Compute the conditional probabilities and class priors for

Question

Part A:

Introduction: K-Nearest Neighbor (KNN) is a supervised learning algorithm where the result of new instance query is classified based on majority of K-nearest neighbor category. The purpose of this algorithm is to classify a new object based on attributes and training samples. Indeed, KNN used neighborhood classification as the prediction value of the new query instance.

The following data classifying the Power Saving Lights by their economical feasibility as Preserver or Wasteful

We consider 2 factors for classifying:

X₁: Lightning Duration

X₂: Power Consuming

We suppose use the number of nearest neighbor's k = 2.

The following data presents six training samples, using the KNN algorithm, classify the last sample as Preserver or Wasteful assuming that X₁ = 10 and X₂ = 500

X1: Lightning Duration (Hours)	X2: Power Consuming (Watts)	Y: Classification
6	900	Wasteful
2	150	Wasteful
5	600	Wasteful
3	80	Preserver
4	200	Wasteful
2	60	Preserver
10	500	???????

Table 1: Training data

1) Calculate the Euclidian distance between the query-instance and all the training samples.

2) Sort the distance and determine nearest neighbors based on the k-th minimum distance.

3) Gather the category Y of the nearest neighbors.

4) Use simple majority of the category of nearest neighbors as the prediction value of the query instance.

Part B:

Let us consider the training data below dealing with "Eye disease problem" to learn Naive Bayes Classifier.

Record ID	Age	Spectacle prescription	Astigmatic	Tear production Rate	Class label Lenses
1	Young	Myope	No	Reduced	Noncontact
2	Young	Myope	No	Normal	Soft contact
3	Young	Myope	Yes	Reduced	Noncontact
4	Young	Myope	Yes	Normal	Hard contact
5	Young	Hypermetrope	No	Reduced	Noncontact
6	Young	Hypermetrope	No	Normal	Soft contact
7	Young	Hypermetrope	Yes	Reduced	Noncontact
8	Young	Hypermetrope	Yes	Normal	Hard contact
9	Pre-presbyopic	Myope	No	Reduced	Noncontact
10	Pre-presbyopic	Myope	no	Normal	Soft contact

The goal is to classify (as "Noncontact", as "Soft Contact or as "Hard contact") a new record: R11: (Pre-presbyopic, Hypermetrope, Yes, Reduced)

For this purpose you have to calculate P(NonContact), P(Hard Contact), and P(Soft Contact)

1. Compute the conditional probabilities and class priors for each class label in the training set.

2. Compute the probability to assign each class label for the new record.

Class Label = Soft Contact:

Class Label = Hard Contact:

Class Label = NonContact:

3. Which class is to assign to the new record? Justify your answer.