We provide a framework for modeling social network formation through conditional multinomial logit models from discrete choice and random utility theory, in which each new edge is viewed as a “choice” made by a node to connect to another node, based on (generic) features of the other nodes available to make a connection. This perspective on network formation unifies existing models such as preferential attachment, triadic closure, and node fitness, which are all special cases, and thereby provides a flexible means for conceptualizing, estimating, and comparing models. The lens of discrete choice theory also provides several new tools for analyzing social network formation; for example, the significance of node features can be evaluated in a statistically rigorous manner, and mixtures of existing models can be estimated by adapting known expectation-maximization algorithms. We demonstrate the flexibility of our framework through examples that analyze a number of synthetic and real-world datasets. For example, we provide rigorous methods for estimating preferential attachment models and show how to separate the effects of preferential attachment and triadic closure. Non-parametric estimates of the importance of degree show a highly linear trend, and we expose the importance of looking carefully at nodes with degree zero. Examining the formation of a large citation graph, we find evidence for an increased role of degree when accounting for age.
There is also a connection with the literature on link prediction in social networks @cite_9 . A network formation model implicitly makes claims about what edges are most likely to form next, and so can be evaluated by the same metrics as link prediction algorithms @cite_14 . Features like distance, common neighbors and degree have been shown to be predictive of link formation in multiple contexts @cite_9 @cite_29 . However, in that literature, the main focus of interest is usually predictive accuracy, rather than a robust understanding of the drivers of formation. While we use predictive accuracy as a measure of goodness of fit, we are more concerned with interpretability of the model and estimates, which is one of the advantages of the conditional logit model.
@cite_29 @cite_9 @cite_14
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Predicting the occurrence of links is a fundamental problem in networks. In the link prediction problem we are given a snapshot of a network and would like to infer which interactions among existing members are likely to occur in the near future or which existing interactions are we missing. Although this problem has been extensively studied, the challenge of how to effectively combine the information from the network structure with rich node and edge attribute data remains largely open. We develop an algorithm based on Supervised Random Walks that naturally combines the information from the network structure with node and edge level attributes. We achieve this by using these attributes to guide a random walk on the graph. We formulate a supervised learning task where the goal is to learn a function that assigns strengths to edges in the network such that a random walker is more likely to visit the nodes to which new links will be created in the future. We develop an efficient training algorithm to directly learn the edge strength estimation function. Our experiments on the Facebook social graph and large collaboration networks show that our approach outperforms state-of-the-art unsupervised approaches as well as approaches that are based on feature extraction. Predicting the occurrence of links is a fundamental problem in networks. In the link prediction problem we are given a snapshot of a network and would like to infer which interactions among existing members are likely to occur in the near future or which existing interactions are we missing. Although this problem has been extensively studied, the challenge of how to effectively combine the information from the network structure with rich node and edge attribute data remains largely open. We develop an algorithm based on Supervised Random Walks that naturally combines the information from the network structure with node and edge level attributes. We achieve this by using these attributes to guide a random walk on the graph. We formulate a supervised learning task where the goal is to learn a function that assigns strengths to edges in the network such that a random walker is more likely to visit the nodes to which new links will be created in the future. We develop an efficient training algorithm to directly learn the edge strength estimation function. Our experiments on the Facebook social graph and large collaboration networks show that our approach outperforms state-of-the-art unsupervised approaches as well as approaches that are based on feature extraction. Link prediction for knowledge graphs is the task of predicting missing relationships between entities. Previous work on link prediction has focused on shallow, fast models which can scale to large knowledge graphs. However, these models learn less expressive features than deep, multi-layer models -- which potentially limits performance. In this work, we introduce ConvE, a multi-layer convolutional network model for link prediction, and report state-of-the-art results for several established datasets. We also show that the model is highly parameter