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

An Overview on Application of Machine Learning Techniques in Optical Networks

Today's telecommunication networks have become sources of enormous amounts of widely heterogeneous data. This information can be retrieved from network traffic traces, network alarms, signal quality indicators, users' behavioral data, etc. Advanced mathematical tools are required to extract meaningful information from these data and take decisions pertaining to the proper functioning of the networks from the network-generated data. Among these mathematical tools, Machine Learning (ML) is regarded as one of the most promising methodological approaches to perform network-data analysis and enable automated network self-configuration and fault management. The adoption of ML techniques in the field of optical communication networks is motivated by the unprecedented growth of network complexity faced by optical networks in the last few years. Such complexity increase is due to the introduction of a huge number of adjustable and interdependent system parameters (e.g., routing configurations, modulation format, symbol rate, coding schemes, etc.) that are enabled by the usage of coherent transmission/reception technologies, advanced digital signal processing and compensation of nonlinear effects in optical fiber propagation. In this paper we provide an overview of the application of ML to optical communications and networking. We classify and survey relevant literature dealing with the topic, and we also provide an introductory tutorial on ML for researchers and practitioners interested in this field. Although a good number of research papers have recently appeared, the application of ML to optical networks is still in its infancy: to stimulate further work in this area, we conclude the paper proposing new possible research directions

Disentangling causal webs in the brain using functional Magnetic Resonance Imaging: A review of current approaches

In the past two decades, functional Magnetic Resonance Imaging has been used to relate neuronal network activity to cognitive processing and behaviour. Recently this approach has been augmented by algorithms that allow us to infer causal links between component populations of neuronal networks. Multiple inference procedures have been proposed to approach this research question but so far, each method has limitations when it comes to establishing whole-brain connectivity patterns. In this work, we discuss eight ways to infer causality in fMRI research: Bayesian Nets, Dynamical Causal Modelling, Granger Causality, Likelihood Ratios, LiNGAM, Patel's Tau, Structural Equation Modelling, and Transfer Entropy. We finish with formulating some recommendations for the future directions in this area

REPUTATION COMPUTATION IN SOCIAL NETWORKS AND ITS APPLICATIONS

This thesis focuses on a quantification of reputation and presents models which compute reputation within networked environments. Reputation manifests past behaviors of users and helps others to predict behaviors of users and therefore reduce risks in future interactions. There are two approaches in computing reputation on networks- namely, the macro-level approach and the micro-level approach. A macro-level assumes that there exists a computing entity outside of a given network who can observe the entire network including degree distributions and relationships among nodes. In a micro-level approach, the entity is one of the nodes in a network and therefore can only observe the information local to itself, such as its own neighbors behaviors. In particular, we study reputation computation algorithms in online distributed environments such as social networks and develop reputation computation algorithms to address limitations of existing models. We analyze and discuss some properties of reputation values of a large number of agents including power-law distribution and their diffusion property. Computing reputation of another within a network requires knowledge of degrees of its neighbors. We develop an algorithm for estimating degrees of each neighbor. The algorithm considers observations associated with neighbors as a Bernoulli trial and repeatedly estimate degrees of neighbors as a new observation occurs. We experimentally show that the algorithm can compute the degrees of neighbors more accurately than a simple counting of observations. Finally, we design a bayesian reputation game where reputation is used as payoffs. The game theoretic view of reputation computation reflects another level of reality in which all agents are rational in sharing reputation information of others. An interesting behavior of agents within such a game theoretic environment is that cooperation- i.e., sharing true reputation information- emerges without an explicit punishment mechanism nor a direct reward mechanisms