Auxiliary Gibbs Sampling for Inference in Piecewise-Constant Conditional Intensity Models

A piecewise-constant conditional intensity model (PCIM) is a non-Markovian model of temporal stochastic dependencies in continuous-time event streams. It allows efficient learning and forecasting given complete trajectories. However, no general inference algorithm has been developed for PCIMs. We propose an effective and efficient auxiliary Gibbs sampler for inference in PCIM, based on the idea of thinning for inhomogeneous Poisson processes. The sampler alternates between sampling a finite set of auxiliary virtual events with adaptive rates, and performing an efficient forward-backward pass at discrete times to generate samples. We show that our sampler can successfully perform inference tasks in both Markovian and non-Markovian models, and can be employed in Expectation-Maximization PCIM parameter estimation and structural learning with partially observed data.