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Machine Learning Algorithms

Let's consider two probabilistic events, A and B. We can correlate the marginal probabilities P(A) and P(B) with the conditional probabilities P(A|B) and P(B|A), using the product rule:
Considering that the intersection is commutative, the first members are equal, so we can derive Bayes' theorem:
In the general discrete case, the formula can be re-expressed considering all possible outcomes for the random variable A:
As the denominator is a normalization factor, the formula is often expressed as a proportionality relationship:
This formula has very deep philosophical implications, and it's a fundamental element of statistical learning. First of all, let's consider the marginal probability, P(A). This is normally a value that determines how probable a target event is, such as P(Spam) or P(Rain). As there are no other elements, this kind of probability is called Apriori, because it's often determined by mathematical or contextual considerations. For example, imagine we want to implement...