efficient, yielding the same performance as DistMult and R-GCN with 8x and 17x fewer parameters. Analysis of our model suggests that it is particularly effective at modelling nodes with high indegree -- which are common in highly-connected, complex knowledge graphs such as Freebase and YAGO3. In addition, it has been noted that the WN18 and FB15k datasets suffer from test set leakage, due to inverse relations from the training set being present in the test set -- however, the extent of this issue has so far not been quantified. We find this problem to be severe: a simple rule-based model can achieve state-of-the-art results on both WN18 and FB15k. To ensure that models are evaluated on datasets where simply exploiting inverse relations cannot yield competitive results, we investigate and validate several commonly used datasets -- deriving robust variants where necessary. We then perform experiments on these robust datasets for our own and several previously proposed models and find that ConvE achieves state-of-the-art Mean Reciprocal Rank across most datasets. Link prediction for knowledge graphs is the task of predicting missing relationships between entities. Previous work on link prediction has focused on shallow, fast models which can scale to large knowledge graphs. However, these models learn less expressive features than deep, multi-layer models - which potentially limits performance. In this work we introduce ConvE, a multi-layer convolutional network model for link prediction, and report state-of-the-art results for several established datasets. We also show that the model is highly parameter efficient, yielding the same performance as DistMult and R-GCN with 8x and 17x fewer parameters. Analysis of our model suggests that it is particularly effective at modelling nodes with high indegree - which are common in highly-connected, complex knowledge graphs such as Freebase and YAGO3. In addition, it has been noted that the WN18 and FB15k datasets suffer from test set leakage, due to inverse relations from the training set being present in the test set - however, the extent of this issue has so far not been quantified. We find this problem to be severe: a simple rule-based model can achieve state-of-the-art results on both WN18 and FB15k. To ensure that models are evaluated on datasets where simply exploiting inverse relations cannot yield competitive results, we investigate and validate several commonly used datasets - deriving robust variants where necessary. We then perform experiments on these robust datasets for our own and several previously proposed models, and find that ConvE achieves state-of-the-art Mean Reciprocal Rank across all datasets. In this paper, we introduce new edge-based features for the task of recovering the 3D layout of an indoor scene from a single image. Indoor scenes have certain edges that are very informative about the spatial layout of the room, namely, the edges formed by the pairwise intersections of room faces (two walls, wall and ceiling, wall and floor). In contrast with previous approaches that rely on area-based features like geometric context and orientation maps, our method attempts to directly detect these informative edges. We learn to predict 'informative edge' probability maps using two recent methods that exploit local and global context, respectively: structured edge detection forests, and a fully convolutional network for pixelwise labeling. We show that the fully convolutional network is quite successful at predicting the informative edges even when they lack contrast or are occluded, and that the accuracy can be further improved by training the network to jointly predict the edges and the geometric context. Using features derived from the 'informative edge' maps, we learn a maximum margin structured classifier that achieves state-of-the-art performance on layout prediction. One of the core tasks in social network analysis is to predict the formation of links (i.e. various types of relationships) over time. Previous research has generally represented the social network in the form of a graph and has leveraged topological and semantic measures of similarity between two nodes to evaluate the probability of link formation. Here we introduce a novel local probabilistic graphical model method that can scale to large graphs to estimate the joint co-occurrence probability of two nodes. Such a probability measure captures information that is not captured by either topological measures or measures of semantic similarity, which are the dominant measures used for link prediction. We demonstrate the effectiveness of the co-occurrence probability feature by using it both in isolation and in combination with other topological and semantic features for predicting co-authorship collaborations on real datasets. We consider the problem of link prediction in signed networks. Such networks arise on the web in a variety of ways when users can implicitly or explicitly tag their relationship with other users as positive or negative. The signed links thus created reflect social attitudes of the users towards each other in terms of friendship or trust. Our first contribution is to show how any quantitative measure of social imbalance in a network can be used to derive a link prediction algorithm. Our framework allows us to reinterpret some existing algorithms as well as derive new ones. Second, we extend the approach