bayes

Bayes’s Theorem

Bayes's Thorem, for conditional probability

$$P(H\mid x)=\frac{P(x\mid H)P(H)}{P(x)}$$

aka Bayesian Inference.

• $P(H\mid X)$ - posterior probability
• $P(X\mid H)$ - likelihood
• $P(H)$ - prior probability
• $P(X)$ - evidence

Naive Bayes

• Assume the features are conditionally independent (hence “naïve”), to obtain the likelihood, then apply Bayes’ theorem.
• Advantages
  • Easy to implement
  • Good results in most of the cases
• Disadvantages
  • Assumes there is at least one training object that has any feature value of the test case. Otherwise, the predicted probability will be zero.
  • Assumes conditional independence.