Question $4$ Model hyperparameter tuning $[25$ marks$]$

$($a$)$ Write code to train a random forest classifier for the scikit$-$learn$$s breast cancer dataset $($see the load$\_$breast$\_$cancer$()$ function$).$ Use the default $($hyper$)$parameters of the classifier, apply $10-$fold cross$-$validation, find and display the test score of the model. $[5]$

$($b$)$ Write code to display the hyperparameters of the random forest classifier model. $[3]$

$($c$)$ Write code to perform a randomized search to find the potentially best hyperparameters of applying the random forest model to the breast cancer dataset. Search in $50$ random samples of parameter settings. Use the search parameter settings below, and output the best model instance, score, and parameter values.

$[13]$

$$the number of trees: integer range from $10$ to $1000$ in increments of $10$

$$ the number of features to consider when looking for the best split: integer range from $1$ to the number of features of the breast cancer data

$$ the maximum depth of the tree: integer range from $1$ to $20$

$($d$)$ Refer to the documentation of scikit$-$learn and answer the following questions. $[4]$

$($i$)$ In the sklearn.model$\_$selection module, beside GridSearchCV and RandomizedSearchCV, there are two other classes that search for optimized hyperparameters. What are the two classes?

$($ii$)$ Briefly describe the search strategy of the two classes.