Efficient Inference in Multi-task Cox Process Models

Virginia Aglietti, Theodoros Damoulas, Edwin V. Bonilla
Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, PMLR 89:537-546, 2019.

Abstract

We generalize the log Gaussian Cox process (LGCP) framework to model multiple correlated point data jointly. The observations are treated as realizations of multiple LGCPs, whose log intensities are given by linear combinations of latent functions drawn from Gaussian process priors. The combination coefficients are also drawn from Gaussian processes and can incorporate additional dependencies. We derive closed-form expressions for the moments of the intensity functions and develop an efficient variational inference algorithm that is orders of magnitude faster than competing deterministic and stochastic approximations of multivariate LGCPs, coregionalization models, and multi-task permanental processes. Our approach outperforms these benchmarks in multiple problems, offering the current state of the art in modeling multivariate point processes.

Cite this Paper

BibTeX
@InProceedings{pmlr-v89-aglietti19a, title = {Efficient Inference in Multi-task Cox Process Models}, author = {Aglietti, Virginia and Damoulas, Theodoros and Bonilla, Edwin V.}, booktitle = {Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics}, pages = {537--546}, 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/aglietti19a/aglietti19a.pdf}, url = {https://proceedings.mlr.press/v89/aglietti19a.html}, abstract = {We generalize the log Gaussian Cox process (LGCP) framework to model multiple correlated point data jointly. The observations are treated as realizations of multiple LGCPs, whose log intensities are given by linear combinations of latent functions drawn from Gaussian process priors. The combination coefficients are also drawn from Gaussian processes and can incorporate additional dependencies. We derive closed-form expressions for the moments of the intensity functions and develop an efficient variational inference algorithm that is orders of magnitude faster than competing deterministic and stochastic approximations of multivariate LGCPs, coregionalization models, and multi-task permanental processes. Our approach outperforms these benchmarks in multiple problems, offering the current state of the art in modeling multivariate point processes.} }
Endnote
%0 Conference Paper %T Efficient Inference in Multi-task Cox Process Models %A Virginia Aglietti %A Theodoros Damoulas %A Edwin V. Bonilla %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-aglietti19a %I PMLR %P 537--546 %U https://proceedings.mlr.press/v89/aglietti19a.html %V 89 %X We generalize the log Gaussian Cox process (LGCP) framework to model multiple correlated point data jointly. The observations are treated as realizations of multiple LGCPs, whose log intensities are given by linear combinations of latent functions drawn from Gaussian process priors. The combination coefficients are also drawn from Gaussian processes and can incorporate additional dependencies. We derive closed-form expressions for the moments of the intensity functions and develop an efficient variational inference algorithm that is orders of magnitude faster than competing deterministic and stochastic approximations of multivariate LGCPs, coregionalization models, and multi-task permanental processes. Our approach outperforms these benchmarks in multiple problems, offering the current state of the art in modeling multivariate point processes.
APA
Aglietti, V., Damoulas, T. & Bonilla, E.V.. (2019). Efficient Inference in Multi-task Cox Process Models. Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 89:537-546 Available from https://proceedings.mlr.press/v89/aglietti19a.html.

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