Question11 We will use the dataset below to learn a decision tree which predicts if a patient has COVID-19 (Yes, or No), based on the Temperature (High, Medium, or Low) and whether the patient has dry cough (Yes, or No). (note: [math] )[table]
Temp. | Cough | COVID-19 Low | No | No Low | Yes | Yes Medium | No | No Medium | Yes | Yes High | No | Yes High | Yes | Yes
[/table]Assuming that H(COVID-19) = 0.8 and Gain(S, Temperature) = 0.3 and Gain(S, Cough) = 0.5, which one of the following would be the full decision tree, learnt for this dataset? (select one) ResetMaximum marks: 1.5 Flag question undefined

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BlackTom AI · Accepted Answer

Question restatement and options:
- Question: We will use the dataset below to learn a decision tree which predicts if a patient has COVID-19 (Yes, or No), based on the Temperature (High, Medium, or Low) and whether the patient has dry cough (Yes, or No). Assuming that H(COVID-19) = 0.8 and Gain(S, Temperature) = 0.3 and Gain(S, Cough) = 0.5, which one of the following would be the full decision tree, learnt for this dataset? (select one)
- Answer options: not provided in the prompt (empty).

Dataset interpretation:
- The table describes outputs (COVID-19: Yes/No) for each combination of Temperature and Cough:
  Low & No cough -> No
  Low & Yes cough -> Yes
  Medium & No cough -> No
  Medium & Yes cough -> Yes
  High & No cough -> Yes
  High & Yes cough -> Yes

Reasoning through how to build the full tree with information gain:
- Step 1: Compare the information gains for the possible root splits. Gain(Cough) = 0.5, Gain(Temperature) = 0.3. Since splitting on Cough yields higher information gain, the first decision node should be Cough at the root.
- Step 2: Determine outcomes for each branch of the root split (Cough = Yes vs Cough = No).
  • If Cough = Yes: From the dataset, when Cough is Yes, the COVID-19 outcome is Yes for all Temperature levels (Low, Medium, High). Therefore, the branch Cough = Yes immediately leads to a leaf predictor Yes, with no further splits needed.
  • If Cough = No: The outcomes depend on Temperature:
     - Temperature = Low and Cough = No -> COVID-19 = No
     - Temperature = Medium and Cough = No -> COVID-19 = No
     - Temperature = High and Cough = No -> COVID-19 = Yes
     Hence, for the Cough = No branch, a subsequent split by Temperature is informative, yielding two No leaves (Low, Medium) and one Yes leaf (High).

Constructing the full tree based on this logic:
- Root node: Cough
  - If Cough = Yes: predict COVID-19 = Yes (leaf)
  - If Cough = No: proceed to a Temperature split
    - If Temperature = Low: COVID-19 = No (leaf)
    - If Temperature = Medium: COVID-19 = No (leaf)
    - If Temperature = High: COVID-19 = Yes (leaf)

Variability note:
- Different datasets or different gain values can yield alternative root splits (e.g., Temperature as root if its gain were higher). Here, the given gains favor Cough as the root, followed by a Temperature-based refinement only for the Cough = No branch, which mirrors the typical construction for this small, discrete dataset.

In summary, the full decision tree structure implied by the provided gains and data is:
- Root: Cough
  - Yes -> Yes (leaf)
  - No -> Temperature split
    - Low -> No (leaf)
    - Medium -> No (leaf)
    - High -> Yes (leaf)

Note: The answer options in the prompt are missing, so this explanation derives the intended full tree from the data and the given information gains.

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