Scalable Nonparametric Bayesian Inference on Point Processes with Gaussian Processes
This addresses computational bottlenecks in point process modeling for researchers and practitioners, though it appears incremental as it builds on existing Gaussian Process methods.
The paper tackles the problem of inefficient Bayesian inference for Poisson Point Processes by proposing a non-parametric model using Gaussian Processes with linear complexity and memory requirements, achieving faster and more accurate results than competing models on synthetic and real-life data.
In this paper we propose the first non-parametric Bayesian model using Gaussian Processes to make inference on Poisson Point Processes without resorting to gridding the domain or to introducing latent thinning points. Unlike competing models that scale cubically and have a squared memory requirement in the number of data points, our model has a linear complexity and memory requirement. We propose an MCMC sampler and show that our model is faster, more accurate and generates less correlated samples than competing models on both synthetic and real-life data. Finally, we show that our model easily handles data sizes not considered thus far by alternate approaches.