Anomalous Edge Detection in Edge Exchangeable Social Network Models

This paper studies detecting anomalous edges in directed graphs that model social networks. We exploit edge exchangeability as a criterion for distinguishing anomalous edges from normal edges. Then we present an anomaly detector based on conformal prediction theory; this detector has a guaranteed upper bound for false positive rate. In numerical experiments, we show that the proposed algorithm achieves superior performance to baseline methods

STATISTICAL MODELING AND INFERENCE FOR SOCIAL NETWORKS

275 pagesThe main contributions of this thesis can be organized under two main themes: knowledge discovery from social networks via human social sensing (Theme 1) and systematic emergence of societal consequences via individual actions and decisions (Theme 2). The key aim of Theme 1 is to devise algorithmic methods that can elicit useful information from humans in a social network. In particular, three statistical inference methods that exploit the graph theoretic consequence named the friendship paradox are presented: an algorithm to estimate heavy-tailed (power-law) degree distributions of social networks, a polling algorithm to estimate the fraction of nodes in a network with a specific attribute (e.g., a particular political ideology, a contagious disease, etc.) and an algorithm to dynamically track the fraction of people in a social network who have been exposed to a specific piece of information (e.g., a URL to a news article on Facebook, a hashtag on Twitter). It is shown that the proposed methods outperform the alternative methods via theoretical, numerical and empirical results. The contributions under the Theme 2 aim to understand how various societal consequences systematically emerge as collective consequences of individual actions, decisions and observations. In particular, the second theme explores the emergence of perception bias (i.e., the tendency of individuals to overestimate the prevalence of some attributes) and the glass ceiling effect (i.e., the existence of an invisible barrier that prevents certain social groups from rising to influential positions) in directed social networks (e.g., Twitter, author-citation networks). First, it is shown how the friendship paradox in directed social networks can explain why people on average overestimate the prevalence of certain traits (i.e., the perception bias in directed social networks), and strategies are proposed to mitigate its adverse effects. Then, a novel dynamical model (Directed Mixed Preferential Attachment model) is presented to explain how the glass ceiling effect in directed social networks emerges as a collective consequence of homophily (i.e., preference of individuals to associate with others who have similar attributes), size of the minority, level of preferential attachment (i.e., the preference of individuals to link to others who are already more popular) and growth dynamics (i.e., how frequently new individuals join, how they are incorporated into the social network, etc.). Additionally, the Directed Mixed Preferential Attachment model and its theoretical analysis is also used to shed light on the interplay between the structure and the dynamics of directed networks (which have been relatively less studied compared to their undirected counterparts).2022-12-0