Sequential Inference Methods for Non-Homogeneous Poisson Processes with State-Space Prior

Abstract

The non-homogeneous Poisson process provides a generalised framework for the modelling of random point data by allowing the intensity of point generation to vary across its domain of interest (time or space). The use of non-homogeneous Poisson processes have arisen in many areas of signal processing and machine learning, but application is still largely limited by its intractable likelihood function and the lack of computationally efficient inference schemes, although some methods do exist for the batch data case. In this paper, we propose for the first time a sequential framework for intensity inference which combines the non-homogeneous model of Poisson data with continuoustime state-space models for their time-varying intensity. This approach enables us to design efficient online inference schemes, for which we propose a novel sequential Markov chain Monte Carlo (SMCMC) algorithm, as is demanded by many applications where point data arrive sequentially and decisions need to be made with low latency. The proposed approach is compared with competing methods on synthetic datasets and tested with highfrequency financial order book data, showing in general improved performance and better computational efficiency than the main batch-based competitor algorithm, and better performance than a simple baseline kernel estimation scheme.

Variational Parameter Learning in Sequential State-Space Model Via Particle Filtering

“…The state-space model (SSM) provides a powerful probabilistic modelling framework for real-world dynamical systems and timeseries data. Originated from control engineering [1], the SSM has been developed extensive over the past few decades with its applications in various areas and disciplines including system control [2], object tracking [3], image processing, [4], economics [5], finance [6,7] and neuroscience [8]. The dynamics-controlling parameters of the SSM are crucial in determining the diffusion behaviours of the stochastic process and the learning of these parameters not only provides a better model fit and more accurate predictions but also allows useful insights of the system to be extracted from the learned parameters.…”