The tesm irnplements two logistic regression models, $L_1$ and $L_2,$ defined using

different sets of input vuriables. These models are evulunted and compared

based on their nbility to detect faults in this specific mochnnienl coenponent

of wind turbines. The models produce the following performance metrics:

The tearn of engineers considers it more costly to employ a mnlfunctioning

component in the construction of the wind turbine then to wrongly diseard n

non$-$defective carmponent.

Using the information nvilable, which of the two models would they prefer?

Justify your answer.$($c$)$ A clasificstion tree, a SVM clnssifer with GRBF hernel, nnd a mudom forest

classifier are compared and tuned using the caret $R$ packnge. The classifers

are compared using a $7-$fold cross$-$validntion procedure replicated $10$ times,

cover approprintely specified grids of values of their swocinted hyperparume$-$

ters. The following figures report the avernge vulidation nocuracy as n function

of the hyperparameters of the clnsification tree, of the SVM clasifier, and of

the randoen forest clnssifier.

flacetitionation tran

Random torest

$($i$)$ How many classifiers have been trained in total? Justify your answer.

$($ii$)$ Which is the best clasifier and what are its optimal hyperpanameters?

$($iii$)$ Are there any isuus with the tuning procedure of any of the clnssifiers?

If yes, what solution would you suggest?

$($d$)$ A team of engineers gathered dnta an different material chanucteristics of n

specife mechaniosl companent used in the canstruction of wind turbines, with

the purpose of developing a machine learning systern capable of detecting

faulty components, $90$ to avoid the rase of a potentinlly defoctive component

in the construction of n turbine. The percentnge of faulty components in the

dntn is $5\%.$