MACHINE LEARNING COMS 4771, HOMEWORK 4
Assigned November 5, 2015. Due November 19, 2015 before 10 am.
1
Problem 1 (10 points): EM Derivation
Consider a random variable x that is categorical with M possible values 1, . . . , M . Suppose x is
M
represented

MACHINE LEARNING COMS 4771, HOMEWORK 3
Assigned October 15, 2015. Due November 3, 2015 before 10:00am.
1
Problem 1 (5 points)
Suppose you work at a casino and you are responsible for making sure no one is cheating. Specically,
you are interested in making

COMS4771: Homework 2 Solution
October 7, 2015
Problem 1
(A)
Answer: The VC dimension of perceptron in Rd is d+1.
Proof. It will be proved in two steps:
(1) There exist d+1 points that perceptron can shatter.
(2) No d + 2(or more) points can be shattered b

MACHINE LEARNING COMS 4771, HOMEWORK 2
Assigned October 1, 2015. Due October 15, 2015 before 10am.
Please submit separate les for a) write-up, b) Matlab source les and c) gures (if you choose to
include them separately from the writeup). Do not include an

COMS4771 Machine Learning 2014: Homework 1 Solution
Robert Ying
September 16, 2015
1
Problem 1
The plots for dierent choices of d are given below:
1
As can be seen in the cross-validation plot, the error is minimized for testing at d = 8. Higher
values of

MACHINE LEARNING COMS 4771, HOMEWORK 1
Assigned September 15, 2015. Due October 1, 2015 before 10:00am.
Submit your work via courseworks.columbia.edu.
Please submit separate les for a) write-up, b) Matlab source les and c) gures (if you choose to
include

Tony Jebara, Columbia University
Machine Learning
4771
Instructor: Tony Jebara
Tony Jebara, Columbia University
Topic 8
iscrete Probability Models
D
ndependence
I
ernoulli Distribution
B
ext: Nave Bayes
T
ategorical / Multinomial Distribution
C
ext:

Tony Jebara, Columbia University
Machine Learning
4771
Instructor: Tony Jebara
Tony Jebara, Columbia University
Topic 7
nsupervised Learning
U
tatistical Perspective
S
robability Models
P
iscrete & Continuous: Gaussian, Bernoulli, Multinomial
D
aximu