Variational Bayesian Inference for the Latent Position Cluster Model

Many recent approaches to modeling social networks have focussed on embedding the actors in a latent “social space”. Links are more likely for actors that are close in social space than for actors that are distant in social space. In particular, the Latent Position Cluster Model (LPCM) [1] allows for explicit modelling of the clustering that is exhibited in many network datasets. However, inference for the LPCM model via MCMC is cumbersome and scaling of this model to large or even medium size networks with many interacting nodes is a challenge. Variational Bayesian methods offer one solution to this problem. An approximate, closed form posterior is formed, with unknown variational parameters. These parameters are tuned to minimize the Kullback-Leibler divergence between the approximate variational posterior and the true posterior, which known only up to proportionality. The variational Bayesian approach is shown to give a computationally efficient way of fitting the LPCM. The approach is demonstrated on a number of data sets and it is shown to give a good fit

Modeling and Robust Design of Networks under Risk: The Case of Information Infrastructure

Study of network risks allows to develop insights into the methods of building robust networks, which are also critical elements of infrastructures that are of a paramount importance for the modern society. In this paper we show how the modern quantitative modeling methodologies can be employed for analysis of network risks and for design of robust networks under uncertainty. This is done on the example of important problem arising in the process of building of the information infrastructure: provision of advanced mobile data services. We show how portfolio theory developed in the modern finance can be used for design of robust provision network comprising of independent agents. After this the modeling frameworks of Bayesian nets andMarkov fields are used for the study of several problems fundamental for the process of service adoption such as the sensitivity of networks, the direction of improvements, and the propagation of user attitudes on social networks

Scalable Inference of Customer Similarities from Interactions Data using Dirichlet Processes

Under the sociological theory of homophily, people who are similar to one another are more likely to interact with one another. Marketers often have access to data on interactions among customers from which, with homophily as a guiding principle, inferences could be made about the underlying similarities. However, larger networks face a quadratic explosion in the number of potential interactions that need to be modeled. This scalability problem renders probability models of social interactions computationally infeasible for all but the smallest networks. In this paper we develop a probabilistic framework for modeling customer interactions that is both grounded in the theory of homophily, and is flexible enough to account for random variation in who interacts with whom. In particular, we present a novel Bayesian nonparametric approach, using Dirichlet processes, to moderate the scalability problems that marketing researchers encounter when working with networked data. We find that this framework is a powerful way to draw insights into latent similarities of customers, and we discuss how marketers can apply these insights to segmentation and targeting activities

Dynamics of Information Diffusion and Social Sensing

Statistical inference using social sensors is an area that has witnessed remarkable progress and is relevant in applications including localizing events for targeted advertising, marketing, localization of natural disasters and predicting sentiment of investors in financial markets. This chapter presents a tutorial description of four important aspects of sensing-based information diffusion in social networks from a communications/signal processing perspective. First, diffusion models for information exchange in large scale social networks together with social sensing via social media networks such as Twitter is considered. Second, Bayesian social learning models and risk averse social learning is considered with applications in finance and online reputation systems. Third, the principle of revealed preferences arising in micro-economics theory is used to parse datasets to determine if social sensors are utility maximizers and then determine their utility functions. Finally, the interaction of social sensors with YouTube channel owners is studied using time series analysis methods. All four topics are explained in the context of actual experimental datasets from health networks, social media and psychological experiments. Also, algorithms are given that exploit the above models to infer underlying events based on social sensing. The overview, insights, models and algorithms presented in this chapter stem from recent developments in network science, economics and signal processing. At a deeper level, this chapter considers mean field dynamics of networks, risk averse Bayesian social learning filtering and quickest change detection, data incest in decision making over a directed acyclic graph of social sensors, inverse optimization problems for utility function estimation (revealed preferences) and statistical modeling of interacting social sensors in YouTube social networks.Comment: arXiv admin note: text overlap with arXiv:1405.112

