Many relational domains contain temporal information and dynamics that are important to model (e.g., social networks, protein networks). However, past work in relational learning has focused primarily on modeling static “snapshots” of the data and has largely ignored the temporal dimension of these data. In this work, we extend relational techniques to temporally-evolving domains and outline a representational framework that is capable of modeling both temporal and relational dependencies in the data. We develop efficient learning and inference techniques within the framework by considering a restricted set of temporalrelational dependencies and using parameter-tying methods to generalize across relationships and entities. More specifically, we model dynamic relational data with a twophase process, first summarizing the temporal-relational information with kernel smoothing, and then moderating attribute dependencies with the summarized relational information. We develop a number of novel temporal-relational models using the framework and then show that the current approaches to modeling static relational data are special cases within the framework. We compare the new models to the competing static relational methods on three real-world datasets and show that the temporal-relational models consistently outperform the relational models that ignore temporal information—achieving significant reductions in error ranging from 15 % to 70%. 1

Relational autocorrelation is ubiquitous in relational domains. This observed correlation between class labels of linked instances in a network (e.g., two friends are more likely to share political beliefs than two randomly selected people) can be due to the effects of two different social processes. If social influence effects are present, instances are likely to change their attributes to conform to their neighbor values. If homophily effects are present, instances are likely to link to other individuals with similar attribute values. Both these effects will result in autocorrelated attribute values. When analyzing static relational networks it is impossible to determine how much of the observed correlation is due each of these factors. However, the recent surge of interest in social networks has increased the availability of dynamic network data. In this paper, we present a randomization technique for temporal network data where the attributes and links change over time. Given data from two time steps, we measure the gain in correlation and assess whether a significant portion of this gain is due to influence and/or homophily. We demonstrate the efficacy of our method on semi-synthetic data and then apply the method to a real-world social networks dataset, showing the impact of both influence and homophily effects.

The current methods used to mine and analyze temporal social network data make two assumptions: all edges have the same strength, and all parameters are time-homogeneous. We show that those assumptions may not hold for social networks and propose an alternative model with two novel aspects: (1) the modeling of edges as multi-valued variables that can change in intensity, and (2) the use of a curved exponential family framework to capture time-inhomogeneous properties while retaining a parsimonious and interpretable model. We show that our model outperforms traditional models on two real-world social network data sets.

Abstract. Exposure and adoption of opinions in social networks are important questions in education, business, and government. We describe a novel application of pervasive computing based on using mobile phone sensors to measure and model the face-to-face interactions and subsequent opinion changes amongst undergraduates, during the 2008 US presidential election campaign. We find that self-reported political discussants have characteristic interaction patterns and can be predicted from sensor data. Mobile features can be used to estimate unique individual exposure to different opinions, and help discover surprising patterns of dynamic homophily related to external political events, such as election debates and election day. To our knowledge, this is the first time such dynamic homophily effects have been measured. Automatically estimated exposure explains individual opinions on election day. Finally, we report statistically significant differences in the daily activities of individuals that change political opinions versus those that do not, by modeling and discovering dominant activities using topic models. We find people who decrease their interest in politics are routinely exposed (face-to-face) to friends with little or no interest in politics. 1

Directed graphical models such as Bayesian networks are a favored formalism for modeling the dependency structures in complex multivariate systems such as those encountered in biology and neural science. When a system is undergoing dynamic transformation, temporally rewiring networks are needed for capturing the dynamic causal influences between covariates. In this paper, we propose time-varying dynamic Bayesian networks (TV-DBN) for modeling the structurally varying directed dependency structures underlying non-stationary biological/neural time series. This is a challenging problem due the non-stationarity and sample scarcity of time series data. We present a kernel reweighted ℓ1-regularized auto-regressive procedure for this problem which enjoys nice properties such as computational efficiency and provable asymptotic consistency. To our knowledge, this is the first practical and statistically sound method for structure learning of TV-DBNs. We applied TV-DBNs to time series measurements during yeast cell cycle and brain response to visual stimuli. In both cases, TV-DBNs reveal interesting dynamics underlying the respective biological systems. 1

A principled mechanism for identifying conditional dependencies in time-series data is provided through structure learning of dynamic Bayesian networks (DBNs). An important assumption of DBN structure learning is that the data are generated by a stationary process—an assumption that is not true in many important settings. In this paper, we introduce a new class of graphical models called non-stationary dynamic Bayesian networks, in which the conditional dependence structure of the underlying data-generation process is permitted to change over time. Non-stationary dynamic Bayesian networks represent a new framework for studying problems in which the structure of a network is evolving over time. We define the non-stationary DBN model, present an MCMC sampling algorithm for learning the structure of the model from time-series data under different assumptions, and demonstrate the effectiveness of the algorithm on both simulated and biological data. 1

Classical dynamic Bayesian networks (DBNs) are based on the homogeneous Markov assumption and cannot deal with heterogeneity and non-stationarity in temporal processes. Various approaches to relax the homogeneity assumption have recently been proposed. The present paper aims to improve the shortcomings of three recent versions of heterogeneous DBNs along the following lines: (i) avoiding the need for data discretization, (ii) increasing the flexibility over a time-invariant network structure, (iii) avoiding over-flexibility and overfitting by introducing a regularization scheme based in inter-time segment information sharing. The improved method is evaluated on synthetic data and compared with alternative published methods on gene expression time series from Drosophila melanogaster. 1.

In many problems arising in biology, social sciences and various other fields, it is often necessary to analyze populations of entities such as molecules or individuals that are interconnected by a set of relationships. Studying networks of these kinds can reveal a wide range of information. While there is a rich literature on modeling static networks, much less has been done towards modeling dynamically evolving networks. Recently, [1] proposed the hidden, temporal Exponential Random Graph (htERGM) as a framework for modeling hidden, temporarily evolving networks. In the htERGM, the network structure at each time step t, At, is modeled as a hidden variable that evolves according to a Markovian dynamics, and at each epoch t, a set of data points {Xt} are emitted. Putting

In this paper, we present a novel probabilistic framework for recovering global, latent social network structure from local, noisy observations. We extend curved exponential random graph models to include two types of variables: hidden variables that capture the structure of the network and observational variables that capture the behavior between actors in the network. We develop a novel combination of informative and intuitive conversational (local) and structural (global) features to specify our model. The model learns, in an unsupervised manner, the relationship between observable behavior and hidden social structure while simultaneously learning properties of the latent structure itself. We present empirical results on both synthetic data and a real world dataset of face-to-face conversations collected from 24 individuals using wearable sensors over the course of 6 months.

equally contributing authors Due to the dynamic nature of biological systems, biological networks underlying temporal process such as the development of Drosophila melanogaster can exhibit significant topological changes to facilitate dynamic regulatory functions. Thus it is essential to develop methodologies that capture the temporal evolution of networks, which make it possible to study the driving forces underlying dynamic rewiring of gene regulation circuity, and to predict future network structures. Using a new machine learning method called Tesla, which builds on a novel temporal logistic regression technique, we report the first successful genome-wide reverseengineering of the latent sequence of temporally rewiring gene networks over more than 4000 genes during the life cycle of Drosophila melanogaster, given longitudinal gene expression measurements and even when a single snapshot of such measurement resulted from each (timespecific) network is available. Our methods offer the first glimpse of time-specific snapshots and temporal evolution patterns of gene networks in a living organism during its full developmental course. The recovered networks with this unprecedented resolution chart the onset and