of (2010) by presenting a supervised machine learning based link prediction method that uses features derived from longer cycles in the network. The supervised method outperforms all previous approaches on 3 networks drawn from sources such as Epinions, Slashdot and Wikipedia. The supervised approach easily scales to these networks, the largest of which has 132k nodes and 841k edges. Most real-world networks have an overwhelmingly large proportion of positive edges and it is therefore easy to get a high overall accuracy at the cost of a high false positive rate. We see that our supervised method not only achieves good accuracy for sign prediction but is also especially effective in lowering the false positive rate. Online social networks offering various services have become ubiquitous in our daily life. Meanwhile, users nowadays are usually involved in multiple online social networks simultaneously to enjoy specific services provided by different networks. Formally, social networks that share some common users are named as partially aligned networks. In this paper, we want to predict the formation of social links in multiple partially aligned social networks at the same time, which is formally defined as the multi-network link (formation) prediction problem. In multiple partially aligned social networks, users can be extensively correlated with each other by various connections. To categorize these diverse connections among users, 7 "intra-network social meta paths" and 4 categories of "inter-network social meta paths" are proposed in this paper. These "social meta paths" can cover a wide variety of connection information in the network, some of which can be helpful for solving the multi-network link prediction problem but some can be not. To utilize useful connection, a subset of the most informative "social meta paths" are picked, the process of which is formally defined as "social meta path selection" in this paper. An effective general link formation prediction framework, Mli (Multi-network Link Identifier), is proposed in this paper to solve the multi-network link (formation) prediction problem. Built with heterogenous topological features extracted based on the selected "social meta paths" in the multiple partially aligned social networks, Mli can help refine and disambiguate the prediction results reciprocally in all aligned networks. Extensive experiments conducted on real-world partially aligned heterogeneous networks, Foursquare and Twitter, demonstrate that Mli can solve the multi-network link prediction problem very well. In this paper we discuss a very simple approach of combining content and link information in graph structures for the purpose of community discovery, a fundamental task in network analysis. Our approach hinges on the basic intuition that many networks contain noise in the link structure and that content information can help strengthen the community signal. This enables ones to eliminate the impact of noise (false positives and false negatives), which is particularly prevalent in online social networks and Web-scale information networks. Specifically we introduce a measure of signal strength between two nodes in the network by fusing their link strength with content similarity. Link strength is estimated based on whether the link is likely (with high probability) to reside within a community. Content similarity is estimated through cosine similarity or Jaccard coefficient. We discuss a simple mechanism for fusing content and link similarity. We then present a biased edge sampling procedure which retains edges that are locally relevant for each graph node. The resulting backbone graph can be clustered using standard community discovery algorithms such as Metis and Markov clustering. Through extensive experiments on multiple real-world datasets (Flickr, Wikipedia and CiteSeer) with varying sizes and characteristics, we demonstrate the effectiveness and efficiency of our methods over state-of-the-art learning and mining approaches several of which also attempt to combine link and content analysis for the purposes of community discovery. Specifically we always find a qualitative benefit when combining content with link analysis. Additionally our biased graph sampling approach realizes a quantitative benefit in that it is typically several orders of magnitude faster than competing approaches. The nearestor near-neighbor query problems arise in a large variety of database applications, usually in the context of similarity searching. Of late, there has been increasing interest in building search index structures for performing similarity search over high-dimensional data, e.g., image databases, document collections, time-series databases, and genome databases. Unfortunately, all known techniques for solving this problem fall prey to the of dimensionality." That is, the data structures scale poorly with data dimensionality; in fact, if the number of dimensions exceeds 10 to 20, searching in k-d trees and related structures involves the inspection of a large fraction of the database, thereby doing no better than brute-force linear search. It has been suggested that since the selection of features and the choice of a distance metric in typical applications is rather heuristic, determining an approximate nearest neighbor should su ce for most practical purposes. In this paper, we examine a novel scheme for approximate similarity search based on hashing. The basic idea is to hash the points Supported by NAVY N00014-96-1-1221 grant and NSF Grant IIS-9811904. Supported by Stanford Graduate Fellowship and NSF NYI Award CCR-9357849. Supported by ARO MURI Grant DAAH04-96-1-0007, NSF Grant IIS-9811904, and NSF Young Investigator Award CCR9357849, with matching funds from IBM, Mitsubishi, Schlumberger Foundation, Shell Foundation, and Xerox Corporation. