Multi-output Gaussian Process Modulated Poisson Processes for Event Prediction

Prediction of events such as part replacement and failure events plays a critical role in reliability engineering. Event stream data are commonly observed in manufacturing and teleservice systems. Designing predictive models for individual units based on such event streams is challenging and an under-explored problem. In this work, we propose a non-parametric prognostic framework for individualized event prediction based on the inhomogeneous Poisson processes with a multivariate Gaussian convolution process (MGCP) prior on the intensity functions. The MGCP prior on the intensity functions of the inhomogeneous Poisson processes maps data from similar historical units to the current unit under study which facilitates sharing of information and allows for analysis of flexible event patterns. To facilitate inference, we derive a variational inference scheme for learning and estimation of parameters in the resulting MGCP modulated Poisson process model. Experimental results are shown on both synthetic data as well as real-world data for fleet based event prediction.