Forecasting Robust Gaussian Process State Space Models for Assessing Intervention Impact in Internet of Things Time Series

This article describes a robust Gaussian Prior process state space modeling (GPSSM) approach to assess the impact of an intervention in a time series. Numerous applications can benefit from this approach. Examples include: (1) time series could be the stock price of a company and the intervention could be the acquisition of another company; (2) the time series under concern could be the noise coming out of an engine, and the intervention could be a corrective step taken to reduce the noise; (3) the time series could be the number of visits to a web service, and the intervention is changes done to the user interface; and so on. The approach we describe in this article applies to any times series and intervention combination. It is well known that Gaussian process (GP) prior models provide flexibility by placing a non-parametric prior on the functional form of the model. While GPSSMs enable us to model a time series in a state space framework by placing a Gaussian Process (GP) prior over the state transition function, probabilistic recurrent state space models (PRSSM) employ variational approximations for handling complicated posterior distributions in GPSSMs. The robust PRSSMs (R-PRSSMs) discussed in this article assume a scale mixture of normal distributions instead of the usually proposed normal distribution. This assumption will accommodate heavy-tailed behavior or anomalous observations in the time series. On any exogenous intervention, we use R-PRSSM for Bayesian fitting and forecasting of the IoT time series. By comparing forecasts with the future internal temperature observations, we can assess with a high level of confidence the impact of an intervention. The techniques presented in this paper are very generic and apply to any time series and intervention combination. To illustrate our techniques clearly, we employ a concrete example. The time series of interest will be an Internet of Things (IoT) stream of internal temperatures measured by an insurance firm to address the risk of pipe-freeze hazard in a building. We treat the pipe-freeze hazard alert as an exogenous intervention. A comparison of forecasts and the future observed temperatures will be utilized to assess whether an alerted customer took preventive action to prevent pipe-freeze loss.