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the VLDB copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Very Large Data Base Endowment. To copy otherwise, or to republish, requires a fee and or special permission from the Endowment. Proceedings of the 25th VLDB Conference, Edinburgh, Scotland, 1999. from the database so as to ensure that the probability of collision is much higher for objects that are close to each other than for those that are far apart. We provide experimental evidence that our method gives signi cant improvement in running time over other methods for searching in highdimensional spaces based on hierarchical tree decomposition. Experimental results also indicate that our scheme scales well even for a relatively large number of dimensions (more than 50). One of the most influential recent results in network analysis is that many natural networks exhibit a power-law or log-normal degree distribution. This has inspired numerous generative models that match this property. However, more recent work has shown that while these generative models do have the right degree distribution, they are not good models for real-life networks due to their differences on other important metrics like conductance. We believe this is, in part, because many of these real-world networks have very different joint degree distributions, that is, the probability that a randomly selected edge will be between nodes of degree k and l. Assortativity is a sufficient statistic of the joint degree distribution, and it has been previously noted that social networks tend to be assortative, while biological and technological networks tend to be disassortative. We suggest understanding the relationship between network structure and the joint degree distribution of graphs is an interesting avenue of further research. An important tool for such studies are algorithms that can generate random instances of graphs with the same joint degree distribution. This is the main topic of this article, and we study the problem from both a theoretical and practical perspective. We provide an algorithm for constructing simple graphs from a given joint degree distribution, and a Monte Carlo Markov chain method for sampling them. We also show that the state space of simple graphs with a fixed degree distribution is connected via endpoint switches. We empirically evaluate the mixing time of this Markov chain by using experiments based on the autocorrelation of each edge. These experiments show that our Markov chain mixes quickly on these real graphs, allowing for utilization of our techniques in practice. Our work introduces an approach for estimating the contribution of attachment mechanisms to the formation of growing networks. We present a generic model in which growth is driven by the continuous attachment of new nodes according to random and preferential linkage with a fixed probability. Past approaches apply likelihood analysis to estimate the probability of occurrence of each mechanism at a particular network instance, exploiting the concavity of the likelihood function at each point in time. However, the probability of connecting to existing nodes, and consequently the likelihood function itself, varies as networks grow. We establish conditions under which applying likelihood analysis guarantees the existence of a local maximum of the time-varying likelihood function and prove that a expectation maximization algorithm provides a convergent estimate. Furthermore, the in-degree distributions of the nodes in the growing networks is analytically characterized. Simulations show that, under the proposed conditions, expectation maximization and maximum-likelihood accurately estimate the actual contribution of each mechanism, and in-degree distributions converge to a stationary distributions. The problem of predicting links or interactions between objects in a network, is an important task in network analysis. Along this line, link prediction between co-authors in a co-author network is a frequently studied problem. In most of these studies, authors are considered in a homogeneous network, .e., only one type of objects(author type) and one type of links (co-authorship) exist in the network. However, in a real bibliographic network, there are multiple types of objects ( .g., venues, topics, papers) and multiple types of links among these objects. In this paper, we study the problem of co-author relationship prediction in the heterogeneous bibliographic network, and a new methodology called, .e., meta path-based relationship prediction model, is proposed to solve this problem. First, meta path-based topological features are systematically extracted from the network. Then, a supervised model is used to learn the best weights associated with different topological features in deciding the co-author relationships. We present experiments on a real bibliographic network, the DBLP network, which show that metapath-based heterogeneous topological