A Stein–Papangelou Goodness-of-Fit Test for Point Processes
Jiasen Yang, Vinayak Rao, Jennifer Neville
Abstract
Point processes provide a powerful framework for modeling the distribution and interactions of events in time or space. Their flexibility has given rise to a variety of sophisticated models in statistics and machine learning, yet model diagnostic and criticism techniques remain underdeveloped. In this work, we propose a general Stein operator for point processes based on the Papangelou conditional intensity function. We then establish a kernel goodness-of-fit test by defining a Stein discrepancy measure for general point processes. Notably, our test also applies to non-Poisson point processes whose intensity functions contain intractable normalization constants due to the presence of complex interactions among points. We apply our proposed test to several point process models, and show that it outperforms a two-sample test based on the maximum mean discrepancy.
BibTeX
@InProceedings{pmlr-v89-yang19a,
title = {A Stein–Papangelou Goodness-of-Fit Test for Point Processes},
author = {Yang, Jiasen and Rao, Vinayak and Neville, Jennifer},
booktitle = {Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics},
pages = {226--235},
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/yang19a/yang19a.pdf},
url = {https://proceedings.mlr.press/v89/yang19a.html},
abstract = {Point processes provide a powerful framework for modeling the distribution and interactions of events in time or space. Their flexibility has given rise to a variety of sophisticated models in statistics and machine learning, yet model diagnostic and criticism techniques remain underdeveloped. In this work, we propose a general Stein operator for point processes based on the Papangelou conditional intensity function. We then establish a kernel goodness-of-fit test by defining a Stein discrepancy measure for general point processes. Notably, our test also applies to non-Poisson point processes whose intensity functions contain intractable normalization constants due to the presence of complex interactions among points. We apply our proposed test to several point process models, and show that it outperforms a two-sample test based on the maximum mean discrepancy.}
}