Latent Point Process Allocation

Chris Lloyd, Tom Gunter, Michael Osborne, Stephen Roberts, Tom Nickson
Proceedings of the 19th International Conference on Artificial Intelligence and Statistics, PMLR 51:389-397, 2016.

Abstract

We introduce a probabilistic model for the factorisation of continuous Poisson process rate functions. Our model can be thought of as a topic model for Poisson point processes in which each point is assigned to one of a set of latent rate functions that are shared across multiple outputs. We show that the model brings a means of incorporating structure in point process inference beyond the state-of-the-art. We derive an efficient variational inference scheme for the model based on sparse Gaussian processes that scales linearly in the number of data points. Finally, we demonstrate, using examples from spatial and temporal statistics, how the model can be used for discovering hidden structure with greater precision than standard frequentist approaches.

Cite this Paper

BibTeX
@InProceedings{pmlr-v51-lloyd16, title = {Latent Point Process Allocation}, author = {Lloyd, Chris and Gunter, Tom and Osborne, Michael and Roberts, Stephen and Nickson, Tom}, booktitle = {Proceedings of the 19th International Conference on Artificial Intelligence and Statistics}, pages = {389--397}, year = {2016}, editor = {Gretton, Arthur and Robert, Christian C.}, volume = {51}, series = {Proceedings of Machine Learning Research}, address = {Cadiz, Spain}, month = {09--11 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v51/lloyd16.pdf}, url = {https://proceedings.mlr.press/v51/lloyd16.html}, abstract = {We introduce a probabilistic model for the factorisation of continuous Poisson process rate functions. Our model can be thought of as a topic model for Poisson point processes in which each point is assigned to one of a set of latent rate functions that are shared across multiple outputs. We show that the model brings a means of incorporating structure in point process inference beyond the state-of-the-art. We derive an efficient variational inference scheme for the model based on sparse Gaussian processes that scales linearly in the number of data points. Finally, we demonstrate, using examples from spatial and temporal statistics, how the model can be used for discovering hidden structure with greater precision than standard frequentist approaches.} }
Endnote
%0 Conference Paper %T Latent Point Process Allocation %A Chris Lloyd %A Tom Gunter %A Michael Osborne %A Stephen Roberts %A Tom Nickson %B Proceedings of the 19th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2016 %E Arthur Gretton %E Christian C. Robert %F pmlr-v51-lloyd16 %I PMLR %P 389--397 %U https://proceedings.mlr.press/v51/lloyd16.html %V 51 %X We introduce a probabilistic model for the factorisation of continuous Poisson process rate functions. Our model can be thought of as a topic model for Poisson point processes in which each point is assigned to one of a set of latent rate functions that are shared across multiple outputs. We show that the model brings a means of incorporating structure in point process inference beyond the state-of-the-art. We derive an efficient variational inference scheme for the model based on sparse Gaussian processes that scales linearly in the number of data points. Finally, we demonstrate, using examples from spatial and temporal statistics, how the model can be used for discovering hidden structure with greater precision than standard frequentist approaches.
RIS
TY - CPAPER TI - Latent Point Process Allocation AU - Chris Lloyd AU - Tom Gunter AU - Michael Osborne AU - Stephen Roberts AU - Tom Nickson BT - Proceedings of the 19th International Conference on Artificial Intelligence and Statistics DA - 2016/05/02 ED - Arthur Gretton ED - Christian C. Robert ID - pmlr-v51-lloyd16 PB - PMLR DP - Proceedings of Machine Learning Research VL - 51 SP - 389 EP - 397 L1 - http://proceedings.mlr.press/v51/lloyd16.pdf UR - https://proceedings.mlr.press/v51/lloyd16.html AB - We introduce a probabilistic model for the factorisation of continuous Poisson process rate functions. Our model can be thought of as a topic model for Poisson point processes in which each point is assigned to one of a set of latent rate functions that are shared across multiple outputs. We show that the model brings a means of incorporating structure in point process inference beyond the state-of-the-art. We derive an efficient variational inference scheme for the model based on sparse Gaussian processes that scales linearly in the number of data points. Finally, we demonstrate, using examples from spatial and temporal statistics, how the model can be used for discovering hidden structure with greater precision than standard frequentist approaches. ER -
APA
Lloyd, C., Gunter, T., Osborne, M., Roberts, S. & Nickson, T.. (2016). Latent Point Process Allocation. Proceedings of the 19th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 51:389-397 Available from https://proceedings.mlr.press/v51/lloyd16.html.

Related Material