Probability of Error: For performing classification, Bayesian selection criteria minimizes theprobability of misclassification. When classifying an input x, the Bayesian selection criteriawill assign x to its most probable class. Given a set of L classes (c1, c2, ..., cL), the probability ofx belonging to class ci is given as P (ci|x). The maximum conditional probability is describedas: P (ci∗ |x) = argmaxiP (ci|x). From this, derive the Bayesian conditional probability ofmisclassification, P ∗(e|x), for a given input x and express its average over the prior distributionof x.

Another training data point, xm, is the 2nd nearest neighbor of x. Show the conditionalprobability of misclassification error considering both xn and xm, P (e|x, xn, xm).

The function is used to convert logits into probabilities in a multi-class classification problem.

Consider a binary classification problem with two classes, A and B with prior probability P(A)=0.6𝑃(𝐴)=0.6 and P(B)=0.4𝑃(𝐵)=0.4 .Let X be a single binary feature that can take values 00 or 11. Given: P(X=1|A)=0.8𝑃(𝑋=1|𝐴)=0.8 and P(X=0|B)=0.7𝑃(𝑋=0|𝐵)=0.7. Determine which class the classifier will classify when X=1𝑋=1.

A Classification rule is said?*1 pointc. Probabilistic classificationa. Discriminative classificationd. Both a and cb. Generative classification

Introduction to Naive Bayes algorithm for classification.