$($c$)$ A clasification tree, a SVM clnssifier with GRBF kernel, and a randen farest

dasifier are compared and tuned using the caret $R$ porknge. The classifiers

are compared using a $7-$fold cross$-$validation procedure replicsated $10$ times,

over approprintely specified grids of vulues of their associnted hyperparame$-$

ters. The following figures report the avernge validation nocunacy as a function

of the hyperparameters of the classification tree, of the SVM classifier, and of

the randoen forest clnssifier.

Lampataxy renameter

Random forest

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

$($ii$)$ Which is the best clnsifier and what are its optimal hyperparameters?

$($iii$)$ Are there any issues with the tuning procedure of any of the clasifiers?

If yes, what solution would you suggest?

$($d$)$ A team of engineers gnthered data on different material characteristics of a

specific mechanical component usad in the construction of wind turbines, with

the purpose of developing a machine learning system capable of detecting

falty components, so to avoid the use of a potentially defective camponent

in the canstruction of a turbine. The percentage of faulty components in the

dnta is $5\%.$ The team implements two logistic regression models, $L_1$ and $L_2,$ defined using

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

bosed on their ahility to detect fanlts in this specific mochanical camponemt

of wind turbines. The models produce the following performance metrics

The team af engineers cansiders it more costly to empley a malfunctioning

component in the canstruction of the wind turbine than to wrongly discard a

non$-$defective component.

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

Justify your nnswer.Provide your answer and a concise explanation for soch of the following questions.

$($a$)$ Association rule analysis is npplied to a large dntaset concerning $4078$ food

and beverage purchness of n cafe in Dublin. The rule $\{$Cof fee $=>$ Croissant $\}$

is considered for nnalysis. The rule hns a support meseure of $0\mathrm{.}3648347,$ and

it wns mined using the npriori algorithm with support threshold set to $0\mathrm{.}30$

and confidence threshold set to $0\mathrm{.}70.$ In the dntn$,$ there are $2047$ transactions

involving Coffee, and $1621$ transacticns involving Croissant. Campute the

confidence and lift mensures of this rule.

$($b$)$ Data on the chemical analysis of $5$ different types of glass of differemt socurce:

w$1$ndov, vehicle, conta$1$ner, tableware, nnd lamp. A clossification tree is

trained an these: data with the purpose of predicting the type of glass on the

busis of the chemical camponents far criminologiosal investigation. The output

from the tree is reported below.

$n=214$

node

dosotes torainal node

root $21468$ uindow $(0\mathrm{.}630\mathrm{.}079,0\mathrm{.}061,0\mathrm{.}0420\mathrm{.}14$

Bar $0\mathrm{.}33518541$ uindow $(0\mathrm{.}780\mathrm{.}0920\mathrm{.}0650\mathrm{.}049,0\mathrm{.}016)$

$M{g}_g-2\mathrm{.}56,150,18$ vindow $(0\mathrm{.}83,0\mathrm{.}11000\mathrm{.}0067)$

g$)$ Cac$8\mathrm{.}315,52,0$ vindow $(10000$