# STA 410, ASSIGNMENT 2, SPRING 2004.
# PLOT DATA AS POINTS ON A CIRCLE.
plot.circle <- function (x)
cfw_
g <- seq(0,2*pi,length=100)
plot(cos(g),sin(g),type="l")
points(cos(x),sin(x),pch=20)
# FIND VALUES OF NUMBERS IN A VECTOR MODULO 2PI.
mod2pi <- fun
STA 414/2104, Spring 2014, Practice Problem Set #1
Note: these problems are not for credit, and not to be handed in
Question 1: Consider a classification problem in which there are two real-valued inputs, x1 and
x2 , and a binary (0/1) target (class) vari
STA 414/2104, Spring 2014, Answers to Practice Problem Set #1
Note: these problems are not for credit, and not to be handed in
Question 1: Consider a classification problem in which there are two real-valued inputs, x1 and
x2 , and a binary (0/1) target (
w
w w.
oxd
ia
.c
om
!#"$&%(')%+*-,(').+%0/ 132547698:";<6=8>/ ,+.-.+?)@A.+,)@A.+B
C DFEGD+DH+I)J-KLDMNOI)J-DPRQOSTUQWVTXSYMZDPZI[SYPZNSTXT D)\3N^]`_
acbdfehgOikjmlonmprq ts SAPZHfIFu>vDKLI)wU]<NOPxStQOTXSYIZI)w yzQOSYM)w DK|cfw_LPZDEzT N s w K|\~wX
STA 414/2104
Statistical Methods for Machine Learning and Data Mining
Radford M. Neal, University of Toronto, 2012
Week 1
What are Machine Learning and Data Mining?
Typical Machine Learning and Data Mining Problems
Document search:
Given counts of words i
STA 414/2104
Statistical Methods for Machine Learning and Data Mining
Radford M. Neal, University of Toronto, 2012
Week 11
Dimensionality Reduction
Dimensionality Reduction
High dimensional data is often really lower-dimensional: For example:
20
0.517
0.6
STA 414/2104
Statistical Methods for Machine Learning and Data Mining
Radford M. Neal, University of Toronto, 2012
Week 8
Classication
Classication Problems
Many machine learning applications can be seen as classication problems
given a vector of p input
STA 414/2104
Statistical Methods for Machine Learning and Data Mining
Radford M. Neal, University of Toronto, 2012
Week 5
More on Bayesian Linear Basis Function Models
Comparison with Regularized Estimates
In a Bayesian linear basis function model, the pr
STA 414/2104
Statistical Methods for Machine Learning and Data Mining
Radford M. Neal, University of Toronto, 2012
Week 10
Clustering and Mixture Models
Unsupervised Learning, Clustering, and Mixture Distributions
Recall that unsupervised learning does no
Background Knowledge Quiz - STA414
1. What year and program are you in?
2. Are you taking this course for credit, auditing, or something else?
Gaussians
3. If p(x) = N (x|, 2 ),
(a) For some x R, R, R+ , can p(x) < 0?
(b) For some x R, R, R+ , can p(x) >
STA 414/2104, Spring 2014, Practice Problem Set #2, Answers
Question 1: Suppose we model the relationship of a real-valued response variable, y, to a single
real input, x, using a Gaussian process model in which the mean is zero and the covariances of
the
STA 410/2102, Spring 2004 Assignment #1
Due at start of class on February 13. Worth 15% of the nal mark.
Note that this assignment is to be done by each student individually. You may discuss it in general
terms with other students, but the work you hand i
# STA 410, ASSIGNMENT 3, SPRING 2004.
# FIND VALUES OF NUMBERS IN A VECTOR MODULO 2PI.
mod2pi <- function (x)
cfw_
f <- x/(2*pi)
f <- f-floor(f)
f*(2*pi)
# FIND THE PROBABILITY DENSITY OF POINTS UNDER THE
WRAPPED NORMAL DISTRIBUTION.
