

Student Area

This is the right page for you if you are interested in/inscribed to
the
Stochastics 2 Exercises.
It is also the right page if you are a math or computer science
student thinking about doing
a master's project in
Sardinia.
Over the next years this page will
further become useful if you are looking for a
bachelor's or
master's project in Innsbruck.
For completeness sake here is also a list of
past and potentially future courses.
Office hours are before/after the course,
or by arrangement.
Sprechstunde vor/nach der Lehrveranstaltung,
bzw. nach Vereinbarung.


Exercises: Stochastics 2 [WS17/18]
When?
Wednesdays 10.1511.45
What?
To digest the theory in the lecture we will calculate and sweat through
several examples and verify the theory in concrete cases. Whenever
possible we will also have look at applications of the theoretical results.

In case of interest in one of the proposed projects, contact me
before the beginning of the 'Seminar with Bachelorarbeit'.
If the project you are interested in is not mentioned below but
should be, come for a chat way before the beginning of
the 'Seminar with Bachelorarbeit'.
Initialisation strategies for dictionary learning
Compare graph clustering to random initialisation for dictionary learning,
detailed project description.
Masked Hard Thresholding Pursuit for dictionary based inpainting
Modify the Hard Thresholding Pursuit algorithm for data with missing entries
and use it for inpainting,
detailed project description.
Integrating lowrank components into weighted KSVD for dictionary based inpainting
Modify the weighted KSVD algorithm to take into account lowrank components
of arbitrary sizes and use it for inpainting,
detailed project description.
Free the bird  Inpainting
Develop an iterative inpainting procedure to fill in large gaps in
an image and use it to free the bird,
detailed project description.
Hard Thresholding Pursuit for Sparse Approximation,
E. Höck, Bachelor thesis, University of Innsbruck, 2016.
[thesis]
[description].

I offer master's projects in the areas of signal processing,
sparse approximation, dictionary learning and machine learning.
Recommended prerequisites are good knowledge of linear
algebra and probability theory and/or functional analysis.
The goal is to contribute to an active area of research
and so the project will be tailored to currently open questions and
your personal interests. If you are superstrong and megamotivated
there is also the possibility to do a more substantial
but paid master's thesis within the
STARTproject
'Optimisation Principles, Models & Algorithms for Dictionary Learning',
which can continue on to a PhD.
In case of interest have a look at the research or
publications page and contact me for a first chat.

Master's project in Bella Sardegna
for math or computer science students
The Computer Vision Laboratory of the
University of Sassari offers the possibility
to do a master's project in
 mobile biometrics (face and voice recognition),
 image matching or
 industrial control (image calibration, image measurement).
Other especially more computer sciency topics can be arranged.
Students can spend 6 months (January to June) doing a research (master's)
project at Porto Conte Ricerche (PCR)
under the supervision of
Prof. Enrico Grosso and based on their results write their master's
thesis in Innsbruck under my supervision (math) or under the supervision of
Prof. Justus Piater (cs).
The requirements on top of interest in one of the mentioned subjects
are good programming skills in Java, C++ or C#.
For practical reasons, PCR lies within a
natural park
about 18km from Alghero and 40km from Sassari, a driving license
is absolutely necessary.
Students will receive a lump sum of about 2000
to 2500EUR to contribute to car rental and petrol costs or, in case
of a private car, housing and living costs. A student room in Alghero
between January and June costs about 200EUR/month. Several projects are
available per year and teaming up might be useful for carsharing etc.
In case of interest contact me about 4 months before the
planned stay, e.g. until September for a departure in January.


Seminar: Channel Coding [SS17]
When?
Wednesdays 12.1513.45  possible shifts discussed 8th of March.
What?
We will teach each other the basics of channel coding and decoding, until
we are ready to understand a bit about turbo codes, ldpc codes and other
stuff that is used nowadays.

