Question

The posterior probabilities of four hypothesis h1,h2,h3,h4 are (0.2, 0.5,0.2, 0.1) respectively. A new training sample is classified +ve by h2 and h3, while h1 and h4 classify the same data instance as -ve. Find the classification with Bayes Optimal Classifier and Brute Force Classification?

Answer 1

The naive bayes classifier treats every attribute independently It will sum up the weightage of the classifiers which identified the tuple as +ve and -ve separately and compare them The sample will be assigned to the class with more value

given h2 and h3 identified as +ve Sum of weight of h2 and h3 = 0.5 + 0.2 = 0.7

h1 and h4 identified as -ve Sum of weight of h1 and h4 = 0.2 + 0.1 = 0.3

Since sum of +ve class is more hence the new sample will be classified as +ve

In brute force classification, the posterior do not matters It will check the number of classifiers which identified the sample as +ve and -ve and The sample will be assigned to the class with one with the more value

Since sample is identified as -ve by 2 classifiers(h1 and h4) and +ve by 2 classifiers(h2 and h3) Therefore it is a tie and the sample will be assigned to the default class (Default class is pre decided by the developer)

I have tried to explain it in very simple language and I hope that i have answered your question satisfactorily.Leave doubts in comment section if any