Q1: Is at Least one Predictor Useful?
This amounts to the hypothesis
test
H0: b1=b2=bp=0 vs.
Ha: at least one bi is nonzero
In multilinear regression this test
is performed using the F-statistic
(TSS RSS)/p
F
RSS/(n - p -1)
If the linear model assump
Dierential Equations in Image Processing and Computer Vision
Joachim Weickert, Summer Term 2012
MI
A
Lecture 24:
12
Curvature-Based Morphology I:
Mean Curvature Motion
56
34
78
Contents
9 10
1. Motivation
11 12
2. Mean Curvature Motion as Image Evolution
Dierential Equations in Image Processing and Computer Vision
Joachim Weickert, Summer Term 2012
MI
A
Lecture 21:
12
Image Sequence Analysis IV:
Numerical Methods
56
34
78
9 10
Contents
11 12
13 14
1. Basic Idea
2. Numerical Methods for the Parabolic Probl
Dierential Equations in Image Processing and Computer Vision
Joachim Weickert, Summer Term 2012
MI
A
Lecture 20:
12
Image Sequence Analysis III:
Large Displacements, High Accuracy Methods,
and Condence Measures
34
56
78
9 10
Contents
11 12
1. Large Displa
Dierential Equations in Image Processing and Computer Vision
Joachim Weickert, Summer Term 2012
MI
A
12
Lecture 19:
34
Image Sequence Analysis II:
Models for the Data Term
56
78
9 10
Contents
11 12
1. Introduction
13 14
2. Constancy of Brightness Derivati
Dierential Equations in Image Processing and Computer Vision
Joachim Weickert, Summer Term 2012
MI
A
12
Lecture 18:
Image Sequence Analysis I:
Models for the Smoothness Term
34
56
78
9 10
Contents
11 12
1. Introduction
13 14
2. General Structure
15 16
3.
Dierential Equations in Image Processing and Computer Vision
Joachim Weickert, Summer Term 2012
Lecture 26:
Self-Snakes and Active Contours
MI
A
12
34
56
Contents
78
1. Self-Snakes
9 10
2. Geodesic Active Contours
11 12
3. Region-Based Active Contours
13
3.1 Simple Linear Regression
We assume the following relationship among the data
Y b0 b1 X
regressing Y on (onto) X
sales b0 b1 TV
Univariate model: b0 intercept, b1 slope, both are coefficients or
parameters
Minimize RSS (residual sum of squares) to
4.4 Linear Discriminant Analysis (LDA)
Bayesian Methods
Formula for joint probabilities
Pr( X , Y ) = Pr(Y | X ) Pr( X )
= Pr( X | Y ) Pr(Y )
Bayes Formula
Classification into K classes
Class posterior density
Pr(
=
Y k=
| X x)
based on Bayes formula
6.1.1 Best Subset Selection
Idea: Do not only find the best full
model but the best model comprising
(only) every given subset of predictors
There are 2p such models
Assess the test error of each of these
models and choose the best model
There are var
5. Resampling Methods
1
Introduction
Resampling or subsampling denotes methods which
repeatedly draw samples from the training data set in
order to
learn about the variability of the fitted models, as the training set
changes (model variability)
assess
2.2 Assessing model accuracy
In regression problems we use
the mean square error to assess
the quality of fit, here over the
training data
Synthetic data example 1
Moderately nonlinear
1 n
( yi f ( xi ) 2
=
MSE
n i =1
Training error
We are more interes
The Elements of Statistical Learning
Thomas Lengauer, [email protected]
Nora Speicher, [email protected]
1
Course Material
Primary reference: An Introduction to Statistical Learning
with Applications in R by Gareth James, Daniela Witten,
Trevor H
4. Classification
1
4.1 Overview
Classification deals with categorical
outputs
Often the probability of an output to
belong to a class is regressed
Default data set
Output: Did individual default in a given
month? Yes or no?
Inputs: annual income, mo
MI
A
Dierential Equations in Image Processing and Computer Vision
Joachim Weickert, Summer Term 2011
1
Lecture 29:
Summary and Outlook
2
3
Contents
4
1. What Have We Done?
5
2. Current Research Directions
6
3. Projects for Bachelor or Master Theses
7
4. L
Dierential Equations in Image Processing and Computer Vision
Joachim Weickert, Summer Term 2012
MI
A
Lecture 17:
12
Osmosis II:
Incompatible Case and Applications
56
34
78
Contents
9 10
1. Incompatible Case
11 12
2. Relation to Gradient Domain Methods
13
Dierential Equations in Image Processing and Computer Vision
Joachim Weickert, Summer Term 2012
MI
A
Lecture 16:
12
Osmosis I:
Modelling and Analysis of the Compatible Case
34
56
78
Contents
9 10
1. Motivation
2. Discrete Linear Diusion Theory
11 12
3. Di
MI
A
Dierential Equations in Image Processing and Computer Vision
Joachim Weickert, Summer Term 2012
Lecture 15:
Unication of Denoising Methods
12
34
56
Contents
78
1. Motivation
9 10
2. From M-Estimators to Windowed Data Terms
3. From Bilateral Filters t
Dierential Equations in Image Processing and Computer Vision
Joachim Weickert, Summer Term 2012
Lecture 3:
Linear Diusion Filtering II:
Numerical Aspects, Limitations, Alternatives
Contents
1. Numerical Aspects
2. Advantages and Limitations of Gaussian Sm
Dierential Equations in Image Processing and Computer Vision
Joachim Weickert, Summer Term 2012
MI
A
12
Dierential Equations in
Image Processing and Computer Vision
34
56
78
9 10
Joachim Weickert
Faculty of Mathematics and Computer Science
Saarland Univer
Language-based control for
information flow and release
Andrei Sabelfeld
Chalmers
http:/www.cse.chalmers.se/~andrei
Marktoberdorf, Aug. 2009
2
<!- Input validation ->
<form name="cform" action="script.cgi"
method="post" onsubmit="return
checkform();">
<sc
Security (WS2010)
Prof. Michael Backes & Dr. Matteo Maei
Exercise Sheet 1
Due: 3 November 2010
Saarland University
Problem 1: Real and eective user ID (5 points)
Every Unix process is associated a real user ID (RUID) as well as an eective
user ID (EUID).
Security (WS2010)
Prof. Michael Backes & Dr. Matteo Maei
Solution for Exercise Sheet 1
Due: 3 November 2010
Saarland University
Problem 1: Real and eective user ID (5 points)
Every Unix process is associated with a real user ID (RUID) as well as an
eectiv
Security (WS2010)
Prof. Dr. Michael Backes & Dr. Matteo Maei
Exercise Sheet 2
Due on: 16 November 2010
Saarland University
Problem 1: Evaluating Defenses (5 points, one each)
Consider the following vulnerable code (target):
int foo(int* a, int n, int i, i