Using Social Dynamics to Make Individual Predictions: Variational Inference with Stochastic Kinetic Model
Social dynamics is concerned with the interactions of individuals and the resulting group behaviors. It models the temporal evolution of social systems via the interactions of the individuals within these systems. The availability of large-scale data in social networks and sensor networks offers an unprecedented opportunity to predict state changing events at the individual level. Examples of such events are disease infection, rumor propagation and opinion transition in elections, etc. Unlike previous research focusing on the collective effects of social systems, we want to make efficient inferences on the individual level. Two main challenges are addressed: temporal modeling and computational complexity. The interaction pattern for each individual keeps changing over the time, i.e., an individual interacts with different individuals at different times. Second, as the number of tracked individual increases, the computational complexity grows exponentially with traditional sequential data analysis. The contributions are: (i) leverage social networks and sensor networks data to make tractable inferences on both individual behaviors and collective effects in social dynamics. (ii) use the stochastic kinetic model to summarize dynamic interactions among individuals and simplify the state transition probabilities. (iii) propose an efficient variational inference algorithm whose complexity grows linearly with the number of tracked individuals M . Given the state space K of a single individual and the total number of time steps T , the complexity of naive brute-force approach is O(K MT ) and the complexity of existing exact inference approach is O(K M T) . In comparison, the complexity of the proposed algorithm is O(K 2 MT) . In practice, it requires several iterations to converge. In the empirical study concerning epidemics dynamics, given wireless sensor network data collected from more than ten thousand people (M = 13,888) over three years (T = 3465), we use the proposed algorithm to track disease transmission, and predict the probability of infection for each individual (K = 2) along the time until convergence (I=5). It is more efficient than state of the art sampling methods, i.e., MCMC and particle filter, while achieving high accuracy.