In: Statistics and Probability
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?
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)