# The arguments are
STA 414/2104, Spring 2012, Practice Problem Set #2, Answers (partial, more to come)
Note: these problems are not for credit, and not to be handed in
Question 1: Recall that a multilayer perceptron network with m hidden units using the tanh
activation func
STA 414/2104, Spring 2013, Practice Problem Set #2, Answers
Question 1: Suppose we model the relationship of a real-valued response variable, y, to a single
real input, x, using a Gaussian process model in which the mean is zero and the covariances of
the
STA 414/2104, Spring 2012, Answers to Practice Problem Set #3
Question 1: Suppose that we are tting a Gaussian mixture model for data items consisting
of a single real value, x, using K = 2 components. We have N = 5 training cases, in which the
values of
STA 414/2104, Spring 2013, Answers to Practice Problem Set #1
Note: these problems are not for credit, and not to be handed in
Question 1: Consider a classication problem in which there are two real-valued inputs, x1 and
x2 , and a binary (0/1) target (cl
STA 414/2104, Spring 2014, Answers to Practice Problem Set #1
Note: these problems are not for credit, and not to be handed in
Question 1: Consider a classication problem in which there are two real-valued inputs, x1 and
x2 , and a binary (0/1) target (cl
STA 414/2104, Spring 2013, Answers to Practice Problem Set #3
Question 1: Recall that a multilayer perceptron network with m hidden units using the tanh
activation function computes a function dened as follows:
(2)
f (x, w) = w0
m
(2)
p
(1)
wj j (x, w),
+
STA 414/2104, Spring 2014, Answers to Practice Problem Set #3
Question 1: Recall that a multilayer perceptron network with m hidden units using the tanh
activation function computes a function dened as follows:
(2)
f (x, w) = w0
p
m
(2)
(1)
wj j (x, w),
+
STA 414/2104
Statistical Methods for Machine Learning and Data Mining
Radford M. Neal, University of Toronto, 2012
Week 2
Modeling Data with Linear Combinations of Basis Functions
A Type of Supervised Learning Problem
We want to model data (x1 , y1 ), . .
STA 414/2104
Statistical Methods for Machine Learning and Data Mining
Radford M. Neal, University of Toronto, 2012
Week 9
Support Vector Machines
Another Way to Find the Hyperplane with Largest Margin
Recall that we if dene a hyperplane by the equation wT
STA 414/2104
Statistical Methods for Machine Learning and Data Mining
Radford M. Neal, University of Toronto, 2012
Week 6
Neural Networks
Curse of Dimensionality for Linear Basis Function Models
Modeling a general non-linear relationship of y to x with a
STA 414/2104 Jan 19, 2010
Administration
Homework 1 available Thursday Discussion of project requirements on Thursday NSERC summer undergraduate awards Fields-MITACS undergraduate summer research
http:/www.fields.utoronto.ca/programs/scientific/10-11/summ
STA 414/2104 Jan 12, 2010
Administration
Please check web page regularly for updates
http:/www.utstat.utoronto.ca/reid/414S10.html
Blackboard is used only for email and grades You should by now have have R on your PC, or be planning to go your own route r
Sta 414/2104 S
http:/www.utstat.utoronto.ca/reid/414S10.html
STA414S/2104S:StatisticalMethodsforDataMiningandMachineLearning
JanuaryApril,2010,Tuesday122,Thursday121,SS2105 CourseInformation Thiscoursewillconsidertopicsinstatisticsthathaveplayedaroleint
STA 414S/2104S: Homework #2
Due Mar. 4, 2010 at 1 pm
Late homework is penalized at 20% deduction per day. You are welcome to discuss your work on this homework with your classmates. You are required to write up the work on your own, using your own words,
STA 414S/2104S: Homework #1
Due Feb.11, 2010 at 1 pm
Late homework is penalized at 20% deduction per day. You are welcome to discuss your work on this homework with your classmates. You are required to write up the work on your own, using your own words,
# some fake regression data x = rnorm(20) y = rnorm(20) plot(x,y) y.0 = lm(y ~ 1) abline(h=y.0$coef[1]) d = seq(-2,2,length=200) # polynomial fits for(degree in 1:9)cfw_ fm = lm(y ~ poly(x,degree) assign(paste("y",degree,sep="."),fm) lines(d,predict(fm,da