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Sparse non-Gaussian component analysis is an unsupervised linear method of extracting any structure from high-dimensional distributed data based on estimating a lowdimensional non-Gaussian data component. In this paper we discuss a new approach with known apriori reduced dimension to direct estimation of the projector on the target space using semidefinite programming. The new approach avoids the estimation of the data covariance matrix and overcomes the traditional separation of element estimation of the target space and target space reconstruction. This allows to reduced the sampling size while improving the sensitivity to a broad variety of deviations from normality. Moreover the complexity of the new approach is limited to O(d log d). We also discuss the procedures which allows to recover the structure when its effective dimension is unknown.

In technical chemistry, systems biology and biotechnology, the construction of predictive models has become an essential step in process design and product optimization. Accurate modelling of the reactions requires detailed knowledge about the processes involved. However, when concerned with the development of new products and production techniques for example, this knowledge often is not available due to the lack of experimental data. Thus, when one has to work with a selection of proposed models, the main tasks of early development is to discriminate these models. In this article, a new statistical approach to model discrimination is described that ranks models wrt. the probability with which they reproduce the given data. The article introduces the new approach, discusses its statistical background, presents numerical techniques for its implementation and illustrates the application to examples from biokinetics.

Non-gaussian component analysis (NGCA) introduced in [24] offered a method for high dimensional data analysis allowing for identifying a low-dimensional non-Gaussian component of the whole distribution in an iterative and structure adaptive way. An important step of the NGCA procedure is identification of the non-Gaussian subspace using Principle Component Analysis (PCA) method. This article proposes a new approach to NGCA called sparse NGCA which replaces the PCAbased procedure with a new the algorithm we refer to as convex projection.

Reinforcement learning provides a cognitive science perspective to behavior and sequential decision making provided that RL-algorithms introduce a computational concept of agency to the learning problem. Hence it addresses an abstract class of problems that can be characterized as follows: An algorithm confronted with information from an unknown environment is supposed to find stepwise an optimal way to behave based only on some sparse, delayed or noisy feedback from some environment, that changes according to the algorithm's behavior. Hence reinforcement learning offers an abstraction to the problem of goal-directed learning from interaction. The paper offers an opintionated introduction in the algorithmic advantages and drawbacks of several algorithmic approaches such that one can understand recent developments and open problems in reinforcement learning.