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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]

Wednesdays 10.15-11.45

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.

Bachelor's projects

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 low-rank components into weighted KSVD for dictionary based inpainting
Modify the weighted KSVD algorithm to take into account low-rank 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].

Master's projects

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 super-strong and mega-motivated there is also the possibility to do a more substantial but paid master's thesis within the START-project '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 car-sharing 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]

Wednesdays 12.15-13.45 - possible shifts discussed 8th of March.

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]

Mondays 10.15-12.45
Wednesdays 10.15-12.45

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]

Wednesdays 12.15-13.45
Thursdays 10.15-11.45

I teach the first part of the course, covering time-frequency 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 Bi-orthogonal Wavelet Bases
- Function Approximation
- Optimal Statistical Estimation

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:

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):

Seminar: Randomness, matrices and random matrices [SS15]

Thursdays 12.15-13.45

We will start with some historic papers covering concentration of measure inequalities, have a look at the workhorse of the data-scientist also known as Johnson Lindenstrauss Lemma, and then progress to more non-asymptotic results on random matrices as well as a very useful paper about the conditioning of random sub-matrices. 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 sub-Gaussian random vectors, 2011.
M. Rudelson, R. Vershynin, Hanson-Wright inequality and sub-Gaussian concentration, 2013.

Johnson-Lindenstrauss Lemma (1984)
S. Dasgupta, A. Gupta, An elementary proof of a theorem of Johnson and Lindenstrauss, 2002(1999).
D. Achlioptas, Data-base friendly random projections, 2001.
R. Baraniuk, M. Davenport, R. DeVore, and M. Wakin. The Johnson-Lindenstrauss lemma meets compressed sensing, 2006.
F. Krahmer, R. Ward, New and improved Johnson-Lindenstrauss 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, User-friendly 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 sub-dictionaries, 2008.

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