**PhD stipend available in Machine Learning / Stochastic Systems Modeling**

In the Machine Learning Group of Herbert Jaeger at Jacobs University Bremen, funding is available for a 3-year PhD stipend, starting in August 2010 or later. The stipend amounts to 1000 Euro / month. The PhD research under this stipend offers great freedom, because it is not tied to a funded project. There are only two constraints: the research should have a strong mathematical / analytical flavor, and it should contribute to the further development of observable operator models (OOMs).

Indicative topics. OOMs are an approach to model arbitrary stochastic processes with linear operators. This leads, on the one hand, to a general mathematical theory of stochastic processes in terms of linear algebra concepts. On the other hand, it leads to novel learning algorithms for stochastic system identification. OOM research in our group has always been heading into both of these two directions – mathematical theory, and practical (but mathematically well-founded) learning algorithms. It is up to the successful candidate to select an area in OOM research of his/her liking, after a decent time of initial training. Here is a choice of exemplary topics, where initial work has been done and which wait for a motivated craftsperson (or genius) to be further pursued:

1. Working out the connections between the formalism of quantum mechanics and OOMs. Both formalisms have conspicuous structural similarities, and there is hope they can be unified. This could lead to efficient algorithms for learning quantum models from observation data.

2. Develop novel methods for reinforcement learning and agent decision making. OOMs are closely related to predictive state representations, a recent innovation in reinforcement learning and agent modeling. We have a torso of a conceptually new approach to learning of optimal decision making in stochastic environments, waiting to be worked out.

3. Develop a theory which unifies stochastic grammars with stochastic processes. Grammar models of random sequences afford a structural analysis of such sequences, while process models lead to temporal analyses. It is an open and fundamental question how the two are related, with great potential impact on biosequence and speech analysis. Initial insights have been obtained in the group.

4. Extend the current core OOM formalism, which is defined using un-normed vector spaces, to a Hilbert space based theory. At least two ways of how this can be done have already been outlined. A completion of this line of research would lead to a deeper understanding of important statistical issues, especially concerning the approximation of high(or infinite-)dimensional models by low-dimensional ones.

5. Develop efficient online learning algorithms for OOMs. Currently only offline algorithms are statistically and computationally efficient; the few known online learning algorithms are inefficient to the degree of being useless in practice.

*Requirements.*

Simple to state: very good math skills, a formal-analytical mindset, and an interest in interdisciplinary exposure. It is not important (but of course gladly accepted) to have previous experience in probability or stochastic processes, but fluency in general math thinking and formula-writing and proof-finding is expected. A Master (or equivalent) degree in a suitable field would be the default formal requirement, but exceptionally motivated BSc degree holders will also be considered – and filed into the integrated PhD track of Jacob`s freshly founded Mathematics, Modeling, and Computing research center.

*Working environment.*

Our machine learning group, which currently comprises 4 PhD students and 2 postdocs, pursues two major fields of research: recurrent neural networks of the reservoir computing flavor, and the modeling of stochastic dynamical systems with OOMs. Roughly speaking, the neural network research tends more to the engineering and applications side, while the OOM work is more foundational and mathematical. The group is coordinating the European project ORGANIC, which is about complex and partly biologically inspired architectures for speech recognition based on recurrent neural networks. Furthermore, the group is a partner in the European AMARSi consortium, which is is about biologically inspired architectures for humanoid robot motor control, again using recurrent neural networks. Finally, there is a project funded by the German National Research Society (DFG) which concerns OOM architectures for analyzing high-dimensional stochastic data, for instance from neural recordings, EEG, brain imaging, or gene regulation dynamics. Besides the intense working relationships with European groups afforded by these projects, we also enjoy a regular exchange of ideas (and sometimes, students) with world leading researchers in machine learning, especially Joshua Bengio and Richard Sutton.

Our group meets several times a week for extended study and discussion of the research we are doing ourselves, and of relevant developments in the neighboring disciplines: computational neuroscience, cognitive science, robotics, AI, bio-informatics, statistical physics, and more. This breadth of exposure reflects the interdisciplinary history of the group itself, and its current embedding in multidisciplinary large-scale projects.

Jacobs University is a special place: Germany`s only full-fledged private university (with about 20 majors from the natural sciences, the social sciences and humanities, and engineering). Founded only 10 years ago, in some disciplines Jacobs has already reached the top position in the CHE ranking, Germany`s most relevant university ranking. Students from more than 90 nations make Jacobs one of the most international universities on this planet. The campus language is English (also of course in our group). And our campus is beautiful.

Bremen is an ancient trading and harbor town close to the North Sea. It used to be Germany`s port for coffee, cacao and wine, from which times a culture of open-mindedness has been preserved – it is easy to feel welcome in this town and its environments. Costs of living are among the lowest in Germany (average rent per square meter for small-to-medium-sized flats is about 6 Euros; Jacobs runs its own student accomodations which are even cheaper).

** Prolongation and transformation of stipend.**After the research topic is settled, the project will be submitted for funding to the DFG. The outcome of this will become known at about the end of the second year; if positive, the stipend will be transformed into a work contract with a regular salary, and from then on continue for 2 (+1) years. If an external grant cannot be secured, a prolongation beyond three years cannot be guaranteed, but everything will be done to arrange this if the PhD project is not finished after three years (I don`t think that a very good PhD thesis is typically achievable within 3 years if there is a demanding working-in phase involved, as I would expect in this case).

First step. Please contactby email to h.jaeger@jacobs-university.de with an informal statement of interest, then we`ll see further.