We are interested in the following questions. Given a finite data set S , with neither labels nor side information, and an unsupervised learning algorithm A, can the generalization of A be assessed on S? Similarly, given two unsupervised learning algorithms, A1 and A2, for the same learning task, can one assess whether one will generalize “better” on future data drawn from the same source as S?...

This thesis considers training algorithms for machine learning and their applications for classification, regression and automatic speech recognition. Particularly, supervised learning, which is also called learning from samples, is considered. Starting with a short introduction into statistical learning theory it is shown, that supervised learning can be formulated as a function estimation pro...

In recent years, Deep Reinforcement Learning has made impressive advances in solving several important benchmark problems for sequential decision making. Many control applications use a generic multilayer perceptron (MLP) for non-vision parts of the policy network. In this work, we propose a new neural network architecture for the policy network representation that is simple yet effective. The ...

This work deals with the fault detection and localization in the case of uncertain nonlinear systems. The presented method uses the diagnosis based on mathematical models. To model nonlinear systems, the multiple model approach is used. This method uses the Takagi-Sugeno fuzzy systems principle to obtain a nonlinear system named multiple models. This modeling principle has the advantage of obta...

The nonlinear Schrödinger (NLS) equation is a fundamental model for the nonlinear propagation of light pulses in optical fibers. We consider an integrable generalization of the NLS equation which was first derived by means of bi-Hamiltonian methods in [A. S. Fokas, Phys. D 87 (1995), 145–150]. The purpose of the present paper is threefold: (a) We show how this generalized NLS equation arises as...

The wave digital filter (WDF) theory provides us with a systematic methodology for building digital models of analog filters through the discretization of their individual circuit components. In some situations, WDF principles can also be successfully used for modeling circuits in which a nonlinear circuit element is present under mild conditions on its characteristic. In this paper, we propose...

This paper generalizes Elkies’ construction of error-correcting nonlinear codes found in [N. Elkies, Excellent nonlinear codes from modular curves, in: Proceedings of the 33rd Annual ACM Symposium on the Theory of Computing, STOC’01, Hersonissos, Crete, Greece, 2001, pp. 200–208]. The generalization produces a precise average code size over codes in the new construction. The result is a larger ...