Markov Modulated Gaussian Cox Processes for Semi-Stationary Intensity Modeling of Events Data

Minyoung Kim
Proceedings of the 35th International Conference on Machine Learning, PMLR 80:2640-2648, 2018.

Abstract

The Cox process is a flexible event model that can account for uncertainty of the intensity function in the Poisson process. However, previous approaches make strong assumptions in terms of time stationarity, potentially failing to generalize when the data do not conform to the assumed stationarity conditions. In this paper we bring up two most popular Cox models representing two extremes, and propose a novel semi-stationary Cox process model that can take benefits from both models. Our model has a set of Gaussian process latent functions governed by a latent stationary Markov process where we provide analytic derivations for the variational inference. Empirical evaluations on several synthetic and real-world events data including the football shot attempts and daily earthquakes, demonstrate that the proposed model is promising, can yield improved generalization performance over existing approaches.

Cite this Paper


BibTeX
@InProceedings{pmlr-v80-kim18a, title = {{M}arkov Modulated {G}aussian {C}ox Processes for Semi-Stationary Intensity Modeling of Events Data}, author = {Kim, Minyoung}, booktitle = {Proceedings of the 35th International Conference on Machine Learning}, pages = {2640--2648}, year = {2018}, editor = {Dy, Jennifer and Krause, Andreas}, volume = {80}, series = {Proceedings of Machine Learning Research}, month = {10--15 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v80/kim18a/kim18a.pdf}, url = {https://proceedings.mlr.press/v80/kim18a.html}, abstract = {The Cox process is a flexible event model that can account for uncertainty of the intensity function in the Poisson process. However, previous approaches make strong assumptions in terms of time stationarity, potentially failing to generalize when the data do not conform to the assumed stationarity conditions. In this paper we bring up two most popular Cox models representing two extremes, and propose a novel semi-stationary Cox process model that can take benefits from both models. Our model has a set of Gaussian process latent functions governed by a latent stationary Markov process where we provide analytic derivations for the variational inference. Empirical evaluations on several synthetic and real-world events data including the football shot attempts and daily earthquakes, demonstrate that the proposed model is promising, can yield improved generalization performance over existing approaches.} }
Endnote
%0 Conference Paper %T Markov Modulated Gaussian Cox Processes for Semi-Stationary Intensity Modeling of Events Data %A Minyoung Kim %B Proceedings of the 35th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2018 %E Jennifer Dy %E Andreas Krause %F pmlr-v80-kim18a %I PMLR %P 2640--2648 %U https://proceedings.mlr.press/v80/kim18a.html %V 80 %X The Cox process is a flexible event model that can account for uncertainty of the intensity function in the Poisson process. However, previous approaches make strong assumptions in terms of time stationarity, potentially failing to generalize when the data do not conform to the assumed stationarity conditions. In this paper we bring up two most popular Cox models representing two extremes, and propose a novel semi-stationary Cox process model that can take benefits from both models. Our model has a set of Gaussian process latent functions governed by a latent stationary Markov process where we provide analytic derivations for the variational inference. Empirical evaluations on several synthetic and real-world events data including the football shot attempts and daily earthquakes, demonstrate that the proposed model is promising, can yield improved generalization performance over existing approaches.
APA
Kim, M.. (2018). Markov Modulated Gaussian Cox Processes for Semi-Stationary Intensity Modeling of Events Data. Proceedings of the 35th International Conference on Machine Learning, in Proceedings of Machine Learning Research 80:2640-2648 Available from https://proceedings.mlr.press/v80/kim18a.html.

Related Material