When is a Network a Network? Multi-Order Graphical Model Selection in Pathways and Temporal Networks

We introduce a framework for the modeling of sequential data capturing pathways of varying lengths observed in a network. Such data are important, e.g., when studying click streams in information networks, travel patterns in transportation systems, information cascades in social networks, biological pathways or time-stamped social interactions. While it is common to apply graph analytics and network analysis to such data, recent works have shown that temporal correlations can invalidate the results of such methods. This raises a fundamental question: when is a network abstraction of sequential data justified? Addressing this open question, we propose a framework which combines Markov chains of multiple, higher orders into a multi-layer graphical model that captures temporal correlations in pathways at multiple length scales simultaneously. We develop a model selection technique to infer the optimal number of layers of such a model and show that it outperforms previously used Markov order detection techniques. An application to eight real-world data sets on pathways and temporal networks shows that it allows to infer graphical models which capture both topological and temporal characteristics of such data. Our work highlights fallacies of network abstractions and provides a principled answer to the open question when they are justified. Generalizing network representations to multi-order graphical models, it opens perspectives for new data mining and knowledge discovery algorithms.Comment: 10 pages, 4 figures, 1 table, companion python package pathpy available on gitHu

Fairness und Qualität algorithmischer Entscheidungen

Algorithmische Entscheidungssysteme werden immer häufiger zur Klassifikation und Prognose von menschlichem Verhalten herangezogen. Hierbei gibt es einen breiten Diskurs um die Messung der Entscheidungsqualität solcher Systeme (Qualität) und die mögliche Diskriminierung von Teilgruppen (Fairness), welchen sich dieser Artikel widmet. Wir zeigen auf, dass es miteinander unvereinbare Fairnessmaße gibt, wobei wir auf zwei im Speziellen eingehen. Für sich allein betrachtet sind die zwei Maße zwar logisch und haben je nach Anwendungsgebiet auch ihre Daseinsberechtigung, jedoch können nicht beide zugleich erfüllt werden. Somit zeigt sich, dass gerade im Einsatz algorithmischer Entscheidungssysteme im Bereich der öffentlichen IT aufgrund ihres großen Wirkungsbereichs auf das Gemein-wohl höchste Vorsicht bei der Wahl solcher Maßstäbe herrschen muss. Wird im Anwendungsfall die Erfüllung sich widersprechender Maßstäbe gefordert, so muss darüber nachgedacht werden, ob eine algorithmische Lösung an dieser Stelle überhaupt eingesetzt werden darf

Wie Gesellschaft algorithmischen Entscheidungen auf den Zahn fühlen kann

Zunehmend treffen algorithmische Entscheidungssysteme (ADM-Systeme) Entscheidungen über Menschen und beeinflussen damit öffentliche Räume oder die gesellschaftlichen Teilhabemöglichkeiten von Individuen; damit gehören derartige Systeme zur öffentlichen IT. Hier zeigen wir, am Beispiel der Analyse von Rückfälligkeitsvorhersagesystemen und dem Datenspende-Projekt zur Bundestagswahl 2017, wie solche Systeme mit Hilfe von Black-Box-Analysen von der Öffentlichkeit untersucht werden können und wo die Grenzen dieses Ansatzes liegen. Insbesondere bei ADM-Systemen der öffentlichen Hand zeigt sich hierbei, dass eine Black-Box-Analyse nicht ausreichend ist, sondern hier ein qualitätsgesicherter Prozess der Entwicklung und Evaluation solcher Systeme notwendig ist

Breaking the hierarchy - a new cluster selection mechanism for hierarchical clustering methods

<p>Abstract</p> <p>Background</p> <p>Hierarchical clustering methods like Ward's method have been used since decades to understand biological and chemical data sets. In order to get a partition of the data set, it is necessary to choose an optimal level of the hierarchy by a so-called level selection algorithm. In 2005, a new kind of hierarchical clustering method was introduced by Palla et al. that differs in two ways from Ward's method: it can be used on data on which no full similarity matrix is defined and it can produce overlapping clusters, i.e., allow for multiple membership of items in clusters. These features are optimal for biological and chemical data sets but until now no level selection algorithm has been published for this method.</p> <p>Results</p> <p>In this article we provide a general selection scheme, the <it>level independent clustering selection method</it>, called LInCS. With it, clusters can be selected from any level in quadratic time with respect to the number of clusters. Since hierarchically clustered data is not necessarily associated with a similarity measure, the selection is based on a graph theoretic notion of <it>cohesive clusters</it>. We present results of our method on two data sets, a set of drug like molecules and set of protein-protein interaction (PPI) data. In both cases the method provides a clustering with very good sensitivity and specificity values according to a given reference clustering. Moreover, we can show for the PPI data set that our graph theoretic cohesiveness measure indeed chooses biologically homogeneous clusters and disregards inhomogeneous ones in most cases. We finally discuss how the method can be generalized to other hierarchical clustering methods to allow for a level independent cluster selection.</p> <p>Conclusion</p> <p>Using our new cluster selection method together with the method by Palla et al. provides a new interesting clustering mechanism that allows to compute overlapping clusters, which is especially valuable for biological and chemical data sets.</p

