CAP 5615 Introduction to Neural Networks Question 5 [2 pts]:

CAP 5615 Introduction to Neural Networks

Question 5 [2 pts]: In database showing in Table 1, please manually construct a Naïve Bayes Classifier, by using m-estimate to calculate the conditional probabilities (m=1, and p equals to 1 divided by the number of attribute values for each attribute). Please report priori probabilities and the conditional probabilities [1 pt]. Please use your Naïve Bayes classifier to determine whether a person should play tennis or not, under conditions that "Outlook=Overcast & Temperature=Hot & Humidity =Normal& Wind=Weak". Why or why not? [1 pt]

Question 6 [2 pts]: Please download mtcars.header.binary.categorical.txt dataset from Canvas (the "cyl" and "gear" are changed as categorical attributes, instead of numerical numbers). Please use R to implement tasks below:

·        Please use all instances from mtcars.header.binary.categorical.txt to train a Naïve Bayes classifier, and use the classifier to predict all instances in  mtcars.header.binary.categorical.txt, and report the classification accuracy [1 pt]

·        Please report the conditional probabilities for attributes "cyl" and "gear", and explain the meaning of the conditional probability values [1 pt]

Question 7 [3 pts]: Please download housing.header.binary.txt dataset from Canvas, and use R to implement tasks below (a brief description of this dataset is available from the following URL) https://archive.ics.uci.edu/ml/datasets/housing [The Medv attribute in housing.header.binary.txt is binarized with Medv value of the house greater than 200k being 1, or 0 otherwise. ]

1.     Please use 80% of instances in the "housing.header.binary.txt" dataset to build a Naïve Bayes Classifier. Report the performance of the NB classifier on the remaining 20% of instances in the "housing.header.binary.txt"

o  Report source code to build the NB classifier and answer the following tasks [0.5 pt]

o  Report confusion table, TPR, FPR, and the Accuracy [0.5 pt]

o  Report the ROC curve [0.5 pt]

o  Report the AUC value [0.5 pt]

o  Create a new instance with "Crim=0.03, Zn=13, Indus=3.5, Chas=0.3, Nox=0.58, Rm=4.1, Age=68, Dis=4.98, Rad =3, Tax=225, Ptratio=17, B=396, Lstat=7.56", and predict the Medv value of the instance. Report the posterior probability, and the classification result [1.0 pt]