Catálogo de publicaciones - libros

One property of networks that has received comparatively little attention is hierarchy, i.e., the property of having vertices that cluster together in groups, which then join to form groups of groups, and so forth, up through all levels of organization in the network. Here, we give a precise definition of hierarchical structure, give a generic model for generating arbitrary hierarchical structure in a random graph, and describe a statistically principled way to learn the set of hierarchical features that most plausibly explain a particular real-world network. By applying this approach to two example networks, we demonstrate its advantages for the interpretation of network data, the annotation of graphs with edge, vertex and community properties, and the generation of generic null models for further hypothesis testing.

Heider’s balance theory is ubiquitous in the field of social networks as an explanation for why we so frequently observe symmetry and transitivity in social relations. We propose that Simmelian tie theory could explain the same phenomena without resorting to motivational tautologies that characterize psychological explanations. Further, while both theories predict the same equilibrium state, we argue that they suggest different processes by which this equilibrium is reached. We develop a dynamic exponential random graph model (ERGM) and apply it to the classic panel data collected by Newcomb to empirically explore these two theories. We find strong evidence that Simmelian triads exist and are stable beyond what would be expected through Heiderian tendencies in the data.

We present a probabilistic generative model of entity relationships and textual attributes; the model simultaneously discovers groups among the entities and topics among the corresponding text. Block models of relationship data have been studied in social network analysis for some time, however here we cluster in multiple modalities at once. Significantly, joint inference allows the discovery of groups to be guided by the emerging topics, and vice-versa. We present experimental results on two large data sets: sixteen years of bills put before the U.S. Senate, comprising their corresponding text and voting records, and 43 years of similar data from the United Nations. We show that in comparison with traditional, separate latent-variable models for words or block structures for votes, our Group-Topic model’s joint inference improves both the groups and topics discovered. Additionally, we present a non-Markov continouous-time group model to capture shifting group structure over time.

We begin with a graph (or a directed graph), a single set of nodes $\mathcal{N}$ , and a set of lines or arcs $\mathcal{L}$ . It is common to use this mathematical concept to represent a network. We use the notation of [1], especially Chapters 13 and 15. There are extensions of these ideas to a wide range of networks, including multiple relations, affiliation relations, valued relations, and social influence and selection situations (in which information on attributes of the nodes is available), all of which can be found in the chapters of [2].

Data in the form of multiple matrices of relations among objects of a single type, representable as a collection of unipartite graphs, arise in a variety of biological settings, with collections of author-recipient email, and in social networks. Clustering the objects of study or situating them in a low dimensional space (e.g., a simplex) is only one of the goals of the analysis of such data; being able to estimate relational structures among the clusters themselves may be important. In , we introduced the family of stochastic block models of mixed membership to support such integrated data analyses. Our models combine features of mixed-membership models and block models for relational data in a hierarchical Bayesian framework. Here we present a nested variational inference scheme for this class of models, which is necessary to successfully perform fast approximate posterior inference, and we use the models and the estimation scheme to examine two data sets. (1) a collection of sociometric relations among monks is used to investigate the crisis that took place in a monastery [2], and (2) data from a school-based longitudinal study of the health-related behaviors of adolescents. Both data sets have recently been reanalyzed in [3] using a latent position clustering model and we compare our analyses with those presented there.

The study of social networks has gained new importance with the recent rise of large on-line communities. Most current approaches focus on deterministic (descriptive) models and are usually restricted to a preset number of people. Moreover, the dynamic aspect is often treated as an addendum to the static model. Taking inspiration from real-life friendship formation patterns, we propose a new generative model of evolving social networks that allows for birth and death of social links and addition of new people. Each person has a distribution over social interaction spheres, which we term “contexts.” We study the robustness of our model by examining statistical properties of simulated networks relative to well known properties of real social networks. We discuss the shortcomings of this model and problems that arise during learning. Several extensions are proposed.

Rank data consist of ordered lists of objects. A particular example of these data arises in Irish elections using the proportional representation by means of a single transferable vote (PR-STV) system, where voters list candidates in order of preference. A latent space model is proposed for rank (voting) data, where both voters and candidates are located in the same D dimensional latent space. The relative proximity of candidates to a voter determines the probability of a voter giving high preferences to a candidate. The votes are modelled using a Plackett-Luce model which allows for the ranked nature of the data to be modelled directly. Data from the 2002 Irish general election are analyzed using the proposed model which is fitted in a Bayesian framework. The estimated candidate positions suggest that the party politics play an important role in this election. Methods for choosing D , the dimensionality of the latent space, are discussed and models with D  = 1 or D  = 2 are proposed for the 2002 Irish general election data.

We present a stochastic model for networks with arbitrary degree distributions and average clustering coefficient. Many descriptions of networks are based solely on their computed degree distribution and clustering coefficient. We propose a statistical model based on these characterizations. This model generalizes models based solely on the degree distribution and is within the curved exponential family class. We present alternative parameterizations of the model. Each parameterization of the model is interpretable and tunable. We present a simple Markov Chain Monte Carlo (MCMC) algorithm to generate networks with the specified characteristics. We provide an algorithm based on MCMC to infer the network properties from network data and develop statistical inference for the model. The model is generalizable to include mixing based on attributes and other complex social structure. An application is made to modeling a protein to protein interaction network.

We propose a family of statistical models for social network evolution over time, which represents an extension of Exponential Random Graph Models (ERGMs). Many of the methods for ERGMs are readily adapted for these models, including MCMC maximum likelihood estimation algorithms. We discuss models of this type and give examples, as well as a demonstration of their use for hypothesis testing and classification.

We address the problem of embedding entities into Euclidean space over time based on co-occurrence data. We extend the CODE model of [1] to a dynamic setting. This leads to a non-standard factored state space model with real-valued hidden parent nodes and discrete observation nodes. We investigate the use of variational approximations applied to the observation model that allow us to formulate the entire dynamic model as a Kalman filter. Applying this model to temporal co-occurrence data yields posterior distributions of entity coordinates in Euclidean space that are updated over time. Initial results on per-year co-occurrences of authors and words in the NIPS corpus and on synthetic data, including videos of dynamic embeddings, seem to indicate that the model results in embeddings of co-occurrence data that are meaningful both temporally and contextually.