Machine Learning for OpenCV 4 - Second Edition

Understanding the Naive Bayes classifier

So far, we have only talked about one piece of evidence. However, in most real-world scenarios, we have to predict an outcome (such as a random variable, Y) given multiple pieces of evidence (such as random variables X₁ and X₂). So, instead of calculating p(Y|X), we would often have to calculate p(Y|X₁, X₂, ..., X_n). Unfortunately, this makes the math very complicated. For two random variables, X₁ and X₂, the joint probability would be computed like this:

The ugly part is the term p(X₁|X₂, C), which says that the conditional probability of X₁ depends on all other variables, including C. This gets even ...