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Concept# Pattern

Summary

A pattern is a regularity in the world, in human-made design, or in abstract ideas. As such, the elements of a pattern repeat in a predictable manner. A geometric pattern is a kind of pattern formed of geometric shapes and typically repeated like a wallpaper design.
Any of the senses may directly observe patterns. Conversely, abstract patterns in science, mathematics, or language may be observable only by analysis. Direct observation in practice means seeing visual patterns, which are widespread in nature and in art. Visual patterns in nature are often chaotic, rarely exactly repeating, and often involve fractals. Natural patterns include spirals, meanders, waves, foams, tilings, cracks, and those created by symmetries of rotation and reflection. Patterns have an underlying mathematical structure; indeed, mathematics can be seen as the search for regularities, and the output of any function is a mathematical pattern. Similarly in the sciences, theories explain and predict regulariti

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Monitoring traffic events in computer network has become a critical task for operators to maintain an accurate view of a network's condition, to detect emerging security threats, and to safeguard the availability of resources. Conditions detrimental to a network's performance need to be detected timely and accurately. Such conditions are observed as anomalies in the network traffic and may be caused by malicious attacks, abuse of resources, or failures of mission-critical servers and devices. Behavior-based anomaly detection techniques examine the traffic for patterns that significantly deviate from the network normal activities. Such techniques provide a complementary layer of defense to identify undesired conditions which traditional, signature-based methods fail to detect. These conditions may, for example, emerge from zero-day exploits, outbreaks of new worms, unanticipated user behavior, or deficiencies in the network infrastructure. This thesis is concerned with the challenge of detecting traffic anomalies with behavior-based methods from flow-level network traffic measurements while providing interpretable alert information. We address the problem from two opposite perspectives by analyzing network behavior and individual host behavior. Learning the normal behavior of network activities and detecting relevant deviations thereof is a complex task since behavior changes may also occur under legitimate conditions and should not be reported as anomalies. Due to the absence of explicit detection rules, behavior-based methods moreover provide less precise information as to the causes of aberrant events. Network operators, however, critically depend on meaningful detection results to timely react to alerts by defining effective countermeasures or ruling out potential false alarms. The first part of this work introduces a novel detection scheme which mines for anomalies in the network behavior observed from traffic feature distributions. We study how various types of anomalies may be detected while providing sufficient information to administrators for their characterization. Based on the observation that networks have multiple behavior modes, we propose a method to estimate and model the modes during an unsupervised learning phase. Observed network behavior is compared to the baseline models by means of a two-layered distance computation: Fine-grained anomaly indices indicate suspicious behavior of individual components of traffic features whereas collective anomaly scores for each feature enable effective detection of anomalies that affect multiple components. We show that the two detection layers reliably expose different types of anomalies. Compared with existing detection methods, the resulting alerts provide important additional information that enables administrators to draw early conclusions as to the anomaly causes. In the second part, we address the challenge of processing high-cardinality traffic information in behavior-based anomaly detection. We introduce an adaptive, locality preserving pre-processing method of measurement data into histogram representations with a manageable number of variable-sized bins. Our technique iteratively adapts, with limited, tunable memory requirements, to the empirical distribution of observations in a data stream in order to evenly balance the observations over the histogram bins. As an important result, we show that our method approximates input distributions well and improves the level of detail in histograms compared to traditional methods. Applied to behavior-based anomaly detection, higher detection sensitivity is achieved while, thanks to preserving the locality of observations, the meaning of bins and the interpretability of detection results is retained. In the third part, we focus on the problem that many low-volume anomalies, emerging from individual hosts, are likely to evade from detection because they are not reflected as significant deviations in the variability of aggregate behavior patterns of hosts on the network level. To address this problem, we examine the behavior of individual hosts from their network connection-level activities using an unobtrusive, passive monitoring approach. We develop an unsupervised method to track properties in the activities that recur over time and establish detailed behavior profiles. We propose three anomaly detectors that compare observed activities to the profiles in order to recognize suspicious changes in a host's activities, giving evidence of abnormal behavior. We demonstrate their effectiveness in revealing different types of anomalies, which are not detectable in aggregate network statistics, while providing meaningful alert information to administrators. In addition, we show that the profiles of individual hosts are stable over time and representative of their activities, and may even be used to identify hosts solely from their traffic behavior. In summary, the methods and algorithms presented in this thesis enable practical and interpretable detection of traffic anomalies on the network ow level with behavior-based methods.

