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.

Consider a classification problem where the input space consists of 10 binary features (X₁, X₂, ..., X₁₀) and the output space consists of two classes (0 and 1). A dataset of 100 training examples is given, with the following feature values and corresponding class labels:Example 1: (0, 1, 1, 0, 1, 0, 1, 0, 0, 1) → Class: 0Example 2: (1, 0, 0, 1, 1, 1, 0, 1, 0, 1) → Class: 1Example 3: (1, 1, 1, 0, 0, 1, 0, 0, 1, 0) → Class: 1Example 100: (0, 0, 1, 0, 1, 0, 1, 1, 0, 1) → Class: 0You are tasked with building a supervised learning model using logistic regression. Each feature Xi is binary and can take values 0 or 1. You decide to use one-hot encoding to represent the input features. After applying one-hot encoding, how many features will the dataset have for training the logistic regression model?a)19b)20c)10d)18

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.

k-NN: This problem derives a performance bound on the 1-NN classifier. Consider the 1-NN binaryclassifier on a two-dimensional space. For an input x and its nearest neighbor xn in the trainingdata, the conditional probabilities of belonging to classes c1 and c2 are as follows:◦ p(c1|x) : probability that x belongs to c1◦ p(c2|x) : probability that x belongs to c2◦ p(c1|xn) : probability that xn belongs to c1◦ p(c2|xn) : probability that xn belongs to c2Knowing that p(c1|x) + p(c2|x) = 1 and p(c1|xn) + p(c2|xn) = 1,(a) Express the conditional probability of misclassification error, e, for x, P (e|x, xn), in terms ofthe probabilities provided above.

We are given that P(A | B) = 0.6 and P(A) = 0.9. Since P(A | B) ≠ P(A), the occurrence of event B changes the probability that event A will occur. This implies that A and B are events.

How does the Naive Bayes classifier calculate the probability of a data point belonging to a particular class?Select one:a.By using the least squares methodb.By using the gradient descent algorithmc.By using the maximum likelihood estimationd.By using the Bayes theorem