$($a$)$ What issues are to be considered while selecting a model for applying machine learning in a given problem.

$(4$ Marks$)$

$($b$)($i$)$ Clearly differentiate between feature selection and feature extraction.

$($ii$)$ Describe the forward selection algorithm for implementing the subset selection procedure for dimensionality reduction and specify any requirement$($s$)$ and$/$or limitation$($s$).$

$($iii$)$ Given the data in the following table, use PCA to reduce the dimension from $2$ to $1$ :

$\backslash$table$[[$Feature$,$Example $1,$Example $2,$Example $3,$Example $4],[x_1,4,8,13,7],[x_2,11,4,5,14]]$

$(4+6+11$ Marks $)$

Question $2$: $(25$ Marks$)$

$($a$)$ Consider the problem of finding a rule for determining days on which one can enjoy water sport. The rule is to depend on a few attributes like "temp", "humidity", etc. Suppose we have the following data to help us devise the rule. In the data, a value of $"1"$ for "enjoy" means "yes" and a value of $"0"$ indicates $"$no$".$

Table $1$: Attributes Data.

$\backslash$table$[[$Example$,$Sky$,$Temp,Humidity,wind,Water,Forecast,Enjoy$],[1,$Sunny,Warm,Normal,Strong,Warm,Same,$1],[2,$Sunny,Warm,High,Strong,Warm,Same,$1],[3,$Rainy,Cold,High,Strong,Warm,Change,$0],[4,$Sunny,Warm,High,Strong,Cool,Change,$1]]$

Find the hypothesis space and the version space for the problem.

$(6$ Marks$)$

Please Turn Over

Page $2$ of $4$

$($b$)$ Explain cross$-$validation in machine learning and hence explain the different types of cross$-$validations along with their limitations$,$ if any.

$($c$)$ Given the following data in Table $2,$ construct the ROC curve of the data. Compute the AUC.

Table $2$: Data.

$\backslash$table$[[$Threshold$,$TP$,$TN$,$FP$,$FN$],[1,0,25,0,29],[2,7,25,0,22],[3,18,24,1,11],[4,26,20,5,3],[5,29,11,14,0],[6,29,0,25,0],[7,29,0,25,0]]$

$(6+3$ Marks $)$

Question $3$: $(25$ Marks$)$

$($a$)$ Write down the naive Bayes' algorithm.

$($b$)$ How do we use numeric features with Naive Bayes?

$(6$ Marks$)$

$($c$)$ Find the ML estimate for the parameters representing the mean and that representing the variance in the normal probability function.

$(7$ Marks$)$

$($d$)$ Let $S$ be a set of examples, $A$ a feature having $c$ different values and let the set of values of $A$ be denoted by Values$($A$).$ Define Gain$($S$,$A$),$ Split Information $(S,A)$ and Gain Ratio $(S,A).$