Statistics 315a
Midterm Exam
4:15-5:30pm, February 29, 2012.
You may use the class text, notes and calculators, but not computers or any
device that connects to the Internet. The questions below require fairly short
answers and are of equal value. They ar
HW 3 Solutions
March 18, 2013
Grade distribution: Problems 1 - 5: 12 points each, Problem 6: 15 points
for writeup, 15 points for computation.
Problem 1
a) Let cfw_X, y denote the full original dataset, and let cfw_X(i) , y(i) denote the dataset with the
Statistics 315a
Homework 3, due Wednesday March 12, 2014.
1. ESL 5.7.
2. Let X be the n p regression matrix for a logistic regression, with
p
n, and y the response vector. Assume X has row-rank n. Let
X = UDVT be the full SVD of X. That is, U is nn orthog
Problem Set 1 Solutions
Statistics 315A
Problem 1
(a)
0.05
Both the k -nearest neighbor (KNN) and linear regression classiers are implemented in the code
included in the appendix. The performance of the methods, along with the performance of the
hybrid me
Statistics 315a
Homework 1, due Monday Jan 25, 2010.
1. Compare the classication performance of linear regression and k
nearest neighbor classication on the zipcode data. In particular, consider only the 2s and 3s, and k = 1, 3, 5, 7 and 15. The zipcode
STATS 315A
Winter 2007
Homework 1
Solutions
Prob. #1 (Thanks to Wei Zhen) (a) The function mixG takes a centroid matrix mu, a vector N specifying the number of samples in each group and the noise variance v.
mixG <- function (mu, N, v)cfw_ mu <- rbind(mu)
Statistics 315a
Homework 2, due Wednesday February 13, 2013.
1. ESL 3.12 & 3.30
2. ESL 3.15
3.
(a) Suppose that we run a ridge regression with parameter on a
single variable X , and get coecient a. We now include an exact
copy X = X , and ret our ridge re
Problem Set 3 Solutions
Statistics 315A
Problem 1
1(a) Since it is known that column rank(X ) = row rank(X ) = N , the columns of X span RN . By
denition, it is therefore always possible to nd a satisfying X = y , and so there is a LS
solution with zero r
Statistics 315a
Homework 1, due Wednesday January 29, 2014.
ESL refers to the course textbook, and ESL 2.4 refers to exercise 2.4 in
ESL. Since the homework assignments count 70% of your nal grade, you
must do them on your own. Problem 1 is computing inte
Statistics 315a
Homework 2, due Wednesday February 12, 2014.
1. ESL 3.12 & 3.30
2.
(a) Suppose that we run a ridge regression with parameter on a
single variable X , and get coecient a. We now include an exact
copy X = X , and ret our ridge regression. Sh
Stats 315A HW2 Solutions
February 17, 2014
If there are any questions regarding the solutions or the grades of HW 2, please contact
Austen ([email protected]) with Stats315A-hw2-grading in the subject line.
Grade Distribution: Total 100 Points
Problem 1:
Statistics 315a
Homework 3, due Wednesday March 13, 2013.
1. ESL 7.3. Part (c) is somewhat open ended. Any reasonable suggestions
will be acceptable.
2. With yi = f (xi )+ i , and var(yi |xi ) = 2 , dene the degrees of freedom
by
n
cov(y, yi )/ 2
df( ) =
Statistics 315a
Homework 2, due Wednesday February 12, 2014.
1. ESL 3.12 & 3.30
2.
(a) Suppose that we run a ridge regression with parameter on a
single variable X , and get coecient a. We now include an exact
copy X = X , and ret our ridge regression. Sh
Stats 315A HW1 Solutions
6th February, 2012
If there are any questions regarding the solutions or the grades of HW 1, please contact
Gourab ([email protected]) with Stats315A-hw1-grading in the subject line. Common mistakes are highlighted in blue.
Grad
Generalized additive models
General supervised learning (regression) problem. N observations of
an outcome variable Y and predictors X1 , X2 , , . . . Xp .
Goal is to predict outcome from predictors, and understand the
relationship between them. See
pp
Stats 315A HW2 Solutions
8th February, 2012
If there are any questions regarding the solutions or the grades of HW 2, please contact
Max ([email protected]) with Stats315A-hw2-grading in the subject line.
Grade Distribution: Total 120 Points
Problem 1: 10
STAT 315A Homework 2 Solutions
Problem 1: ESL 4.2
a) For LDA,
k = x 1 k 1/2k 1k + log (Nk /N ).
Substitute this formula into the requirement that 2 (x) 1 (x) > 0 and we get the
solution
x 1 (2 1 ) + 1/21 1 1 1/22 1 2 + log (N2 /N ) log (N1 /N ) > 0.
Statistics 315a
Homework 1, due Wednesday January 30, 2013.
ESL refers to the course textbook, and ESL 2.4 refers to exercise 2.4 in
ESL. Since the homework assignments count 70% of your nal grade, you
must do them on your own. Problem 1 is computing inte
Statistics 315a
Homework 1, due Wednesday Oct 15 , 2008.
1. Compare the classication performance of linear regression and k
nearest neighbor classication on the zipcode data. In particular, consider only the 2s and 3s, and k = 1, 3, 5, 7 and 15. The zipc
STAT 315a
Midterm winter 2013- Solutions
Duration- 1 hour and 15 min
Aids allowed: class text, class notes, and calculators
The questions below require fairly short answers and are of equal value. They are in
no particular order. No one is expected to ans
SS3859: Fall 2011
Solution Manual Homework 2
Chen Yang
1. Solution:
(a) The conditional probability density function for yi given xi is
1
e
fYi |Xi (yi |xi ) =
2
(yi 0 1 xi )2
2 2
.
(b) The joint probability density function for xi and yi is
1
e
fYi ,Xi
Problem Set 3 Solutions
Statistics 315A
Problem 1
1(a) Since it is known that column rank(X ) = row rank(X ) = N , the columns of X span RN . By
denition, it is therefore always possible to nd a satisfying X = y , and so there is a LS
solution with zero r
Problem Set 2 Solutions
Statistics 315A
Problem 1: ESL 4.2
(a)
As in class, the predicted class G(x) is argmaxk k (x) where
1
k (x) = xT 1 k T 1 k + log k
2k
where k , k and must be estimated from the data. Letting k = Nk /N , we see that the LDA
rule cla
1
STAT 315a
Midterm Winter 2009
Duration- 1 hour and 15 min
Aids allowed: class text, class notes, and calculators
The questions below require fairly short answers and are of equal value.
They are in no particular order. No one is expected to answer all o