A naive bayes classifier is used to classify a test sample T. The parameters can be computedfrom the training samples in the table below. What will be the class of T = (R,V,D)?F1 F2 F3 TargetR S D YR S D NR S D YY S D NY S I YY V I NY V I YY V D NR V I NR S I Y
Question
A naive bayes classifier is used to classify a test sample T. The parameters can be computedfrom the training samples in the table below. What will be the class of T = (R,V,D)?F1 F2 F3 TargetR S D YR S D NR S D YY S D NY S I YY V I NY V I YY V D NR V I NR S I Y
Solution
To determine the class of the test sample T = (R, V, D) using a naive Bayes classifier, we need to compute the parameters from the training samples provided in the table.
Step 1: Calculate the prior probabilities of each class.
- Count the number of samples in each class:
- Class Y: 4 samples
- Class N: 4 samples
- Calculate the prior probability of each class:
- P(Y) = 4/8 = 0.5
- P(N) = 4/8 = 0.5
Step 2: Calculate the likelihood probabilities for each feature given each class.
- For each feature F1, F2, and F3, calculate the conditional probabilities for each possible value given each class.
- Count the number of occurrences of each feature value for each class:
- For class Y:
- F1=R: 3 occurrences
- F1=V: 1 occurrence
- F2=S: 3 occurrences
- F2=V: 1 occurrence
- F3=D: 4 occurrences
- F3=I: 0 occurrences
- For class N:
- F1=R: 1 occurrence
- F1=V: 3 occurrences
- F2=S: 2 occurrences
- F2=V: 2 occurrences
- F3=D: 1 occurrence
- F3=I: 3 occurrences
- For class Y:
- Calculate the conditional probabilities for each feature value given each class:
- P(F1=R|Y) = 3/4 = 0.75
- P(F1=V|Y) = 1/4 = 0.25
- P(F1=R|N) = 1/4 = 0.25
- P(F1=V|N) = 3/4 = 0.75
- P(F2=S|Y) = 3/4 = 0.75
- P(F2=V|Y) = 1/4 = 0.25
- P(F2=S|N) = 2/4 = 0.5
- P(F2=V|N) = 2/4 = 0.5
- P(F3=D|Y) = 4/4 = 1.0
- P(F3=I|Y) = 0/4 = 0.0
- P(F3=D|N) = 1/4 = 0.25
- P(F3=I|N) = 3/4 = 0.75
Step 3: Calculate the posterior probabilities for each class given the test sample T.
- Multiply the prior probability of each class by the conditional probabilities of each feature value given that class:
- For class Y:
- P(Y|T) = P(Y) * P(F1=R|Y) * P(F2=V|Y) * P(F3=D|Y) = 0.5 * 0.75 * 0.25 * 1.0 = 0.09375
- For class N:
- P(N|T) = P(N) * P(F1=R|N) * P(F2=V|N) * P(F3=D|N) = 0.5 * 0.25 * 0.75 * 0.25 = 0.0234375
- For class Y:
Step 4: Compare the posterior probabilities and determine the class with the highest probability.
- In this case, P(Y|T) = 0.09375 and P(N|T) = 0.0234375.
- Since P(Y|T) > P(N|T), the class of the test sample T = (R, V, D) is Y.
Therefore, the class of the test sample T = (R, V, D) is Y.
Similar Questions
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