Statistics 24610/37500, Spring 2011
Homework 1 (due in class on Thursday, 7 April 2011)
Note: Problems 1 and 2 are to be done individually. Problem 3 has to be done in groups of 4-5 students.
Turn in
Statistics 24610/37500, Spring 2011
Homework 6 (due in class on Tuesday, 31 May 2011)
Note: All problems are to be done individually. Keep the code you develop.
1. Let p = P (Z > 4.5) for a standard n
Statistics 24610/37500, Spring 2011
Homework 5 (due in class on Tuesday, 24 May 2011)
Problem 1 has to be done individually. Problems 2 and 3 can, but dont have to be done in groups of 2
students. You
Linear Algebra Review
STAT 343, Fall 2011
October 10, 2011
Linear maps
Denition
A function f : Rm ! Rn is linear if
f (x + y ) = f (x ) + f (y );
f (ax ) = af (x ), 8a 2 R.
Denition
A basis for a ve
Stat 246/375
Mixture Model EM Algorithm :
Start: Initialize ,
E-step: compute " ( zik ) =
Spring 2011
19 April 2011
# k p( X k | $ k )
k
% p( X
i
&i, k
|$l )
l =1
!
new
M-step: compute
Stat 246/375 Pattern Recognition
Professor Mathias Drton
Spring 2011
Lecture 1
29 March, 2011
Stochastic Gradient Descent
Stochastic gradient descent is an optimization method for minimizing an object
Spring 2011, STAT 24610/37500
Lecture Notes (April 12th, 2011)
4. Linear Models for Classication
(a) Fishers Discriminant Analysis (continued)
T B
() is given by eigenvector to largest eigenvalue of 1
Statistics 24610/37500, Spring 2011
Homework 2 (due in class on Thursday, 14 April 2011)
1. Let X = (X1 , X2 ) be bivariate normal with mean zero and covariance matrix = (ij ).
(a) Write X2 = X1 + Z w
Statistics 24610/37500, Spring 2011
Homework 4 (due in class on Thursday, 12 May 2011)
Note: Problems 1, 2 and 3 are to be done individually. Problem 4 is a special assignment; pay attention to
the in
STAT246/375 - Lecture 3 Notes
Asymptotic risk of nearest neighbor classication
(X, Y ) p(x, y ), X Rd Test Case
RB = E[L(Y, fB (X )] Bayes Risk
(n)
fN N (x): nearest-neighbor classier based on trainin
Stat 246/375
Lecture Notes
April 21, 2011
6 EM Algorithm in General
X: observed variables
Z: unobserved/ hidden variables/ latent variables
So the joint distribution of X, Z is p(x, z |), the marginal
Spring 2011, STAT 24610/37500
Lecture Notes (April 14th, 2011)
4. Linear Models for Classication (Continued)
(d) Discriminative Model
Consider the linear regression model:
P (Y = y |X = x) = E 1cfw_Y
Stat 246/375 Lecture Notes April 28th
Factorization in undirected graphical models. Let G be an undirected graph on the set of
nodes [m] = cfw_1, 2, . . . , m with edge set E . A clique C [m] in the g
Stat 246/375: Pattern Matching
Lecture 2
Professor Mathias Drton
Spring 2011
31 March 2011
Classication
We wish to minimize
y
L(y, y )p(y |x). In practice, p(x, y ) is unknown, so we must estimate it.
Statistics 24610/37500, Spring 2011
Homework 3 (due in class on Thursday, 28 April 2011)
Note: Problems 1, 2 and 3 are to be done individually. Problem 4 can, but doesnt have to be done in groups
of 2