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Variational Inference for Gaussian Process Modulated Poisson Processes

arXiv 1411.0254 ↗First posted 2 Nov 2014stat.MLcited by 25

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Abstract (arXiv)

We present the first fully variational Bayesian inference scheme for continuous Gaussian-process-modulated Poisson processes. Such point processes are used in a variety of domains, including neuroscience, geo-statistics and astronomy, but their use is hindered by the computational cost of existing inference schemes. Our scheme: requires no discretisation of the domain; scales linearly in the number of observed events; and is many orders of magnitude faster than previous sampling based approaches. The resulting algorithm is shown to outperform standard methods on synthetic examples, coal mining disaster data and in the prediction of Malaria incidences in Kenya.

Key facts. Cited by 25 papers in the map (data through 7 Oct 2026). First posted on arXiv 2 Nov 2014.

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Citing papers per year: 2021: 4; 2022: 2; 2023: 3; 2024: 8; 2025: 6; 2026: 2.

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  1. 2021Reducing the Amortization Gap in Variational Autoencoders: A Bayesian Random Function Approachcited by 6
  2. 2021Deep Neyman-Scott Processescited by 6
  3. 2024Exact, Fast and Expressive Poisson Point Processes via Squared Neural Familiescited by 6
  4. 2022Nonparametric Embeddings of Sparse High-Order Interaction Eventscited by 5
  5. 2024Bayesian Optimization through Gaussian Cox Process Models for Spatio-temporal Datacited by 5
  6. 2023Heterogeneous Multi-Task Gaussian Cox Processescited by 4
  7. 2023Inference and Sampling of Point Processes from Diffusion Excursionscited by 3
  8. 2022Causal Modeling of Policy Interventions From Sequences of Treatments and Outcomescited by 2
  9. 2024Nonstationary Sparse Spectral Permanental Processcited by 2
  10. 2024Nonparametric estimation of Hawkes processes with RKHSscited by 2
  11. 2025Advances in Temporal Point Processes: Bayesian, Neural, and LLM Approachescited by 2
  12. 2025New Bounds for Sparse Variational Gaussian Processescited by 2
13 more
  1. 2021Nonlinear Hawkes Process with Gaussian Process Self Effectscited by 1
  2. 2023Temporal Causal Mediation through a Point Process: Direct and Indirect Effects of Healthcare Interventionscited by 1
  3. 2024Latent variable model for high-dimensional point process with structured missingnesscited by 1
  4. 2025Squared families: Searching beyond regular probability modelscited by 1
  5. 2025STACI: Spatio-Temporal Aleatoric Conformal Inferencecited by 1
  6. 2021Survival Analysis of the Compressor Station Based on Hawkes Process with Weibull Base Intensitycited by 0
  7. 2024Modelling financial volume curves with hierarchical Poisson processescited by 0
  8. 2024Exact Bayesian Gaussian Cox Processes Using Random Integralcited by 0
  9. 2024Unsupervised Event Outlier Detection in Continuous Timecited by 0
  10. 2025K2IE: Kernel Method-based Kernel Intensity Estimators for Inhomogeneous Poisson Processescited by 0
  11. 2025A Semiparametric Discrete Hawkes Model with a Collapsed Gaussian-Process Priorcited by 0
  12. 2026Kronecker-Structured Nonparametric Spatiotemporal Point Processescited by 0
  13. 2026Arbitrarily Conditioned Hierarchical Flows for Spatiotemporal Eventscited by 0