Active Learning of Multiple Source Multiple Destination Topologies

We consider the problem of inferring the topology of a network with $M$ sources and $N$ receivers (hereafter referred to as an $M$-by-$N$ network), by sending probes between the sources and receivers. Prior work has shown that this problem can be decomposed into two parts: first, infer smaller subnetwork components (i.e., $1$-by-$N$'s or $2$-by-$2$'s) and then merge these components to identify the $M$-by-$N$ topology. In this paper, we focus on the second part, which had previously received less attention in the literature. In particular, we assume that a $1$-by-$N$ topology is given and that all $2$-by-$2$ components can be queried and learned using end-to-end probes. The problem is which $2$-by-$2$'s to query and how to merge them with the given $1$-by-$N$, so as to exactly identify the $2$-by-$N$ topology, and optimize a number of performance metrics, including the number of queries (which directly translates into measurement bandwidth), time complexity, and memory usage. We provide a lower bound, $\lceil \frac{N}{2} \rceil$, on the number of $2$-by-$2$'s required by any active learning algorithm and propose two greedy algorithms. The first algorithm follows the framework of multiple hypothesis testing, in particular Generalized Binary Search (GBS), since our problem is one of active learning, from $2$-by-$2$ queries. The second algorithm is called the Receiver Elimination Algorithm (REA) and follows a bottom-up approach: at every step, it selects two receivers, queries the corresponding $2$-by-$2$, and merges it with the given $1$-by-$N$; it requires exactly $N-1$ steps, which is much less than all $\binom{N}{2}$ possible $2$-by-$2$'s. Simulation results over synthetic and realistic topologies demonstrate that both algorithms correctly identify the $2$-by-$N$ topology and are near-optimal, but REA is more efficient in practice

Understanding edge-connectivity in the Internet through core-decomposition

Internet is a complex network composed by several networks: the Autonomous Systems, each one designed to transport information efficiently. Routing protocols aim to find paths between nodes whenever it is possible (i.e., the network is not partitioned), or to find paths verifying specific constraints (e.g., a certain QoS is required). As connectivity is a measure related to both of them (partitions and selected paths) this work provides a formal lower bound to it based on core-decomposition, under certain conditions, and low complexity algorithms to find it. We apply them to analyze maps obtained from the prominent Internet mapping projects, using the LaNet-vi open-source software for its visualization

How Realistic Should Knowledge Diffusion Models Be?

Knowledge diffusion models typically involve two main features: an underlying social network topology on one side, and a particular design of interaction rules driving knowledge transmission on the other side. Acknowledging the need for realistic topologies and adoption behaviors backed by empirical measurements, it becomes unclear how accurately existing models render real-world phenomena: if indeed both topology and transmission mechanisms have a key impact on these phenomena, to which extent does the use of more or less stylized assumptions affect modeling results? In order to evaluate various classical topologies and mechanisms, we push the comparison to more empirical benchmarks: real-world network structures and empirically measured mechanisms. Special attention is paid to appraising the discrepancy between diffusion phenomena (i) on some real network topologies vs. various kinds of scale-free networks, and (ii) using an empirically-measured transmission mechanism, compared with canonical appropriate models such as threshold models. We find very sensible differences between the more realistic settings and their traditional stylized counterparts. On the whole, our point is thus also epistemological by insisting that models should be tested against simulation-based empirical benchmarks.Agent-Based Simulation, Complex Systems, Empirical Calibration and Validation, Knowledge Diffusion, Model Comparison, Social Networks

AI Solutions for MDS: Artificial Intelligence Techniques for Misuse Detection and Localisation in Telecommunication Environments

This report considers the application of Articial Intelligence (AI) techniques to the problem of misuse detection and misuse localisation within telecommunications environments. A broad survey of techniques is provided, that covers inter alia rule based systems, model-based systems, case based reasoning, pattern matching, clustering and feature extraction, articial neural networks, genetic algorithms, arti cial immune systems, agent based systems, data mining and a variety of hybrid approaches. The report then considers the central issue of event correlation, that is at the heart of many misuse detection and localisation systems. The notion of being able to infer misuse by the correlation of individual temporally distributed events within a multiple data stream environment is explored, and a range of techniques, covering model based approaches, `programmed' AI and machine learning paradigms. It is found that, in general, correlation is best achieved via rule based approaches, but that these suffer from a number of drawbacks, such as the difculty of developing and maintaining an appropriate knowledge base, and the lack of ability to generalise from known misuses to new unseen misuses. Two distinct approaches are evident. One attempts to encode knowledge of known misuses, typically within rules, and use this to screen events. This approach cannot generally detect misuses for which it has not been programmed, i.e. it is prone to issuing false negatives. The other attempts to `learn' the features of event patterns that constitute normal behaviour, and, by observing patterns that do not match expected behaviour, detect when a misuse has occurred. This approach is prone to issuing false positives, i.e. inferring misuse from innocent patterns of behaviour that the system was not trained to recognise. Contemporary approaches are seen to favour hybridisation, often combining detection or localisation mechanisms for both abnormal and normal behaviour, the former to capture known cases of misuse, the latter to capture unknown cases. In some systems, these mechanisms even work together to update each other to increase detection rates and lower false positive rates. It is concluded that hybridisation offers the most promising future direction, but that a rule or state based component is likely to remain, being the most natural approach to the correlation of complex events. The challenge, then, is to mitigate the weaknesses of canonical programmed systems such that learning, generalisation and adaptation are more readily facilitated

More "normal" than normal: scaling distributions and complex systems

One feature of many naturally occurring or engineered complex systems is tremendous variability in event sizes. To account for it, the behavior of these systems is often described using power law relationships or scaling distributions, which tend to be viewed as "exotic" because of their unusual properties (e.g., infinite moments). An alternate view is based on mathematical, statistical, and data-analytic arguments and suggests that scaling distributions should be viewed as "more normal than normal". In support of this latter view that has been advocated by Mandelbrot for the last 40 years, we review in this paper some relevant results from probability theory and illustrate a powerful statistical approach for deciding whether the variability associated with observed event sizes is consistent with an underlying Gaussian-type (finite variance) or scaling-type (infinite variance) distribution. We contrast this approach with traditional model fitting techniques and discuss its implications for future modeling of complex systems