Problem $2$: Random Forest Classification

Assume that a dataset contains two columns that are to be used as features in a decision tree classifier. These

columns are named x$0$ and x$1.$ Both features are continuous numerical features. The label is a categorical

variable with two possible values: $0$ and $1.$ The two features are combined $($in order$)$ by a VectorAssembler

object to create a column named features.

Suppose that three decision tree classifiers are trained on bootstrap samples drawn from this dataset. Each tree

uses the features column as its input. The contents of the toDebugString attribute of each tree is shown

below.

Tree Model $1$

If $($feature $0<=3\mathrm{.}0)$

If $($feature $1<=5\mathrm{.}0)$

Predict: $0\mathrm{.}0$

Else $($feature $1>5\mathrm{.}0)$

Predict: $1\mathrm{.}0$

Else $($feature $0>3\mathrm{.}0)$

If $($feature $1<=3\mathrm{.}0)$

Predict: $1\mathrm{.}0$

Else $($feature $1>3\mathrm{.}0)$

Predict: $0\mathrm{.}0$

Tree Model $2$

If $($feature $1<=5\mathrm{.}0)$

If $($feature $1<=3\mathrm{.}0)$

Predict: $1\mathrm{.}0$

Else $($feature $1>3\mathrm{.}0)$

Predict: $0\mathrm{.}0$

Else $($feature $1>5\mathrm{.}0)$

If $($feature $0<=2\mathrm{.}0)$

Predict: $1\mathrm{.}0$

Else $($feature $0>2\mathrm{.}0)$

Predict: $0\mathrm{.}0$

Tree Model $3$

If $($feature $0<=4\mathrm{.}0)$

If $($feature $1<=3\mathrm{.}0)$

Predict: $0\mathrm{.}0$

Else $($feature $1>3\mathrm{.}0)$

Predict: $1\mathrm{.}0$

Else $($feature $0>4\mathrm{.}0)$

If $($feature $0<=6\mathrm{.}0)$

Predict: $1\mathrm{.}0$

Else $($feature $0>6\mathrm{.}0)$

Predict: $0\mathrm{.}0$

Consider a new observation for which x$0=5\mathrm{.}0$ and x$1=4\mathrm{.}0.$ Use the rules above to determine which of the

two labels each tree model would assign to this observation. Then assume that a random forest is created from

these three trees. Determine the label that the random forest would assign to the new observation. Provide

your answers in the format shown below.

Tree Model $1$ Prediction: xxxx

Tree Model $2$ Prediction: xxxx

Tree Model $3$ Prediction: xxxx

Random Forest Prediction: xxx