Practice Problem on Random Forest
The ideal living condition depends on the temperature, wind, and humidity of the day. The
recorded temperature, wind, and humidity are given in the following dataset along with the living
status. We are trying to train a smart-home agent on the following dataset using the Random Forest
algorithm to display the living status of a smart home.
Construct the 1st decision tree using the instances of Day1 to Day5 and considering Temperature
and Wind features; the 2nd decision tree using the instances of Day2 to Day6 and considering
Wind and Humidity features; Please show all the necessary calculations to build the decision trees
considering 2 as the expansion threshold.
Day Temperature Wind Humidity Living status?
Day1 20 Weak Normal Ideal
Day2 22 Strong Abnormal Non-ideal
Day3 30 Strong Normal Ideal
Day4 24 Weak Abnormal Ideal
Day5 32 Strong Normal Non-ideal
Day6 34 Weak Normal Ideal
Day7 36 Weak Abnormal Non-ideal
If the recorded Temperature, Wind, and Humidity of Day 8 are ‘33’, ‘Strong’, and ‘Abnormal’
respectively. Infer the decision of the smart-home agent regarding the living status of Day 8 using
the bagging procedure of the Random Forest classifier.
Day Temp Wind Humidity Living status?
D1 20 Weak Normal Ideal
D2 Strong Abnormal Non-ideal
22
D3 30 Strong Normal Ideal
D4 24 Weak Abnormal Ideal
D5 32 Strong Normal Non-ideal
D6 34 Weak Normal Ideal
D7 36 Weak Abnormal Non-ideal
1st
Bootstrapped
Dataset
Day Temp Wind Humidity Living status?
D1 20 Weak Normal Ideal
D2 22 Strong Abnormal Non-ideal
D3 30 Strong Normal Ideal
D4 24 Weak Abnormal Ideal
D5 32 Strong Normal Non-ideal
Feature
subset:
Day Temp Wind Living status?
D1 20 Weak Ideal
D2 22 Strong Non-ideal
D3 30 Strong Ideal
D4 24 Weak Ideal
D5 32 Strong Non-ideal
Number of Number of Number of
Left side Left side GINI Number of Right side GINI score GINI
instances instances score of Right side instances of Right
Class with "Ideal with "Non- Left side instances with "Non- side
induced
by the
Temp class" Ideal" instances with "Ideal" ideal Class" instances separator
Considering Temp<
Ideal
21 as the separator
1 0 0 3 3 0.5
D1 20 0.6
Considering
Non-ideal Temp<23 as the 1 1 0.5 3 2 0.48
D2 22 separator 0.68
Considering
Ideal Temp<27 as the 2 1 0.4444 2 2 0.5
D4 24 separator 0.666667
Considering
Ideal Temp<31 as the 3 1 0.375 1 2 0.44444444
D3 30 separator 0.566667
D5 32 Non-ideal
Minimum GINI= 0.5667
GINI Impurity
of Temp i.e., 0.5666667
(Temp< 31)=
Living Status:
GINI Impurity of Living Status= 0.48
Wind Ideal Non-ideal GINI Impurity
Weak(2) 2 0 0
Strong(3) 1 2 0.444444444
GINI Impurity of Wind= 0.266666667
Wind
weak strong
Ideal ??
Day Temp Wind Humidity Living status?
D2 22 Strong Abnormal Non-ideal
D3 30 Strong Normal Ideal
D5 32 Strong Normal Non-ideal
Number of Number of Number of
Left side Left side GINI Number of Right side GINI score GINI
instances instances score of Right side instances of Right
Class induced
with "Ideal with "Non- Left side instances with "Non- side by the
Temp class" Ideal" instances with "Ideal" ideal Class" instances separator
Considering
Non-ideal Temp<26 as the 0 1 0 1 1 0.5
D2 22 separator 0.333333
Considering
Ideal Temp<31 as the 1 1 0.5 0 1 0
D3 30 separator 0.333333
D5 32 Non-ideal
Minimum GINI= 0.3333
GINI Impurity
of Temp i.e., 0.3333333
(Temp< 31) OR
(Temp<26)=
Humidity Ideal Non-ideal GINI Impurity
Normal (2) 1 1 0.5
Abnormal(1) 0 1 0
GINI Impurity of Humidity= 0.333333333
Wind Wind
Wind
weak strong weak strong
weak strong
Ideal Humidity Ideal Temp < 26
Ideal Temp < 31
Abnormal Normal No
Yes No Yes
Non-Ideal Ideal / Non-ideal Ideal / Non-Ideal Non-Ideal Ideal / Non-ideal
Non-ideal
2nd
Bootstrapped
Dataset
Day Temp Wind Humidity Living status?
D2 22 Strong Abnormal Non-ideal
D3 30 Strong Normal Ideal
D4 24 Weak Abnormal Ideal
D5 32 Strong Normal Non-ideal
D6 34 Weak Normal Ideal
Feature
subset:
Day Wind Humidity Living status?
D2 Strong Abnormal Non-ideal
D3 Strong Normal Ideal
D4 Weak Abnormal Ideal
D5 Strong Normal Non-ideal
D6 Weak Normal Ideal
Wind Ideal Non-ideal GINI Impurity
Weak(2) 2 0 0
Strong(3) 1 2 0.444444444
GINI Impurity of Wind= 0.266666667
Humidity Ideal Non-ideal GINI Impurity
Normal (3) 2 1 0.444444444
Abnormal(2) 1 1 0.5
GINI Impurity of Humidity= 0.466666667
Wind
weak strong
Ideal ??
Day Temp Wind Humidity Living status?
D2 22 Strong Abnormal Non-ideal
D3 30 Strong Normal Ideal
D5 32 Strong Normal Non-ideal
Number of Number of Number of
Left side Left side GINI Number of Right side GINI score GINI
instances instances score of Right side instances of Right
Class induced
with "Ideal with "Non- Left side instances with "Non- side by the
Temp class" Ideal" instances with "Ideal" ideal Class" instances separator
Considering
Non-ideal Temp<26 as the 0 1 0 1 1 0.5
D2 22 separator 0.333333
Considering
Ideal Temp<31 as the 1 1 0.5 0 1 0
D3 30 separator 0.333333
D5 32 Non-ideal
Minimum GINI= 0.3333
GINI Impurity
of Temp i.e., 0.3333333
(Temp< 31) OR
(Temp<26)=
Humidity Ideal Non-ideal GINI Impurity
Normal (2) 1 1 0.5
Abnormal(1) 0 1 0
GINI Impurity of Humidity= 0.333333333
Wind Wind
Wind
weak strong weak strong
weak strong
Ideal Humidity Ideal Temp < 26
Ideal Temp < 31
Abnormal Normal No
Yes No Yes
Non-Ideal Ideal / Non-ideal Ideal / Non-Ideal Non-Ideal Ideal / Non-ideal
Non-ideal
Query:
The recorded Temperature, Wind, and Humidity of Day 8 are ‘33’, ‘Strong’, and ‘Abnormal’
1st Tree: Non-ideal
2nd Tree: Non-ideal
3rd Tree: Ideal or Non-ideal
Answer: Non-ideal
