CSE 555 Spring 2009 MidTerm Exam
Jason J. Corso
Computer Science and Engineering
University at Buffalo SUNY
[email protected]
Date 5 Mar 2009
The exam is worth 100 points total and each question is marked with its portion. The exam is closed book/notes. You
have 70 minutes to complete the exam. Use the provided white paper, write your name on the top of each sheet and
number them. Write legibly.
Problem 1: “Recall” Questions (25pts)
Answer each in one or two sentences.
1. (5pts) What is the fundamental difference between Maximum Likelihood parameter estimation and Bayesian
parameter estimation?
2. (5pts) What quantity is PCA maximizing during dimension reduction?
3. (5pts) Describe Receiver Operating Characteristics or ROCCurves (illustrate if necessary).
4. (5pts) What is the Curse of Dimensionality?
5. (5pts) What is the key idea of the No Free Lunch Theorem?
Solution:
Answers are all directly in the notes.
Problem 2: Bayesian Reasoning (25pts)
Monty Hall
Formulate and solve this classiﬁcal problem using the Bayes rule. Imagine you are on a gameshow and
you’re given the choice of three doors: behind one door is a car and behind the other two doors are goats. You have
the opportunity to select a door (say No. 1). Then the host, who knows exactly what is behind each door and will not
reveal the car, will open a different door (i.e., one that has a goat). The host then asks you if you want to switch your
selection to the last remaining door.
1. (3pts) Formulate the problem using the Bayes rule, i.e., what are the random variables and the input data. What
are the meaning of the prior and the posterior probabilities in this problem (one sentence each).
Solution:
Without the loss of generality, suppose that we chose door 1 at the beginning.
Random Variables
:
C
i
represents the state that the car is behind door
i,i
∈
[1
,
2
,
3]
,
and
H
j
represents the state that the host opens door
j,j
∈
[2
,
3]
.
Input Data
: The door that the host opens.
Prior Probability
: The probability of winning the car before the host opens the
door.
Posterior Probability
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '10
 wu
 Conditional Probability, Histogram, Nonparametric statistics, Kernel density estimation, Density estimation

Click to edit the document details