D Hockmark lisis paga

Final due Sep $9,202417$:$2915$T

Consider a classification protalem where we are given a training set of $97$ examples and labels

$S_e-\{(x^{(n)}+y^{(\text{'})})$;$i=1,$dots,$n\},$ where at ${?}^{(i)}in{R}^2$ and $g^{(i)}in\{1,-1\}.$

Assume a different data set for the two problems belaw.

$(1)$

$2\mathrm{.}5$ points pessible $[$gradod$,$ results hidden$)$

Consider a classification problem where we are given a training set of $n$ examples and labels

$S_n-\{(x^{(i)},y^{(i)})$;$i=1,$dots,$n\},$ where $x^{(i)}in{R}^2$ and $y^{(2)}in\{1,-1\}.$

Suppose for a moment that we are able to find a linear classifier with parameters ${}^{\text{'}}$ and ${}_0^{\text{'}}$ such that

$y^{\text{'}0}({}^{\text{'}},n^{()}+{}_0)>0$ for all $i=1,$dots,$n.$

Let hat$()$ and hat$({)}_0$ be the parameters of the maximum margin linear classifier, if it exists, obtained by minimizing

$\frac{1}{2}|||{|}^2,$ subject $to{y}^{th}(*x^{(0)}+{}_0)1$ for all $i=1,$dots,$n$

Determine if each of the following statements is True or False. $($As usual, "True" means always true; "False"

means not always true.$\}$

The minimization problem defined by the equation imenediately above has a solution if and only if the

training examples