features can generate more accurate prediction results as compared to homogeneous topological features. In addition, the level of significance of each topological feature can be learned from the model, which is helpful in understanding the mechanism behind the relationship building. In this paper we study the problem of building a constant-degree connected dominating set (CCDS), a network structure that can be used as a communication backbone, in the dual graph radio network model ( in J Parallel Distrib Comput 64:89–96, 2004; in Proceedings of the international symposium on principles of distributed computing 2009, Distrib Comput 24(3–4):187–206 2011, Proceedings of the international symposium on principles of distributed computing 2010). This model includes two types of links: reliable, which always deliver messages, and unreliable, which sometimes fail to deliver messages. Real networks compensate for this differing quality by deploying low-layer detection protocols to filter unreliable from reliable links. With this in mind, we begin by presenting an algorithm that solves the CCDS problem in the dual graph model under the assumption that every process (u ) is provided with a local link detector set consisting of every neighbor connected to (u ) by a reliable link. The algorithm solves the CCDS problem in (O ( ^2 n b + ^3 n ) ) rounds, with high probability, where ( ) is the maximum degree in the reliable link graph, (n ) is the network size, and (b ) is an upper bound in bits on the message size. The algorithm works by first building a Maximal Independent Set (MIS) in ( ^3 n ) time, and then leveraging the local topology knowledge to efficiently connect nearby MIS processes. A natural follow-up question is whether the link detector must be perfectly reliable to solve the CCDS problem. With this in mind, we first describe an algorithm that builds a CCDS in (O( )polylog ((n)) ) time under the assumption of (O(1) ) unreliable links included in each link detector set. We then prove this algorithm to be (almost) tight by showing that the possible inclusion of only a single unreliable link in each process’s local link detector set is sufficient to require ( ( ) ) rounds to solve the CCDS problem, regardless of message size. We conclude by discussing how to apply our algorithm in the setting where the topology of reliable and unreliable links can change over time. We propose a graphical model for representing networks of stochastic processes, the minimal generative model graph. It is based on reduced factorizations of the joint distribution over time. We show that under appropriate conditions, it is unique and consistent with another type of graphical model, the directed information graph, which is based on a generalization of Granger causality. We demonstrate how directed information quantifies Granger causality in a particular sequential prediction setting. We also develop efficient methods to estimate the topological structure from data that obviate estimating the joint statistics. One algorithm assumes upper bounds on the degrees and uses the minimal dimension statistics necessary. In the event that the upper bounds are not valid, the resulting graph is nonetheless an optimal approximation in terms of Kullback-Leibler (KL) divergence. Another algorithm uses near-minimal dimension statistics when no bounds are known, but the distribution satisfies a certain criterion. Analogous to how structure learning algorithms for undirected graphical models use mutual information estimates, these algorithms use directed information estimates. We characterize the sample-complexity of two plug-in directed information estimators and obtain confidence intervals. For the setting when point estimates are unreliable, we propose an algorithm that uses confidence intervals to identify the best approximation that is robust to estimation error. Last, we demonstrate the effectiveness of the proposed algorithms through the analysis of both synthetic data and real data from the Twitter network. In the latter case, we identify which news sources influence users in the network by merely analyzing tweet times. Prediction is one of the most attractive aspects in data mining. Link prediction has recently attracted the attention of many researchers as an effective technique to be used in graph based models in general and in particular for social network analysis due to the recent popularity of the field. Link prediction helps to understand associations between nodes in social communities. Existing link prediction-related approaches described in the literature are limited to predict links that are anticipated to exist in the future. To the best of our knowledge, none of the previous works in this area has explored the prediction of links that could disappear in the future. We argue that the latter set of links are important to know about; they are at least equally important as and do complement the positive link prediction process in order to plan better for the future. In this paper, we propose a link prediction model which is capable of predicting both links that might exist and links that may disappear in the future. The model has been successfully applied in two different though very related domains, namely health care and gene expression networks. The former application concentrates on physicians and their interactions while the second application covers genes