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Motivated by computing functionals of high-dimensional, potentially metastable diffusion processes, this thesis studies robustness issues appearing in the numerical approximation of expectation values and their gradients. A major challenge being high variances of corresponding estimators, we investigate importance sampling of stochastic processes for improving statistical properties and provide novel nonasymptotic bounds on the relative error of corresponding estimators depending on deviations from optimality. Numerical strategies that aim to come close to those optimal sampling strategies can be encompassed in the framework of path space measures, and minimizing suitable divergences between those measures suggests a variational formulation that can be addressed in the spirit of machine learning. A key observation is that while several natural choices of divergences have the same unique minimizer, their finite sample properties differ vastly. We provide the novel log-variance divergence, which turns out to have favorable robustness properties that we investigate theoretically and apply in the context of path space measures as well as in the context of densities, for instance offering promising applications in Bayesian variational inference.
Aiming for optimal importance sampling of diffusions is (more or less) equivalent to solving Hamilton-Jacobi- Bellman PDEs and it turns out that our numerical methods can be equally applied for the approximation of rather general high-dimensional semi-linear PDEs. Motivated by stochastic representations of elliptic and parabolic boundary value problems we refine variational methods based on backward SDEs and provide the novel diffusion loss, which can be related to other state-of-the-art attempts, while offering certain numerical advantages.
The main part of the research outlined in this thesis is to develop Deep Learning models for the linguistic interpretation of the visual contents. This part is split into two research problems: interactive region segmentation and captioning, and selective texture labeling. In the first attempt, we proposed a novel hybrid Deep Learning architecture whereby the user is able to specify an arbitrary region of the image that should be highlighted and described. The proposed model alternates the bounding box indications of the standard object localization process with the output of a deep interactive segmentation module to achieve a better understanding of the dense image captioning and improve the object localization accuracy. The idea of the next part is to establish a bidirectional correlation between deep texture representation and its linguistic description via a hybrid CNN-RNN model that enables end-to-end learning of the selective texture labeling. This novel architecture provides new opportunities to describe, search, and also retrieve texture images from their linguistic descriptions. To be able to train such a model, we generated a multi-label texture dataset that covers color, material, and pattern labeling simultaneously. Our contribution to the automatic generation of texture descriptions provides an excellent opportunity to enrich the existing vocabulary of the image captioning. Such a conceptual extension can be used for fine-grained captioning applicable in geology, meteorology and other natural sciences where fine-grained image structures are of importance to understand complicated patterns. Apart from Deep Learning technologies, in the final section of the thesis, we proposed a novel approach to define mathematical morphology on color images. To this end, we converted common RGB-values of the color images into a new biconal color space and then combined two approaches of mathematical morphology to give meaning to the maximum and the minimum of the matrix field data and formulate our novel strategy.
Intrusion detection is a concept from the field of IT security. Network intrusion detection systems (NIDS) are used in addition to preventative measures, such as firewalls, to enable an automated detection of attacks.
Network security threats often consist of multiple attack phases directed against various components of the network. During each attack phase, varying types of security-related events can be observed at various points in the network. Security monitoring, however, is nowadays essentially limited to the uplink to the internet. Sometimes it is also used to a limited extent at key points within a network, but the analysis methods do not have the same depth as at the uplink. Other areas, such as virtual networks in virtual machines (VMs), are not covered at all, yet. The aim of this thesis has been to improve the detection capability of attacks in local area networks. With a glance at the area of safety engineering, it appears efficient to secure these networks thoroughly and to develop additional monitoring solutions only for the remaining problem cases. This entails several challenges for the analysis of different parts of the TCP/IP stack. The lowermost part of the network stack has to be analyzed for attacks on network components, such as switches and VM bridges. For this, there is still no technology. Although attacks on the layers~2 and 3, such as ARP spoofing and rogue DHCP servers in physical networks, can be controlled to some extent by appropriate switches, equivalent methods are not used in virtual networks. Therefore, a software-defined networking based approach is proposed to counteract the respective attacks, which works for physical and virtual networks. The upper layers are already largely covered by traditional NIDS methods, but the rapidly increasing data rates of local area networks often lead to an uncontrolled discarding of traffic due to overload situations in the monitoring stations.
Therefore, the drawbacks of current optimization approaches are outlined based on a detailed performance profiling of typical intrusion detection systems. A new approach for parallelizing the intrusion detection analysis that copes with the increasing network dynamics is introduced and evaluated. Since further special issues for NIDS particularly go back to the massive use of web technologies in today's networks, a firewall architecture is presented which applies novel NIDS methods based on machine learning to identify web applications and to ward off malicious inputs. The architecture addresses the entire process chain starting from the data transfer with HTTP via the analysis of manipulated web documents to the extraction and analysis of active contents.