Vahan Nanumyan

From Relational Data to Graphs: Inferring Significant Links Using Generalized Hypergeometric Ensembles

The inference of network topologies from relational data is an important problem in data analysis. Exemplary applications include the reconstruction of social ties from data on human interactions, the inference of gene co-expression networks from DNA microarray data, or the learning of semantic relationships based on co-occurrences of words in documents. Solving these problems requires techniques to infer significant links in noisy relational data. In this short paper, we propose a new statistical modeling framework to address this challenge. The framework builds on generalized hypergeometric ensembles, a class of generative stochastic models that give rise to analytically tractable probability spaces of directed, multi-edge graphs. We show how this framework can be used to assess the significance of links in noisy relational data. We illustrate our method in two data sets capturing spatio-temporal proximity relations between actors in a social system. The results show that our analytical framework provides a new approach to infer significant links from relational data, with interesting perspectives for the mining of data on social systems.

A conceptual approach to model co-evolution of urban structures

Urban structures encompass settlements, characterized by the spatial distribution of built-up areas, and also transportation structures, to connect these built-up areas. These two structures are very different in their origin and function, fulfilling complementary needs: (1) to access space and (2) to occupy space. Their evolution cannot be understood by looking at the dynamics of urban aggregations and transportation systems separately. Instead, existing built-up areas feed back on the further development of transportation structures, and the availability of the latter feeds back on the future growth of urban aggregations. To model this co-evolution, we propose an agent-based approach that builds on existing agent-based models for the evolution of trail systems and urban settlements. The key element in these separate approaches is a generalized communication of agents by means of an adaptive landscape. This landscape is only generated by the agents, but once it exists, it feeds back on their further actions. The emerging trail system or urban aggregation results as a self-organized structure from these collective interactions. In our co-evolutionary approach, we couple these two separate models by means of meta-agents that represent humans with their different demands for housing and mobility. We characterize our approach as a statistical ensemble approach, which allows to capture the potential of urban evolution in a bottom-up manner, but can be validated against empirical observations.

The Network of Counterparty Risk: Analysing Correlations in OTC Derivatives

Counterparty risk denotes the risk that a party defaults in a bilateral contract. This risk not only depends on the two parties involved, but also on the risk from various other contracts each of these parties holds. In rather informal markets, such as the OTC (over-the-counter) derivative market, institutions only report their aggregated quarterly risk exposure, but no details about their counterparties. Hence, little is known about the diversification of counterparty risk. In this paper, we reconstruct the weighted and time-dependent network of counterparty risk in the OTC derivatives market of the United States between 1998 and 2012. To proxy unknown bilateral exposures, we first study the co-occurrence patterns of institutions based on their quarterly activity and ranking in the official report. The network obtained this way is further analysed by a weighted k-core decomposition, to reveal a core-periphery structure. This allows us to compare the activity-based ranking with a topology-based ranking, to identify the most important institutions and their mutual dependencies. We also analyse correlations in these activities, to show strong similarities in the behavior of the core institutions. Our analysis clearly demonstrates the clustering of counterparty risk in a small set of about a dozen US banks. This not only increases the default risk of the central institutions, but also the default risk of peripheral institutions which have contracts with the central ones. Hence, all institutions indirectly have to bear (part of) the counterparty risk of all others, which needs to be better reflected in the price of OTC derivatives.