What makes a phase transition? Analysis of the random satisfiability problem

In the last 30 years it was found that many combinatorial systems undergo phase transitions. One of the most important examples of these can be found among the random k-satisfiability problems (often referred to as k-SAT), asking whether there exists an assignment of Boolean values satisfying a Boolean formula composed of clauses with k random variables each. The random 3-SAT problem is reported to show various phase transitions at different critical values of the ratio of the number of clauses to the number of variables. The most famous of these occurs when the probability of finding a satisfiable instance suddenly drops from 1 to 0. This transition is associated with a rise in the hardness of the problem, but until now the correlation between any of the proposed phase transitions and the hardness is not totally clear. In this paper we will first show numerically that the number of solutions universally follows a lognormal distribution, thereby explaining the puzzling question of why the number of solutions is still exponential at the critical point. Moreover we provide evidence that the hardness of the closely related problem of counting the total number of solutions does not show any phase transition-like behavior. This raises the question of whether the probability of finding a satisfiable instance is really an order parameter of a phase transition or whether it is more likely to just show a simple sharp threshold phenomenon. More generally, this paper aims at starting a discussion where a simple sharp threshold phenomenon turns into a genuine phase transition

MMB & DFT 2014 : Proceedings of the International Workshops ; Modeling, Analysis and Management of Social Networks and their Applications (SOCNET 2014) & Demand Modeling and Quantitative Analysis of Future Generation Energy Networks and Energy-Efficient Systems (FGENET 2014)

At present, a comprehensive set of measurement, modeling, analysis, simulation, and performance evaluation techniques are employed to investigate complex networks. A direct transfer of the developed engineering methodologies to related analysis and design tasks in next-generation energy networks, energy-efficient systems and social networks is enabled by a common mathematical foundation. The International Workshop on "Demand Modeling and Quantitative Analysis of Future Generation Energy Networks and Energy-Efficient Systems" (FGENET 2014) and the International Workshop on "Modeling, Analysis and Management of Social Networks and their Applications" (SOCNET 2014) were held on March 19, 2014, at University of Bamberg in Germany as satellite symposia of the 17th International GI/ITG Conference on "Measurement, Modelling and Evaluation of Computing Systems" and "Dependability and Fault-Tolerance" (MMB & DFT 2014). They dealt with current research issues in next-generation energy networks, smart grid communication architectures, energy-efficient systems, social networks and social media. The Proceedings of MMB & DFT 2014 International Workshops summarizes the contributions of 3 invited talks and 13 reviewed papers and intends to stimulate the readers’ future research in these vital areas of modern information societies.Gegenwärtig wird eine reichhaltige Klasse von Verfahren zur Messung, Modellierung, Analyse, Simulation und Leistungsbewertung komplexer Netze eingesetzt. Die unmittelbare Übertragung entwickelter Ingenieurmethoden auf verwandte Analyse- und Entwurfsaufgaben in Energienetzen der nächsten Generation, energieeffizienten Systemen und sozialen Netzwerken wird durch eine gemeinsame mathematische Basis ermöglicht. Die Internationalen Workshops "Demand Modeling and Quantitative Analysis of Future Generation Energy Net-works and Energy-Efficient Systems" (FGENET 2014) und "Modeling, Analysis and Management of Social Networks and their Applications" (SOCNET 2014) wurden am 19. März 2014 als angegliederte Symposien der 17. Internationalen GI/ITG Konferenz "Measurement, Modelling and Evaluation of Computing Systems" und "Dependability and Fault-Tolerance" (MMB & DFT 2014) an der Otto-Friedrich-Universität Bamberg in Deutschland veranstaltet. Es wurden aktuelle Forschungsfragen in Energienetzen der nächsten Generation, Smart Grid Kommunikationsarchitekturen, energieeffizienten Systemen, sozialen Netzwerken und sozialen Medien diskutiert. Der Tagungsband der Internationalen Workshops MMB & DFT 2014 fasst die Inhalte von 3 eingeladenen Vorträgen und 13 begutachteten Beiträgen zusammen und beabsichtigt, den Lesern Anregungen für ihre eigenen Forschungen auf diesen lebenswichtigen Gebieten moderner Informationsgesellschaften zu vermitteln

Network analysis literacy: a practical approach to the analysis of networks

Network Analysis Literacy focuses on design principles for network analytics projects. The text enables readers to: pose a defined network analytic question; build a network to answer the question; choose or design the right network analytic methods for a particular purpose, and more