Gaussian Process Modulated Cox Processes under Linear Inequality Constraints

Andrés F. Lopez-Lopera, ST John, Nicolas Durrande
Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, PMLR 89:1997-2006, 2019.

Abstract

Gaussian process (GP) modulated Cox processes are widely used to model point patterns. Existing approaches require a mapping (link function) between the unconstrained GP and the positive intensity function. This commonly yields solutions that do not have a closed form or that are restricted to specific covariance functions. We introduce a novel finite approximation of GP-modulated Cox processes where positiveness conditions can be imposed directly on the GP, with no restrictions on the covariance function. Our approach can also ensure other types of inequality constraints (e.g. monotonicity, convexity), resulting in more versatile models that can be used for other classes of point processes (e.g. renewal processes). We demonstrate on both synthetic and real-world data that our framework accurately infers the intensity functions. Where monotonicity is a feature of the process, our ability to include this in the inference improves results.

Cite this Paper

BibTeX
@InProceedings{pmlr-v89-lopez-lopera19a, title = {Gaussian Process Modulated Cox Processes under Linear Inequality Constraints}, author = {Lopez-Lopera, Andr\'es F. and John, ST and Durrande, Nicolas}, booktitle = {Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics}, pages = {1997--2006}, year = {2019}, editor = {Chaudhuri, Kamalika and Sugiyama, Masashi}, volume = {89}, series = {Proceedings of Machine Learning Research}, month = {16--18 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v89/lopez-lopera19a/lopez-lopera19a.pdf}, url = {https://proceedings.mlr.press/v89/lopez-lopera19a.html}, abstract = {Gaussian process (GP) modulated Cox processes are widely used to model point patterns. Existing approaches require a mapping (link function) between the unconstrained GP and the positive intensity function. This commonly yields solutions that do not have a closed form or that are restricted to specific covariance functions. We introduce a novel finite approximation of GP-modulated Cox processes where positiveness conditions can be imposed directly on the GP, with no restrictions on the covariance function. Our approach can also ensure other types of inequality constraints (e.g. monotonicity, convexity), resulting in more versatile models that can be used for other classes of point processes (e.g. renewal processes). We demonstrate on both synthetic and real-world data that our framework accurately infers the intensity functions. Where monotonicity is a feature of the process, our ability to include this in the inference improves results.} }
Endnote
%0 Conference Paper %T Gaussian Process Modulated Cox Processes under Linear Inequality Constraints %A Andrés F. Lopez-Lopera %A ST John %A Nicolas Durrande %B Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Masashi Sugiyama %F pmlr-v89-lopez-lopera19a %I PMLR %P 1997--2006 %U https://proceedings.mlr.press/v89/lopez-lopera19a.html %V 89 %X Gaussian process (GP) modulated Cox processes are widely used to model point patterns. Existing approaches require a mapping (link function) between the unconstrained GP and the positive intensity function. This commonly yields solutions that do not have a closed form or that are restricted to specific covariance functions. We introduce a novel finite approximation of GP-modulated Cox processes where positiveness conditions can be imposed directly on the GP, with no restrictions on the covariance function. Our approach can also ensure other types of inequality constraints (e.g. monotonicity, convexity), resulting in more versatile models that can be used for other classes of point processes (e.g. renewal processes). We demonstrate on both synthetic and real-world data that our framework accurately infers the intensity functions. Where monotonicity is a feature of the process, our ability to include this in the inference improves results.
APA
Lopez-Lopera, A.F., John, S. & Durrande, N.. (2019). Gaussian Process Modulated Cox Processes under Linear Inequality Constraints. Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 89:1997-2006 Available from https://proceedings.mlr.press/v89/lopez-lopera19a.html.

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