University AI - All Slides

All Slides of Artificial Intelligence

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~Ex.:

• $p(x|F)$ : Probability that $x$ (the person knocking on our door) is female.
• $p(x|M)$ : Probability that $x$ is male.
• $\theta$ : decision boundary.

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==First 2 Principal Components== : the first 2 eigen-vectors of the covariance matrix of the Gaussian distribution of the data.

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Where:

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

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 $i$ .

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The idea of projecting $\mathbb{X}$ on $\mathbb{Y}$ is the same as in the Unscented Kalman Filter and the Particle Filter, creating a pdf given some data:

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NOTE: We can use this to worsen the data to use in the training test, so to make a more robust model.

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$h=0.4$

$h=0.2$

$h=0.1$

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(Not to study):

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And so on, until we find a solution, usually it is not the optima one, to search for it we should search the whole tree.

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