Understanding Point-wise Mutual Information: A Complete Guide for Beginners

Point-wise Mutual Information (PMI) is an important concept for machine learning and natural language processing. It is used to measure the association between two words in a corpus of text. PMI is an excellent tool to assess the significance of the co-occurrence of two words in a text. In this article, we will explore everything you need to know about PMI.

What is Point-wise Mutual Information?

Point-wise Mutual Information (PMI) is a measure of the association between two words, a and b, in a corpus of text. PMI measures the probability of the co-occurrence of two words, and compares it to the probability of their occurrence independently. For example, if the word ‘car’ occurs more often with the word ‘road’ than alone, PMI measures the strength of their association.

How is PMI calculated?

The formula used to calculate PMI is:

PMI(a, b) = log [P(a, b) / (P(a) * P(b))]

Where:
P(a, b) is the probability of both words occurring together.
P(a) is the probability of the word ‘a’ occurring in the text.
P(b) is the probability of the word ‘b’ occurring in the text.

What does PMI tell us?

PMI measures the likelihood of the co-occurrence of two words. If PMI is positive, it means that two words occur together more often than independently, and thus are closely associated. On the other hand, if PMI is negative, it means that two words are more likely to appear separately than together, indicating a weak association. PMI values can range from negative infinity to positive infinity.

How is PMI used in NLP?

PMI is used in various tasks in natural language processing like text classification, information retrieval, and sentiment analysis. In text classification, PMI helps to identify the most relevant words in a text. In information retrieval, PMI helps to rank the results based on the relevance of the words. In sentiment analysis, PMI helps to identify the most polarizing words to determine the overall sentiment of a text.

Examples of PMI in action:

Let’s take an example of two words ‘wine’ and ‘cheese.’ Suppose in a corpus of text, the probability of ‘wine’ is 0.1 and that of ‘cheese’ is 0.2. The probability of ‘wine and ‘cheese’ occurring together is 0.05. Using the PMI formula, we get:

PMI(wine, cheese) = log(0.05/(0.1*0.2)) = 0.607

Since the value is positive, it signifies that the words are highly associated with each other.

Conclusion:

Point-wise Mutual Information (PMI) is a powerful tool that measures the association between two words in a corpus of text. PMI is essential for various applications in natural language processing and machine learning. Understanding PMI enables you to assess the significance of the co-occurrence of words in a text accurately.

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By knbbs-sharer

Hi, I'm Happy Sharer and I love sharing interesting and useful knowledge with others. I have a passion for learning and enjoy explaining complex concepts in a simple way.

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