Deep neural networks have been empirically successful in a variety of tasks, however their theoretical understanding is still poor. In particular, modern deep neural networks have many more parameters than training data. Thus, in principle they should overfit the training samples and exhibit poor generalization to the complete data distribution. Counter intuitively however, they manage to achieve both high training accuracy and high testing accuracy. One can prove generalization using a validation set, however this can be difficult when training samples are limited and at the same time we do not obtain any information about why deep neural networks generalize well. Another approach is to estimate the complexity of the deep neural network. The hypothesis is that if a network with high training accuracy has high complexity it will have memorized the data, while if it has low complexity it will have learned generalizable patterns. In the first part of this thesis we explore Spectral Complexity, a measure of complexity that depends on combinations of norms of the weight matrices of the deep neural network. For a dataset that is difficult to classify, with no underlying model and/or no recurring pattern, for example one where the labels have been chosen randomly, spectral complexity has a large value, reflecting that the network needs to memorize the labels, and will not generalize well. Putting back the real labels, the spectral complexity becomes lower reflecting that some structure is present and the network has learned patterns that might generalize to unseen data. Spectral complexity results in vacuous estimates of the generalization error (the difference between the training and testing accuracy), and we show that it can lead to counterintuitive results when comparing the generalization error of different architectures. In the second part of the thesis we explore non-vacuous estimates of the generalization error. In Chapter 2 we analyze the case of PAC-Bayes where a posterior distribution over the weights of a deep neural network is learned using stochastic variational inference, and the generalization error is the KL divergence between this posterior and a prior distribution. We find that a common approximation where the posterior is constrained to be Gaussian with diagonal covariance, known as the mean-field approximation, limits significantly any gains in bound tightness. We find that, if we choose the prior mean to be the random network initialization, the generalization error estimate tightens significantly. In Chapter 3 we explore an existing approach to learning the prior mean, in PAC-Bayes, from the training set. Specifically, we explore differential privacy, which ensures that the training samples contribute only a limited amount of information to the prior, making it distribution and not training set dependent. In this way the prior should generalize well to unseen data (as it hasn't memorized individual samples) and at the same time any posterior distribution that is close to it in terms of the KL divergence will also exhibit good generalization.

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In this work, we first revise some extensions of the standard Hopfield model in the low storage limit, namely the correlated attractor case and the multitasking case recently introduced by the authors. The former case is based on a modification of the Hebbian prescription, which induces a coupling between consecutive patterns and this effect is tuned by a parameter a. In the latter case, dilution is introduced in pattern entries, in such a way that a fraction d of them is blank. Then, we merge these two extensions to obtain a system able to retrieve several patterns in parallel and the quality of retrieval, encoded by the set of Mattis magnetizations {m(mu)}, is reminiscent of the correlation among patterns. By tuning the parameters d and a, qualitatively different outputs emerge, ranging from highly hierarchical to symmetric. The investigations are accomplished by means of both numerical simulations and statistical mechanics analysis, properly adapting a novel technique originally developed for spin glasses, i.e. the Hamilton-Jacobi interpolation, with excellent agreement. Finally, we show the thermodynamical equivalence of this associative network with a (restricted) Boltzmann machine and study its stochastic dynamics to obtain even a dynamical picture, perfectly consistent with the static scenario earlier discussed. (c) 2012 Elsevier Ltd. All rights reserved.

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