Bayesian Structure Inference and Interaction Analysis

We investigate models and algorithms for Bayesian inference of time-varying dependencies (interactions) among multiple time-series from noisy observations. Analyzing such dependencies is important in many domains, such as social networks, finance, biology and object interaction analysis. We cast the problem of inference over dependence structures as the problem of learning the structure of a dynamic Bayesian network (DBN). This problem is inherently hard. Interactions are rarely observed directly and need to be inferred from noisy observations of objects’ properties. At the same time, the number of possible dependence structures is super-exponential in the number of time-series. To deal with uncertainty, we adopt a fully-Bayesian approach, in which our objective is to characterize a full posterior distribution over dependence structures. The probability of any structural event, such as “Is there an edge from A to B?”, can be easily computed from the full posterior. We use a modular prior and a bound on the number of parent sets per object to reduce the number of structures (at a single time point) from super-exponential to polynomial in the number of time-series.