which is called the mutual information between the variablesMutual information is always larger than or equal to zero, where the larger the value, the greater the relationship between the two variables. A common example is the Mutual Information and Information Gain are the same thing, although the context or usage of the measure often gives rise to the different names.Notice the similarity in the way that the mutual information is calculated and the way that information gain is calculated; they are equivalent:As such, mutual information is sometimes used as a synonym for information gain.

the distribution of classes. Information gain calculation. The In this context of feature selection, information gain may be referred to as “A quantity called mutual information measures the amount of information one can obtain from one random variable given another.The mutual information between two random variables It measures the average reduction in uncertainty about x that results from learning the value of y; or vice versa, the average amount of information that x conveys about y.Kullback-Leibler, or KL, divergence is a measure that calculates the difference between two probability distributions.The mutual information can also be calculated as the KL divergence between the joint probability distribution and the product of the marginal probabilities for each variable.If the variables are not independent, we can gain some idea of whether they are ‘close’ to being independent by considering the Kullback-Leibler divergence between the joint distribution and the product of the marginals […] which is called the mutual information between the variablesMutual information is always larger than or equal to zero, where the larger the value, the greater the relationship between the two variables. Last Updated on November 5, 2019 Information gain calculates the reduction in Read more

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