University AI - Supervised Parametric Estimation (Slides)

Where:

• ${\nabla }_{\underline{\Theta }}l(\hat{\underline{\Theta }})$ is the gradient of the log-likelihood function $l(\hat{\underline{\Theta }})$ with respect to $\Theta$

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~Ex.: Max-Likelihood Math Formulas

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~Ex.: Handwritten Character Recognition with Supervised Parametric Estimation

Referring to the second “Note*”*:

• $P(w_i|\underline{x})$ : real probability that $\underline{x}$, the data or variable we want to classify belongs to/is identified as the class ${\omega }_i$ (~ex.: in reality the percentage of male and female is $48\%/52\%$).
• $\hat{P}(w_j|\underline{x})$ : $\hat{P}(w_i|\underline{x})$ : estimated probability of $P(w_i|\underline{x})$ (~ex.: we estimate that the the percentage of male and female is $50\%/50\%$ , tho this is not actually true).
• ${\sum }_{j\ne i}\hat{P}(w_j|\underline{x})$ : estimated error probability for the class $i$ .