Maximum Likelihood Decision Rule

Definition

It gives the formula to find the most like state for a given evidence.

$$s^{\ast }=\arg \underset{i\in \mathcal{S}}{\max }\underset{\text{Likelihood}}{\underbrace{p(\mathbf{x}\mid s=i)}}$$

where,

• $s^{\ast }$: Class that maximizes the Likelihood function.
• $\mathbf{x}$: feature vector
• $s$: Class

Note

• When there no Prior i.e. $P(s=i)=1$, the classes are equiprobable, i.e. $P(s=i)=\frac{1}{N}$, then the Bayes Classifier becomes a Maximum Likelihood Decision Rule.
• The act of choosing the state to find the highest Likelihood is the decision here.