CLASSIFICATION AND PREDICTION OF PORT VARIABLES

[EN] Many variables are included in planning and management of port terminals. They can be economic, social, environmental and institutional. Agent needs to know relationship between these variables to modify planning conditions. Use of Bayesian Networks allows for classifying, predicting and diagnosing these variables. Bayesian Networks allow for estimating subsequent probability of unknown variables, basing on know variables. In planning level, it means that it is not necessary to know all variables because their relationships are known. Agent can know interesting information about how port variables are connected. It can be interpreted as cause-effect relationship. Bayesian Networks can be used to make optimal decisions by introduction of possible actions and utility of their results. In proposed methodology, a data base has been generated with more than 40 port variables. They have been classified in economic, social, environmental and institutional variables, in the same way that smart port studies in Spanish Port System make. From this data base, a network has been generated using a non-cyclic conducted grafo which allows for knowing port variable relationships - parents-children relationships-. Obtained network exhibits that economic variables are – in cause-effect terms- cause of rest of variable typologies. Economic variables represent parent role in the most of cases. Moreover, when environmental variables are known, obtained network allows for estimating subsequent probability of social variables. It has been concluded that Bayesian Networks allow for modeling uncertainty in a probabilistic way, even when number of variables is high as occurs in planning and management of port terminals.Molina Serrano, B.; González Cancelas, MN.; Soler Flores, F.; Camarero Orive, A. (2016). CLASSIFICATION AND PREDICTION OF PORT VARIABLES. En XII Congreso de ingeniería del transporte. 7, 8 y 9 de Junio, Valencia (España). Editorial Universitat Politècnica de València. 1437-1444. https://doi.org/10.4995/CIT2016.2015.3226OCS1437144

Non-parametric Bayesian modeling of complex networks

Modeling structure in complex networks using Bayesian non-parametrics makes it possible to specify flexible model structures and infer the adequate model complexity from the observed data. This paper provides a gentle introduction to non-parametric Bayesian modeling of complex networks: Using an infinite mixture model as running example we go through the steps of deriving the model as an infinite limit of a finite parametric model, inferring the model parameters by Markov chain Monte Carlo, and checking the model's fit and predictive performance. We explain how advanced non-parametric models for complex networks can be derived and point out relevant literature

A Bayesian semi-parametric approach for modeling memory decay in dynamic social networks

In relational event networks, the tendency for actors to interact with each other depends greatly on the past interactions between the actors in a social network. Both the volume of past interactions and the time that has elapsed since the past interactions affect the actors’ decision-making to interact with other actors in the network. Recently occurred events may have a stronger influence on current interaction behavior than past events that occurred a long time ago–a phenomenon known as “memory decay”. Previous studies either predefined a short-run and long-run memory or fixed a parametric exponential memory decay using a predefined half-life period. In real-life relational event networks, however, it is generally unknown how the influence of past events fades as time goes by. For this reason, it is not recommendable to fix memory decay in an ad-hoc manner, but instead we should learn the shape of memory decay from the observed data. In this paper, a novel semi-parametric approach based on Bayesian Model Averaging is proposed for learning the shape of the memory decay without requiring any parametric assumptions. The method is applied to relational event history data among socio-political actors in India and a comparison with other relational event models based on predefined memory decays is provided

A Model of Consistent Node Types in Signed Directed Social Networks

Signed directed social networks, in which the relationships between users can be either positive (indicating relations such as trust) or negative (indicating relations such as distrust), are increasingly common. Thus the interplay between positive and negative relationships in such networks has become an important research topic. Most recent investigations focus upon edge sign inference using structural balance theory or social status theory. Neither of these two theories, however, can explain an observed edge sign well when the two nodes connected by this edge do not share a common neighbor (e.g., common friend). In this paper we develop a novel approach to handle this situation by applying a new model for node types. Initially, we analyze the local node structure in a fully observed signed directed network, inferring underlying node types. The sign of an edge between two nodes must be consistent with their types; this explains edge signs well even when there are no common neighbors. We show, moreover, that our approach can be extended to incorporate directed triads, when they exist, just as in models based upon structural balance or social status theory. We compute Bayesian node types within empirical studies based upon partially observed Wikipedia, Slashdot, and Epinions networks in which the largest network (Epinions) has 119K nodes and 841K edges. Our approach yields better performance than state-of-the-art approaches for these three signed directed networks.Comment: To appear in the IEEE/ACM International Conference on Advances in Social Network Analysis and Mining (ASONAM), 201