and their interactions. We have tested our model using different classifiers and the reported results are encouraging. Finally, we compare our approach with the internal links approach and we reached the conclusion that our approach performs very well in both bipartite and non-bipartite graphs. Link prediction is a complex, inherently relational, task. Be it in the domain of scientific citations, social networks or hypertext links, the underlying data are extremely noisy and the characteristics useful for prediction are not readily available in a “flat” file format, but rather involve complex relationships among objects. In this paper, we propose the application of our methodology for Statistical Relational Learning to building link prediction models. We propose an integrated approach to building regression models from data stored in relational databases in which potential predictors are generated by structured search of the space of queries to the database, and then tested for inclusion in a logistic regression. We present experimental results for the task of predicting citations made in scientific literature using relational data taken from CiteSeer. This data includes the citation graph, authorship and publication venues of papers, as well as their word content. Recently there has been much interest in graph-based learning, with applications in collaborative filtering for recommender networks, link prediction for social networks and fraud detection. These networks can consist of millions of entities, and so it is very important to develop highly efficient techniques. We are especially interested in accelerating random walk approaches to compute some very interesting proximity measures of these kinds of graphs. These measures have been shown to do well empirically (Liben-Nowell & Kleinberg, 2003; Brand, 2005). We introduce a truncated variation on a well-known measure, namely commute times arising from random walks on graphs. We present a very novel algorithm to compute all interesting pairs of approximate nearest neighbors in truncated commute times, without computing it between all pairs. We show results on both simulated and real graphs of size up to 100; 000 entities, which indicate near-linear scaling in computation time. We consider the popular and well-studied push model, which is used to spread information in a given network with n vertices. Initially, some vertex owns a rumour and passes it to one of its neighbours, which is chosen randomly. In each of the succeeding rounds, every vertex that knows the rumour informs a random neighbour. It has been shown on various network topologies that this algorithm succeeds in spreading the rumour within O(log n) rounds. However, many studies are quite coarse and involve huge constants that do not allow for a direct comparison between different network topologies. In this paper, we analyse the push model on several important families of graphs, and obtain tight runtime estimates. We first show that, for any almost-regular graph on n vertices with small spectral expansion, rumour spreading completes after log2n + log n+o(log n) rounds with high probability. This is the first result that exhibits a general graph class for which rumour spreading is essentially as fast as on complete graphs. Moreover, for the random graph G(n,p) with p=c log n n, where c > 1, we determine the runtime of rumour spreading to be log2n + γ (c)log n with high probability, where γ(c) = clog(c (c−1)). In particular, this shows that the assumption of almost regularity in our first result is necessary. Finally, for a hypercube on n=2d vertices, the runtime is with high probability at least (1+β) ⋅ (log2n + log n), where β > 0. This reveals that the push model on hypercubes is slower than on complete graphs, and thus shows that the assumption of small spectral expansion in our first result is also necessary. In addition, our results combined with the upper bound of O(log n) for the hypercube (see [11]) imply that the push model is faster on hypercubes than on a random graph G(n, clog n n), where c is sufficiently close to 1. The temporal dynamics of a complex system such as a social network or a communication network can be studied by understanding the patterns of link appearance and disappearance over time. A critical task along this understanding is to predict the link state of the network at a future time given a collection of link states at earlier time points. In existing literature, this task is known as link prediction in dynamic networks. Solving this task is more difficult than its counterpart in static networks because an effective feature representation of node-pair instances for the case of dynamic network is hard to obtain. To overcome this problem, we propose a novel method for metric embedding of node-pair instances of a dynamic network. The proposed method models the metric embedding task as an optimal coding problem where the objective is to minimize the reconstruction error, and it solves this optimization task using a gradient descent method. We validate the effectiveness of the learned feature representation by utilizing it for link prediction in various real-life dynamic networks. Specifically, we show that our proposed link prediction model, which uses the extracted feature representation for the training instances, outperforms several existing methods that use well-known link prediction features.