With the proliferation of network data, researchers are increasingly focusing on questions investigating phenomena occurring on networks. This often includes analysis of peer-effects, i.e., how the connections of an individual affect that individual's behavior. This type of influence is not limited to direct connections of an individual (such as friends), but also to individuals that are connected through longer paths (for example, friends of friends, or friends of friends of friends). In this work, we identify an ambiguity in the definition of what constitutes the extended neighborhood of an individual. This ambiguity gives rise to different semantics and supports different types of underlying phenomena. We present experimental results, both on synthetic and real networks, that quantify differences among the sets of extended neighbors under different semantics. Finally, we provide experimental evidence that demonstrates how the use of different semantics affects model selection.
There is a plethora of work analyzing the properties of social networks. However, the actual construction for sets of peers is relatively understudied. A closely related work is that of @cite_3 , which focuses on analyzing the structure of the Facebook graph. The authors explicitly make a distinction between the number of non-unique friends of friends (the number of paths of length two from the initial node that do not return to the initial node) and unique friends of friends (the set of nodes that can be reached from the initial node with paths of length two). That distinction could be thought of as an additional type of semantics. It is worth pointing out that our work has connections to feature construction for relational learning, as well as to probabilistic relational models, such as PRMs @cite_4 and Markov Logic Networks @cite_5 . More specifically, relational models are lifted representations that can be grounded to propositional models, according to some grounding semantics. Those semantics specify how an edge on the relational level translates'' to an edge on the propositional level.
@cite_5 @cite_4 @cite_3
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Many interesting domains in machine learning can be viewed as networks, with relationships (e.g., friendships) connecting items (e.g., individuals). The Active Exploration (AE) task is to identify all items in a network with a desired trait (i.e., positive labels) given only partial information about the network. The AE process iteratively queries for labels or network structure within a limited budget; thus, accurate predictions prior to making each query is critical to maximizing the number of positives gathered. However, the targeted AE query process produces partially observed networks that can create difficulties for predictive modeling. In particular, we demonstrate that these partial networks can exhibit extreme label correlation bias, which makes it difficult for conventional relational learning methods to accurately estimate relational parameters. To overcome this issue, we model the joint distribution of possible edges and labels to improve learning and inference. Our proposed method, Probabilistic Relational Expectation Maximization (PR-EM), is the first AE approach to accurately learn the complex dependencies between attributes, labels, and structure to improve predictions. PR-EM utilizes collective inference over the missing relationships in the partial network to jointly infer unknown item traits. Further, we develop a linear inference algorithm to facilitate efficient use of PR-EM in large networks. We test our approach on four real world networks, showing that AE with PR-EM gathers significantly more positive items compared to state-of-the-art methods. Many real-life graphs such as social networks and peer-to-peer networks capture the relationships among the nodes by using trust scores to label the edges. Important usage of such networks includes trust prediction, finding the most reliable or trusted node in a local subgraph, etc. For many of these applications, it is crucial to assess the prestige and bias of a node. The bias of a node denotes its propensity to trust mistrust its neighbours and is closely related to truthfulness. If a node trusts all its neighbours, its recommendation of another node as trustworthy is less reliable. It is based on the idea that the recommendation of a highly biased node should weigh less. In this paper, we propose an algorithm to compute the bias and prestige of nodes in networks where the edge weight denotes the trust score. Unlike most other graph-based algorithms, our method works even when the edge weights are not necessarily positive. The algorithm is iterative and runs in O(km) time where k is the number of iterations and m is the total number of edges in the network. The algorithm exhibits several other desirable properties. It converges to a unique value very quickly. Also, the error in bias and prestige values at any particular iteration is bounded. Further, experiments show that our model conforms well to social theories such as the balance theory (enemy of a friend is an enemy, etc.). We propose a framework for inferring the latent attitudes or preferences of users by performing probabilistic first-order logical reasoning over the social network graph. Our method answers questions about Twitter users like Does this user like sushi? or Is this user a New York Knicks fan? by building a probabilistic model that reasons over user attributes (the user's location or gender) and the social network (the user's friends and spouse), via inferences like homophily (I am more likely to like sushi if spouse or friends like sushi, I am more likely to like the Knicks if I live in New York). The algorithm uses distant supervision, semi-supervised data harvesting and vector space models to extract user attributes (e.g. spouse, education, location) and preferences (likes and dislikes) from text. The extracted propositions are then fed into a probabilistic reasoner (we investigate both Markov Logic and Probabilistic Soft Logic). Our experiments show that probabilistic logical reasoning significantly improves the performance on attribute and relation extraction, and also achieves an F-score of 0.791 at predicting a users likes or dislikes, significantly better than two strong baselines. We study the problem of labeling the edges of a social network graph (e.g., acquaintance connections in Facebook) as either positive (i.e., trust, true friendship) or negative (i.e., distrust, possible frenemy) relations. Such signed relations provide much stronger signal in tying the behavior of online users than the unipolar Homophily effect, yet are largely unavailable as most social graphs only contain unsigned edges. We show the surprising fact that it is possible to infer signed social ties with good accuracy solely based on users' behavior of decision making (or using only a small fraction of supervision information) via unsupervised and semi-supervised algorithms. This work hereby makes it possible to turn an unsigned acquaintance network (e.g. Facebook, Myspace) into a signed trust-distrust network (e.g. Epinion, Slashdot). Our results are based on a mixed effects framework that simultaneously captures users' behavior, social interactions as well as the interplay between the two. The framework includes a series of latent factor models and it also encodes the principles of balance and status from Social psychology. Experiments on Epinion and Yahoo! Pulse networks illustrate that (1) signed social ties can be predicted with high-accuracy even in fully unsupervised settings, and (2) the predicted signed ties are significantly more useful for social behavior prediction than simple Homophily.