VU: Selected Statistical Methods [WS16/17]
When?
Mondays 10.1512.45
Wednesdays 10.1512.45
What?
The course is invented on the fly together with Tobias Hell
and will probably include linear regression,
classification, principal component analysis, clustering and a bit of measure concentration.

VU: Time Frequency Analysis, Wavelets and Signal Processing [SS16]
When?
Wednesdays 12.1513.45
Thursdays 10.1511.45
What?
I teach the first part of the course, covering timefrequency analysis,
the second part on wavelets is taught by Markus Haltmeier.
Always with signal processing in the back of our head,
in the first part we will have a look at:
 Basic Fourier Analysis
 Uncertainty Principles
 Short Time Fourier Transform
 Quadratic Time Frequency Representations
 Gabor Frames
and in the second part you will learn about:
 Continuous Wavelet Transform
 Wavelet Frames
 Orthogonal and Biorthogonal Wavelet Bases
 Function Approximation
 Optimal Statistical Estimation
Important!!!
To be admitted to the exam you have to scribe
at least one lecture! Scribing means taking notes and typesetting them in latex
using this template:
lecture_yy.mm.dd.tex.
The notes will then be available for everybody to enjoy here:
1.
lecture_16.03.09.pdf
2.
lecture_16.03.10.pdf
3.
lecture_16.03.16.pdf
4.
lecture_16.03.17.pdf
5.
lecture_16.04.06.pdf
6.
lecture_16.04.07.pdf
7.
lecture_16.04.14.pdf
8.
lecture_16.04.20.pdf
9.
lecture_16.04.21.pdf
10.
lecture_16.04.28.pdf
11.
lecture_16.05.04.pdf
And here the exercise sheets (date = due date):
exercises_16.04.13.pdf
exercises_16.05.17.pdf
exercises_16.05.25.pdf

Seminar: Randomness,
matrices and random matrices [SS15]
When?
Thursdays 12.1513.45
What?
We will start with some historic papers covering concentration
of measure inequalities, have a look at the
workhorse of the datascientist also known as Johnson Lindenstrauss Lemma,
and then progress to more nonasymptotic results on random matrices
as well as a very useful paper about the conditioning of random
submatrices. Depending on the participants' interests we will then
dive further into one of the topics or its applications or play around
with Matlab.
A proposed collection of papers spanning half a century:
Concentration of measure inequalities
G. Bennet, Probability inequalities for the sum
of independent random variables, 1962.
W. Hoeffding, Probability inequalities for
sums of bounded random variables, 1963.
Concentration of chaos variables
D.L. Hanson, F.T. Wright, A bound on tail probabilities for
quadratic forms in independent random variables, 1971.
D. Hsu, S.M. Kakade, T. Zhang, A tail inequality for quadratic
forms of subGaussian random vectors, 2011.
M. Rudelson, R. Vershynin, HansonWright inequality and
subGaussian concentration, 2013.
JohnsonLindenstrauss Lemma (1984)
S. Dasgupta, A. Gupta, An elementary proof of a theorem
of Johnson and Lindenstrauss, 2002(1999).
D. Achlioptas, Database friendly random projections, 2001.
R. Baraniuk, M. Davenport, R. DeVore, and M. Wakin.
The JohnsonLindenstrauss lemma meets compressed sensing, 2006.
F. Krahmer, R. Ward, New and improved JohnsonLindenstrauss
embeddings via the restricted isometry property, 2011.
Concentration of measure for matrices
R. Ahlswede, A. Winter, Strong converse for
identification via quantum channels, 2001.
R.I. Oliveira, Sums of random Hermitian matrices and
an inequality by Rudelson, 2010.
J. Tropp, Userfriendly tail bounds for sums of random matrices, 2010.
Miscellaneous papers, I consider interesting
G.W. Stewart, Perturbation theory for the
singular value decomposition, 1990.
J. Tropp, On the conditioning of random subdictionaries, 2008.

