Hw assignment 1
Due Tuesday February 19, 2006
Guidelines:
Write a short report to present your results. Be sure to include all the relevant graphs as well as a copy of your code. Teamwork is encouraged, but the write up of your report must be your own. Please write the names of your collaborators on the cover page of your report.
Question 1: Design and execute an experiment that illustrates the Central Limit Theorem. (You may use problem 5 in DHS p. 80 for inspiration.)
Question 2: Consider n-dimensional feature vectors coming from two classes. Assume that the distributions of the feature vectors for the two classes are (known) normal distributions and that the priors for the classes P(w1) and P(w2) are also known. Write a computer program that classifies the feature vectors according to Bayes decision rule. Generate some artificial (normally distributed) data, and test your program on the data you generated. Try feature vectors of various dimensions. Quantify the accuracy of your results. How does the dimension of the feature vectors affect accuracy? (You may use problem 2 in DHS p. 80 for inspiration.)
Question 3: Take a subset of the data you used for Question 2. Use maximum likelihood estimation to estimate the parameters of the feature distribution. Experiment to illustrate the accuracy of the classifier obtained with this estimate. Then repeat the experiments using approximately Gaussian data generated using your answer in Question 1.
Question 4: Replace the words “maximum likelihood estimation” by “Bayesian parameter estimation” in Question 3.
