Homework 5
36-464/36-664: Applied Multivariate Methods
Thursday January 30 2014
Due on Wednesday Feb 5 at 11:59 pm
1. (20 pts) Show how to solve the generalized eigenvalue problem max aT Ba
subject to aT W a = 1 by transforming to a standard eigenvalue pr
Homework 3
36-464/36-664: Applied Multivariate Methods
Thursday January 30 2014
Due on Wednesday Feb 5 at 11:59 pm
Please download the rst patient data (data from subject P1) from http:/
www.cs.cmu.edu/afs/cs/project/theo-73/www/science2008/data.html. Upl
Lecture 5 Notes
36-464/664: Applied Multivariate Methods
Kairavi Chahal and Julian Zhou
1
Recap: Principal Component Analysis
Suppose there are n observations with p features X1 , ., Xp . We seek a low-dimensional
representation of the data with minimal l
Scribe Notes for Lecture 4, 36-464/664
Jaclyn Wolf (jnwolf) and Judy Shi (congs)
January 29, 2014
A few notes:
Homework 2 is due next Wednesday at midnight. Part of it will be proofs and part of it will be in
R.
Homework 1 solutions will be posted today a
Homework 4
36-464/36-664: Applied Multivariate Methods
Thursday February 6 2014
Due on Wednesday February 12 at 11:59 pm
Please use the same data from homework 3. That is, download the rst
patient data (data from subject P1) from http:/www.cs.cmu.edu/afs/
SCRIBE NOTES FOR 36464 APPLIED MULTIVARIATE METHODS 1/21/2014
JOSH JELIN AND STEFAN KHOO
1. OVERVIEW
The goal of todays lecture is to understand the basic properties of the multivariate normal distribution
(MVN). But before we can launch in, well need to
SCRIBE NOTES MULTIVARIATE METHODS 1/16/14
ZACH BRANSON, SHANNON GALLAGHER
1. M ORE M ULTIVARIATE M ETHODS
In this lecture, we go over more matrix properties, the Spectral Decomposition Theorem, and quadratic forms.
1.1. Properties of Matrices. The followi
Homework 5
36-464/36-664: Applied Multivariate Methods
Thursday Feb 13 2014
Due on Wednesday Feb 19 at 11:59 pm
Answer all questions fully, backing up your statements. Attach all plots and
code. Your .pdf (LaTex le) and R code should be submitted to black
SCRIBE NOTES FOR LECTURE 1, 36-464/664
MIKE PANE AND LIZ LORENZI
1. C OURSE O UTLINE AND E XPECTATIONS
Applied Multivariate Methods is a joint masters and undergraduate course
focused on topics including dimension reduction, unsupervised and supervised ap
Homework 4
36-464/36-664: Applied Multivariate Methods
Thursday February 6 2014
Due on Wednesday February 12 at 11:59 pm
Please use the same data from homework 3. That is, download the rst
patient data (data from subject P1) from http:/www.cs.cmu.edu/afs/
HW 1 solutions, 36-464/36-664: Applied Multivariate Methods
1. (25 pts) The total variance of X is the MSE of the mean:
E|X E(X)|2 = tr(Var(X).
Prove this. You can nd the trace of a matrix dene in the lecture notes.
Proof.
E[ X E[X] 2 ] = E
(Xi E[Xi ])2
i
Homework 1
36-464/36-664: Applied Multivariate Methods
Wednesday January 15 2014
Due on Wednesday Jan 22 at 11:59 pm
1. The total variance of X is the MSE of the mean:
E|X E(X)|2 = tr(Var(X).
Prove this. You can nd the trace of a matrix dene in the lectur
Homework 2
36-464/36-664: Applied Multivariate Methods
Thursday January 23 2014
Due on Wednesday Jan 29 at 11:59 pm
A very simple model of poverty rates would be as follows: for state i in year
t, the poverty rate Yit is
Yit = t + Ui + it
where t is a nat
Homework 2
36-464/36-664: Applied Multivariate Methods
Thursday January 23 2014
Due on Wednesday Jan 29 at 11:59 pm
A very simple model of poverty rates would be as follows: for state i in year
t, the poverty rate Yit is
Yit = t + Ui + it
where t is a nat
Homework 3
36-464/36-664: Applied Multivariate Methods
Thursday January 30 2014
Due on Wednesday Feb 5 at 11:59 pm
Please download the rst patient data (data from subject P1) from http:/
www.cs.cmu.edu/afs/cs/project/theo-73/www/science2008/data.html. Upl