Natural Language Processing(Part 14)-Probability and Bayes’ Rule
📚Chapter 3: Sentiment Analysis (Naive Bayes)
Probability and Bayes’ Rule
Outline
- Introduction
Probabilities
Probability of the Intersection
Probability is fundamental to many applications in NLP. You’ll see how you can use it to help classify whether a tweet is positive or negative. Let’s get started.
1- Introduction
To start, we are going to first review what’s probabilities and conditional probabilities are, how they operate, and how they can be expressed mathematically. Then I’ll go over how to derive Bayes rule from the definition of conditional probabilities. Bayes rule is applied in many different fields, ranging from medicine to education and is used extensively in NLP. Once you understand the theory behind Bayes rule, you can use it to perform sentiment analysis on tweets,
Imagine you have an extensive corpus of tweets that can be categorized as either positive or negative sentiment, but not both. Within that corpus, the word happy is sometimes being labeled positive and sometimes negative.
2- Probabilities
Let’s explore why this situation is occurring.
One way to think about probabilities is by counting how frequently events occur. Suppose you define event A as a tweets being labeled positive, then the probability of event A, shown as B of A here, is calculated as the ratio between the counts of positive tweets in the corpus divided by the total number of tweets in the corpus.
In this example, that number comes out to 13 over 20, or 0.65. You could also express this value as a percentage, 65 percent positive. It’s worth noting that the complimentary probability here, which is the probability of the tweets expressing a negative sentiment is just equal to one minus the probability of a positive sentiment.
Note that for this to be true, all tweets must be categorized as either positive or negative but not both. Let’s define Event B in a similar way by counting tweets containing the word happy. In this case, the total number of tweets containing the word happy, shown here as N-happy is 4.
3- Probability of the Intersection
Here’s another way of looking at it. Take a look at the section of the diagram were tweets are labeled positive and also contain the word happy. In the context of this diagram, the probability that a tweet is labeled positive and also contains the word happy is just the ratio of the area of the intersection divided by the area of the entire corpus.
In other words, if there were 20 tweets in the corpus, and three of them are labeled positive and also contain the word happy, then the associated probability is 3 divided by 20 or 0.15. You now know how to calculate the probability of an intersection. You know how to calculate the probability of a word, namely happy with the probability of being positive. In the next Tutorial, we willtalk about Naive Bayes.
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References
1- Natural Language Processing with Classification and Vector Spaces
