Goodness-of-Fit Test for Mismatched Self-Exciting Processes

Song Wei, Shixiang Zhu, Minghe Zhang, Yao Xie
Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:1243-1251, 2021.

Abstract

Recently there have been many research efforts in developing generative models for self-exciting point processes, partly due to their broad applicability for real-world applications. However, rarely can we quantify how well the generative model captures the nature or ground-truth since it is usually unknown. The challenge typically lies in the fact that the generative models typically provide, at most, good approximations to the ground-truth (e.g., through the rich representative power of neural networks), but they cannot be precisely the ground-truth. We thus cannot use the classic goodness-of-fit (GOF) test framework to evaluate their performance. In this paper, we develop a GOF test for generative models of self-exciting processes by making a new connection to this problem with the classical statistical theory of Quasi-maximum-likelihood estimator (QMLE). We present a non-parametric self-normalizing statistic for the GOF test: the Generalized Score (GS) statistics, and explicitly capture the model misspecification when establishing the asymptotic distribution of the GS statistic. Numerical simulation and real-data experiments validate our theory and demonstrate the proposed GS test’s good performance.

Cite this Paper

BibTeX
@InProceedings{pmlr-v130-wei21a, title = { Goodness-of-Fit Test for Mismatched Self-Exciting Processes }, author = {Wei, Song and Zhu, Shixiang and Zhang, Minghe and Xie, Yao}, booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics}, pages = {1243--1251}, year = {2021}, editor = {Banerjee, Arindam and Fukumizu, Kenji}, volume = {130}, series = {Proceedings of Machine Learning Research}, month = {13--15 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v130/wei21a/wei21a.pdf}, url = {https://proceedings.mlr.press/v130/wei21a.html}, abstract = { Recently there have been many research efforts in developing generative models for self-exciting point processes, partly due to their broad applicability for real-world applications. However, rarely can we quantify how well the generative model captures the nature or ground-truth since it is usually unknown. The challenge typically lies in the fact that the generative models typically provide, at most, good approximations to the ground-truth (e.g., through the rich representative power of neural networks), but they cannot be precisely the ground-truth. We thus cannot use the classic goodness-of-fit (GOF) test framework to evaluate their performance. In this paper, we develop a GOF test for generative models of self-exciting processes by making a new connection to this problem with the classical statistical theory of Quasi-maximum-likelihood estimator (QMLE). We present a non-parametric self-normalizing statistic for the GOF test: the Generalized Score (GS) statistics, and explicitly capture the model misspecification when establishing the asymptotic distribution of the GS statistic. Numerical simulation and real-data experiments validate our theory and demonstrate the proposed GS test’s good performance. } }
Endnote
%0 Conference Paper %T Goodness-of-Fit Test for Mismatched Self-Exciting Processes %A Song Wei %A Shixiang Zhu %A Minghe Zhang %A Yao Xie %B Proceedings of The 24th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2021 %E Arindam Banerjee %E Kenji Fukumizu %F pmlr-v130-wei21a %I PMLR %P 1243--1251 %U https://proceedings.mlr.press/v130/wei21a.html %V 130 %X Recently there have been many research efforts in developing generative models for self-exciting point processes, partly due to their broad applicability for real-world applications. However, rarely can we quantify how well the generative model captures the nature or ground-truth since it is usually unknown. The challenge typically lies in the fact that the generative models typically provide, at most, good approximations to the ground-truth (e.g., through the rich representative power of neural networks), but they cannot be precisely the ground-truth. We thus cannot use the classic goodness-of-fit (GOF) test framework to evaluate their performance. In this paper, we develop a GOF test for generative models of self-exciting processes by making a new connection to this problem with the classical statistical theory of Quasi-maximum-likelihood estimator (QMLE). We present a non-parametric self-normalizing statistic for the GOF test: the Generalized Score (GS) statistics, and explicitly capture the model misspecification when establishing the asymptotic distribution of the GS statistic. Numerical simulation and real-data experiments validate our theory and demonstrate the proposed GS test’s good performance.
APA
Wei, S., Zhu, S., Zhang, M. & Xie, Y.. (2021). Goodness-of-Fit Test for Mismatched Self-Exciting Processes . Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 130:1243-1251 Available from https://proceedings.mlr.press/v130/wei21a.html.

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