Description
Problem 1
(Non-parameteric density estimation 35pts)
1. (20pts) Write a function [p, x] = mykde(X,h) that performs kernel density estimation on data X
with bandwidth h. It should return the estimated density p(x) and its domain x where you estimated
the p(x) for X in 1-D and 2-D.
• Generate N = 1000 Gaussian random data with µ1 = 5 and σ1 = 1. Test your function mykde on
this data with h = {0.1, 1, 5, 10}. In your report, report the histogram of X along with the figures
of estimated densities.
• Generate N = 1000 1-D Gaussian random data with µ1 = 5 and σ1 = 1 and another Gaussian
random data with µ2 = 0 and σ2 = 0.2. Test your function mykde on this data with h =
{0.1, 1, 5, 10}. In your report, report the histogram of X along with the figures of estimated
densities.
2. (15pts) Generate 2 sets of 2-D Gaussian random data with N1 = 500 and N2 = 500 using the following
parameters:
µ1 = [1, 0], µ2 = [0, 2.5], Σ1 =
0.9 0.4
0.4 0.9
, Σ2 =
0.9 0.4
0.4 0.9
. (1)
Test your function mykde on this data with h = {0.1, 1, 5, 10}. In your report, report figures of estimated
densities.
CSE5334 Data Mining Assignment 2
Problem 2
(Naive Bayes, 65pts)
Generate 1000 training instances in two different classes (500 in each) from multi-variate normal distribution using the following parameters for each class
µ1 = [1, 0], µ2 = [0, 1], Σ1 =
1 0.75
0.75 1
, Σ2 =
1 0.75
0.75 1
(2)
and label them 0 and 1. Then, generate testing data in the same manner with 500 instances for each class,
i.e., 1000 in total.
1. (30pt) Implement your Naive Bayes Classifier [pred, posterior, err] = myNB(X,Y,X test,Y test)
whose inputs are the training data X, labels Y for X, testing data X test and labels Y test for X test
and returns predicted labels pred, posterior probability posterior with which the prediction was made
and error rate err. Assume Gaussian (normal) distribution on the data: there are two parameters that
realizes the probability density function (pdf), i.e., µ and σ. You can use functions such as normpdf
or pdf in matlab (or equivalent functions in Python) to obtain likelihood from Gaussian pdf.
For the experiments below, you should perform the experiments several times (e.g., 10 times) to find
out meaningful performance (e.g., take an average) since the data generated are random every time.
Derivation of Naive Bayes looks complicated, but its actual implementation should be simple if you
understand the concept of Naive Bayes Classifier.
• Perform prediction on the testing data with your code. In your report, report the accuracy,
precision and recall as well as a confusion matrix. Also, make sure to include a scatter plot of
data points whose labels are color coded (i.e., the samples in the same class should have the same
color) in the report.
• In your training data, change the number of examples in each class to {10, 20, 50, 100, 300, 500}
and perform prediction on the testing data with your code. In your report, show a plot of changes
of accuracies w.r.t. the number of examples and write your brief obervation.
• Now, in your training data, change the number of examples in class 0 as 700 and the other as 300.
Perform prediction on the testing dataset. How does the accuracy change? Why is it changing?
Write your own observation.
2. (15pt) Write a code to plot an ROC curve and calculate Area Under the Curve (AUC) based on the
posterior for class 1 (i.e., the confidence measure for class 1 is the posterior). The implementation
should be done on your own without using explicit library that lets you draw the curve. Report the
ROC curves from the two cases discussed in above (i.e., 1) equal number of samples for each class and
2) unequal number of samples in the training data).
3. (20pt) Download Amazon reviews dataset with labels (Dataset: https://www.kaggle.com/noushad24/
amazon-reviews/download). Use tf-idf weight matrix (You’ve done it in HW1) as features and perform 5-fold cross-validation with the Naive Bayes classifier. In your report, report the result (average
accuracy, precision and reacall across all folds) and your observation.
