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. It 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. Keywords: Statistical Analysis · Graph Theory · Network Inference · Statistical Ensemble · Relational Data · Graph Mining · Graph Analysis · Network Analysis · Social Network · Social Network Analysis · Community Structures · Data Mining · Social Interactions Advances in data sensing and collection give rise to an increasing volume of data that capture dyadic relations between elements or actors in social, natural, and technical systems. While it is common to apply graph mining and network analysis to such relational data, it is often questionable whether the application of these techniques is actually justified. Consider, for instance, various forms of time series data, which not only tell us which elements of a complex system are related but also when or in which order relations occur. Such data give rise to temporal networks, which question the application of widely used network-based modeling and data mining techniques [24, 13, 27, 30, 26] . Apart from temporal information, we often have access to data that capture multiple types of relations or interactions. The resulting multi-layer network topologies give rise to complications that threaten standard techniques, e.g., to infer and analyze social networks, detect community structures, or to model and control dynamical processes in networked systems [28, 16, 7, 35, 3] . The challenges outlined above are due to the growing availability of additional information -such as time-stamped, sequential or multi-dimensional relational data -which must be incorporated into networkbased techniques to model and analyze relational data. However, we are often confronted with situations in which we lack information that is needed to interpret observed relations. Consider, for instance, data
Casiraghi et al. REF developed a generalized hypergeometric ensembles approach to address the problem of inferring connections within relational data.
From Relational Data to Graphs: Inferring Significant Links using Generalized Hypergeometric Ensembles
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