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

Structure and Dynamics of Information Pathways in Online Media

Diffusion of information, spread of rumors and infectious diseases are all instances of stochastic processes that occur over the edges of an underlying network. Many times networks over which contagions spread are unobserved, and such networks are often dynamic and change over time. In this paper, we investigate the problem of inferring dynamic networks based on information diffusion data. We assume there is an unobserved dynamic network that changes over time, while we observe the results of a dynamic process spreading over the edges of the network. The task then is to infer the edges and the dynamics of the underlying network. We develop an on-line algorithm that relies on stochastic convex optimization to efficiently solve the dynamic network inference problem. We apply our algorithm to information diffusion among 3.3 million mainstream media and blog sites and experiment with more than 179 million different pieces of information spreading over the network in a one year period. We study the evolution of information pathways in the online media space and find interesting insights. Information pathways for general recurrent topics are more stable across time than for on-going news events. Clusters of news media sites and blogs often emerge and vanish in matter of days for on-going news events. Major social movements and events involving civil population, such as the Libyan's civil war or Syria's uprise, lead to an increased amount of information pathways among blogs as well as in the overall increase in the network centrality of blogs and social media sites.Comment: To Appear at the 6th International Conference on Web Search and Data Mining (WSDM '13

Numeric Input Relations for Relational Learning with Applications to Community Structure Analysis

Most work in the area of statistical relational learning (SRL) is focussed on discrete data, even though a few approaches for hybrid SRL models have been proposed that combine numerical and discrete variables. In this paper we distinguish numerical random variables for which a probability distribution is defined by the model from numerical input variables that are only used for conditioning the distribution of discrete response variables. We show how numerical input relations can very easily be used in the Relational Bayesian Network framework, and that existing inference and learning methods need only minor adjustments to be applied in this generalized setting. The resulting framework provides natural relational extensions of classical probabilistic models for categorical data. We demonstrate the usefulness of RBN models with numeric input relations by several examples. In particular, we use the augmented RBN framework to define probabilistic models for multi-relational (social) networks in which the probability of a link between two nodes depends on numeric latent feature vectors associated with the nodes. A generic learning procedure can be used to obtain a maximum-likelihood fit of model parameters and latent feature values for a variety of models that can be expressed in the high-level RBN representation. Specifically, we propose a model that allows us to interpret learned latent feature values as community centrality degrees by which we can identify nodes that are central for one community, that are hubs between communities, or that are isolated nodes. In a multi-relational setting, the model also provides a characterization of how different relations are associated with each community

Modeling Information Propagation with Survival Theory

Networks provide a skeleton for the spread of contagions, like, information, ideas, behaviors and diseases. Many times networks over which contagions diffuse are unobserved and need to be inferred. Here we apply survival theory to develop general additive and multiplicative risk models under which the network inference problems can be solved efficiently by exploiting their convexity. Our additive risk model generalizes several existing network inference models. We show all these models are particular cases of our more general model. Our multiplicative model allows for modeling scenarios in which a node can either increase or decrease the risk of activation of another node, in contrast with previous approaches, which consider only positive risk increments. We evaluate the performance of our network inference algorithms on large synthetic and real cascade datasets, and show that our models are able to predict the length and duration of cascades in real data.Comment: To appear at ICML '1

Estimating spillovers using imprecisely measured networks

In many experimental contexts, whether and how network interactions impact the outcome of interest for both treated and untreated individuals are key concerns. Networks data is often assumed to perfectly represent these possible interactions. This paper considers the problem of estimating treatment effects when measured connections are, instead, a noisy representation of the true spillover pathways. We show that existing methods, using the potential outcomes framework, yield biased estimators in the presence of this mismeasurement. We develop a new method, using a class of mixture models, that can account for missing connections and discuss its estimation via the Expectation-Maximization algorithm. We check our method's performance by simulating experiments on real network data from 43 villages in India. Finally, we use data from a previously published study to show that estimates using our method are more robust to the choice of network measure

Topics in social network analysis and network science

This chapter introduces statistical methods used in the analysis of social networks and in the rapidly evolving parallel-field of network science. Although several instances of social network analysis in health services research have appeared recently, the majority involve only the most basic methods and thus scratch the surface of what might be accomplished. Cutting-edge methods using relevant examples and illustrations in health services research are provided