Essential Maths for ML – Part 3
In my last blog [ Essential Maths for ML - Part 2 ] we have discussed about addition rule, multiplication rule of probability and conditional probability . In this blog, we will discuss the Bayes Theorem which plays an important role in most of the machine learning algorithms. So let’s consider A1, A2, A3, and A4 be the mutually exclusive and exhaustive event of a random experiment. Let B be the common event i.e. the event B is made-up of 4- mutually exclusive and exhaustive events. P(B) = P(A1 ⋂ B) + P(A2⋂B) + P(A3⋂B) + P(A4⋂B) P(B) = Σ P(Ai ⋂ B)…………(1) We already know from the concept of the conditional probability that P(A1⋂ B) = P(B) * P(A1/B) P(A1/B) = P(A1⋂ B) / P(B)………(2) Replacing the value of P(B) from the eq2 we can say that P(A1/B) = P(A1 ⋂ B) / Σ P(Ai ⋂ B) P(A1/B) = P(A1) * P(B/A1) / Σ P(Ai ⋂ B) So the Bayes Theorem states that if A1, A2, A3……….An, are n mutually exclusive and exhaustive events with prior probabilities P(A...