Non-parametric learning to infer wireless relays, routes and traffic patterns from time series of spectrum activity

Non-parametric inference techniques are proposed to understand latent structure behind sequences of spectral activity indicators, i.e. packet start and stop times, of networked wireless transmitters. We aim to infer the latent network structure and characterize information flow between spectrally monitored nodes. The practical aspect of learning is to aid the reasoning of a cognitive network about its unknown and dynamic spectrum environment. We first segment the observed on-off time series into temporal segments of statistically discernible behavioral states. Each state segment has distinct emission statistics and a specific duration, learned by using a Bayesian non-parametric method, referred to as HDP-HSMM [1] in our prior work [2]. The end result is that new times series of state segments are derived from the observations of each nodes activity. We propose test statistics, loosely related to Granger-causality between per-node sequences of state segments, to trace the impact of one nodes traffic to another. We define extendable statistical models of causality in which not only state changes are considered as events, but also the nature of those changes, i.e. whether the new state has similar observation statistics in both nodes. Our approach is non-parametric as it does not require knowledge about underlying network protocols.