CS 7641 CSE/ISYE 6740 Final Exam Solution (2013 Fall)
Le Song
12/10 Tue, 2:50 - 5:40 pm
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GT ID:
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Problem
Point
1
Your Score
Problem
Point
20
6
20
2
20
7
30
3
20
8
30
4
20
9
20
5
20
Total
200
Your Score
Instructions:
Try your best to be cle
CS 7641 CSE/ISYE 6740 Homework 2 Solutions
October 11, 2016
1
EM for Mixture of Gaussians
Mixture of K Gaussians is represented as
p(x) =
K
X
k N (x|k , k ),
(1)
k=1
where k represents the probability
that a data point belongs to the kth component. As it
CS 7641 CSE/ISYE 6740 Mid-term Exam (2015 Fall) Q3 solution
December 5, 2015
1
Expectation Maximization [18 pts]
You have learned the Gaussian Mixture Model in class. For some discrete valued problems, like binary
images, Bernoulli Mixture Model (BMM) is
CS 7641 CSE/ISYE 6740 Homework 4 Solutions
Le Song
1
Kernels [20 points]
(a) Identify which of the followings is a valid kernel. If it is a kernel, please write your
answer explicitly as True and give mathematical proofs. If it is not a kernel, please
wri
CS 7641 CSE/ISYE 6740 Homework 3 Solutions
Le Song
1
Linear Regression [30 pts]
In class, we derived a closed form solution (normal equation) for linear regression problem: = (X T X)1 X T Y .
A probabilistic interpretation of linear regression tells us th
CSE 6140:
NP-completeness
based partially on course slides from Jennifer
Welch, George Bebis, and Kevin Wayne
Basic reduction strategies.
Reduction by simple equivalence.
Reduction from special case to general case.
Reduction by encoding with gadgets.
Ind
CSE 6140:
NP-completeness
based partially on course slides from Jennifer
Welch, George Bebis, and Kevin Wayne
The Class NP
NP is the class of problems for which a candidate solution
can be verified in polynomial time
NP=nondeterministic polynomial
P is a
CSE 6140:
NP-completeness
based partially on course slides from Jennifer
Welch, George Bebis, and Kevin Wayne
CFN Satisfiability
CFN is a special case of SAT
F is in Conjunctive Normal Form (CNF)
AND of expressions (i.e., clauses)
Each clause contains o
CSE 6140/ CX 4140:
Computational Science and Engineering
ALGORITHMS
Instructor: Bistra Dilkina
Assistant Professor, CSE
Minimum Spanning Tree
Minimum spanning tree. Given a connected graph G = (V, E) with realvalued edge weights ce, an MST is a subset of
Mixture of Gaussian &
Feature Selection
Le Song
Machine Learning
CS 7641,CSE/ISYE 6740, Fall 2016
Gaussian mixture model
A density model
may be multi-modal: model it as a
mixture of uni-modal distributions (e.g. Gaussians)
,
1
1
2
2
Consider a mixture of
Why recommendation?
Collaborative Filtering
Le Song
Machine Learning
CS 7641,CSE/ISYE 6740, Fall 2015
Tapestry: [Goldberg1992]
2
Examples
Recommendation vs. Advertisement
Product recommendation
Q. Is advertisement recommendation?
A.
Yes, in broad sense.
F
Machine learning for apartment hunting
Suppose you are to move to Atlanta
And you want to find the most
reasonably priced apartment satisfying
your needs:
Regression
square-ft., # of bedroom, distance to campus
Le Song
Machine Learning I
CSE 6740, Fall 2
1
CS 7641 CSE/ISYE 6740 Mid-term Exam Solution (2013 Fall)
Maximum Likelihood [15 pts]
You are playing a game with two coins. Coin 1 has a probability of heads. Coin 2 has a 2 probability of
heads. You flip these coins several times and record your result
CS 7641 CSE/ISYE 6740 Mid-term Exam Solutions
Le Song
10/13/2016
1
Expectation, Co-variance and Independence [14 pts]
(a) Suppose X, Y and Z are discrete random variables.
EZP (Z) [E(X,Y )P (X,Y |Z) [XY ]. [4 pts]
Show that E(X,Y )P (X,Y ) [XY ] =
Answer:
Clustering
Le Song
Machine Learning
CS 7641,CSE/ISYE 6740, Fall 2015
Clustering images
Image
Databases
Goal of clustering:
Divide object into groups,
and objects within a group
are more similar than
those outside the group
2
Cluster other things
3
Cluste
Regression
Le Song
Machine Learning I
CSE 6740, Fall 2015
Machine learning for apartment hunting
Suppose you are to move to Atlanta
And you want to find the most
reasonably priced apartment satisfying
your needs:
square-ft., # of bedroom, distance to camp
CS 7641 CSE/ISYE 6740 2015 Final Exam Sample Question
Le Song
12/7 Mon
1
Maximum Likelihood [10 pts]
(a) Pareto Distribution [5 pts]
The Pareto distribution has been used in economics as a model for a density function with a slowly decaying
tail:
f (x|x0
Machine learning for apartment hunting
Suppose you are to move to Atlanta
And you want to find the most
reasonably priced apartment satisfying
your needs:
Regression
square-ft., # of bedroom, distance to campus
Le Song
Machine Learning I
CSE 6740, Fall 2
Clustering
Le Song
Machine Learning
CS 7641,CSE/ISYE 6740, Fall 2015
Clustering images
Image
Databases
Goal of clustering:
Divide object into groups,
and objects within a group
are more similar than
those outside the group
2
Cluster other things
3
Cluste
Machine Learning for Social Activity Modeling
Mehrdad Farajtabar
Computational Science and Engineering
College of Computing
Georgia Institute of Technology
Networks Everywhere!
SOCIAL
NETWORKS
TRANSPORTATION
NETWORKS
WORLD WIDE
WEB
PROTEIN
INTERACTIONS
IN
CS 7641 CSE/ISYE 6740 Mid-term Exam 2 (Fall 2016) Solutions
Le Song
1
Probability and Bayes Rule [14 pts]
(a)
A probability density function (pdf) is defined by
(
C(x + 2y) if 0 < y < 1 and 0 < x < 2
f (x, y) =
0
otherwise
(i)
Find the value of C [3 pts].
From static to dynamic mixture models
Static mixture
Markov Random Fields
Dynamic mixture
Le Song
Machine Learning
CS 7641,CSE/ISYE 6740, Fall 2015
Y1
A1
X
N
Y1
Y2
Y3
.
YT
A1
X
A2
X
A3
X
.
XAT
2
HMM with discrete hidden states
Observation space for !"
Alp