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

Zhen Qin, Christian Shelton
Proceedings of the 31st Conference on Uncertainty in Artificial Intelligence, PMLR R13:860-869, 2015.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR13-qin15a, title = {Auxiliary {G}ibbs Sampling for Inference in Piecewise-Constant Conditional Intensity Models}, author = {Qin, Zhen and Shelton, Christian}, booktitle = {Proceedings of the 31st Conference on Uncertainty in Artificial Intelligence}, pages = {860--869}, year = {2015}, editor = {Meila, Marina and Heskes, Tom}, volume = {R13}, series = {Proceedings of Machine Learning Research}, month = {12--16 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r13/main/assets/qin15a/qin15a.pdf}, url = {https://proceedings.mlr.press/r13/qin15a.html}, abstract = {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.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Auxiliary Gibbs Sampling for Inference in Piecewise-Constant Conditional Intensity Models %A Zhen Qin %A Christian Shelton %B Proceedings of the 31st Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2015 %E Marina Meila %E Tom Heskes %F pmlr-vR13-qin15a %I PMLR %P 860--869 %U https://proceedings.mlr.press/r13/qin15a.html %V R13 %X 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. %Z Reissued by PMLR on 04 October 2026.
APA
Qin, Z. & Shelton, C.. (2015). Auxiliary Gibbs Sampling for Inference in Piecewise-Constant Conditional Intensity Models. Proceedings of the 31st Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R13:860-869 Available from https://proceedings.mlr.press/r13/qin15a.html. Reissued by PMLR on 04 October 2026.

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