A survey of statistical network models

Networks are ubiquitous in science and have become a focal point for discussion in everyday life. Formal statistical models for the analysis of network data have emerged as a major topic of interest in diverse areas of study, and most of these involve a form of graphical representation. Probability models on graphs date back to 1959. Along with empirical studies in social psychology and sociology from the 1960s, these early works generated an active network community and a substantial literature in the 1970s. This effort moved into the statistical literature in the late 1970s and 1980s, and the past decade has seen a burgeoning network literature in statistical physics and computer science. The growth of the World Wide Web and the emergence of online networking communities such as Facebook, MySpace, and LinkedIn, and a host of more specialized professional network communities has intensified interest in the study of networks and network data. Our goal in this review is to provide the reader with an entry point to this burgeoning literature. We begin with an overview of the historical development of statistical network modeling and then we introduce a number of examples that have been studied in the network literature. Our subsequent discussion focuses on a number of prominent static and dynamic network models and their interconnections. We emphasize formal model descriptions, and pay special attention to the interpretation of parameters and their estimation. We end with a description of some open problems and challenges for machine learning and statistics.Comment: 96 pages, 14 figures, 333 reference

Classification in Networked Data: A Toolkit and a Univariate Case Study

This paper1 is about classifying entities that are interlinked with entities for which the class is known. After surveying prior work, we present NetKit, a modular toolkit for classification in networked data, and a case-study of its application to networked data used in prior machine learning research. NetKit is based on a node-centric framework in which classifiers comprise a local classifier, a relational classifier, and a collective inference procedure. Various existing node-centric relational learning algorithms can be instantiated with appropriate choices for these components, and new combinations of components realize new algorithms. The case study focuses on univariate network classification, for which the only information used is the structure of class linkage in the network (i.e., only links and some class labels). To our knowledge, no work previously has evaluated systematically the power of class-linkage alone for classification in machine learning benchmark data sets. The results demonstrate that very simple network-classification models perform quite well—well enough that they should be used regularly as baseline classifiers for studies of learning with networked data. The simplest method (which performs remarkably well) highlights the close correspondence between several existing methods introduced for different purposes—that is, Gaussian-field classifiers, Hopfield networks, and relational-neighbor classifiers. The case study also shows that there are two sets of techniques that are preferable in different situations, namely when few versus many labels are known initially. We also demonstrate that link selection plays an important role similar to traditional feature selectionNYU, Stern School of Business, IOMS Department, Center for Digital Economy Researc

Implications of Computational Cognitive Models for Information Retrieval

This dissertation explores the implications of computational cognitive modeling for information retrieval. The parallel between information retrieval and human memory is that the goal of an information retrieval system is to find the set of documents most relevant to the query whereas the goal for the human memory system is to access the relevance of items stored in memory given a memory probe (Steyvers & Griffiths, 2010). The two major topics of this dissertation are desirability and information scent. Desirability is the context independent probability of an item receiving attention (Recker & Pitkow, 1996). Desirability has been widely utilized in numerous experiments to model the probability that a given memory item would be retrieved (Anderson, 2007). Information scent is a context dependent measure defined as the utility of an information item (Pirolli & Card, 1996b). Information scent has been widely utilized to predict the memory item that would be retrieved given a probe (Anderson, 2007) and to predict the browsing behavior of humans (Pirolli & Card, 1996b). In this dissertation, I proposed the theory that desirability observed in human memory is caused by preferential attachment in networks. Additionally, I showed that documents accessed in large repositories mirror the observed statistical properties in human memory and that these properties can be used to improve document ranking. Finally, I showed that the combination of information scent and desirability improves document ranking over existing well-established approaches

LexRank: Graph-based Lexical Centrality as Salience in Text Summarization

We introduce a stochastic graph-based method for computing relative importance of textual units for Natural Language Processing. We test the technique on the problem of Text Summarization (TS). Extractive TS relies on the concept of sentence salience to identify the most important sentences in a document or set of documents. Salience is typically defined in terms of the presence of particular important words or in terms of similarity to a centroid pseudo-sentence. We consider a new approach, LexRank, for computing sentence importance based on the concept of eigenvector centrality in a graph representation of sentences. In this model, a connectivity matrix based on intra-sentence cosine similarity is used as the adjacency matrix of the graph representation of sentences. Our system, based on LexRank ranked in first place in more than one task in the recent DUC 2004 evaluation. In this paper we present a detailed analysis of our approach and apply it to a larger data set including data from earlier DUC evaluations. We discuss several methods to compute centrality using the similarity graph. The results show that degree-based methods (including LexRank) outperform both centroid-based methods and other systems participating in DUC in most of the cases. Furthermore, the LexRank with threshold method outperforms the other degree-based techniques including continuous LexRank. We also show that our approach is quite insensitive to the noise in the data that may result from an imperfect topical clustering of documents

Term-community-based topic detection with variable resolution

Network-based procedures for topic detection in huge text collections offer an intuitive alternative to probabilistic topic models. We present in detail a method that is especially designed with the requirements of domain experts in mind. Like similar methods, it employs community detection in term co-occurrence graphs, but it is enhanced by including a resolution parameter that can be used for changing the targeted topic granularity. We also establish a term ranking and use semantic word-embedding for presenting term communities in a way that facilitates their interpretation. We demonstrate the application of our method with a widely used corpus of general news articles and show the results of detailed social-sciences expert evaluations of detected topics at various resolutions. A comparison with topics detected by Latent Dirichlet Allocation is also included. Finally, we discuss factors that influence topic interpretation.Comment: 31 pages, 6 figure