Scalable Nonparametric Bayesian Inference on Point Processes with Gaussian Processes

Abstract

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.

To appear at the International Conference on Machine Learning (ICML), 2015

References in corpus (1)

• Elliptical slice sampling

Cited by in corpus (11)

• Learning Granger Causality for Hawkes Processes
• MCMC for Variationally Sparse Gaussian Processes
• Efficient Bayesian Inference for a Gaussian Process Density Model
• Efficient EM-Variational Inference for Hawkes Process
• Efficient Bayesian Inference of Sigmoidal Gaussian Cox Processes
• Efficient Non-parametric Bayesian Hawkes Processes
• Scalable Inference for Nonparametric Hawkes Process Using Pólya-Gamma Augmentation
• Better Approximate Inference for Partial Likelihood Models with a Latent Structure
• Deep Neyman-Scott Processes
• Bayesian Heatmaps: Probabilistic Classification with Multiple Unreliable Information Sources
• String and Membrane Gaussian Processes