Inferring serial correlation with dynamic backgrounds

Song Wei, Yao Xie, Dobromir Rahnev
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:11047-11057, 2021.

Abstract

Sequential data with serial correlation and an unknown, unstructured, and dynamic background is ubiquitous in neuroscience, psychology, and econometrics. Inferring serial correlation for such data is a fundamental challenge in statistics. We propose a Total Variation (TV) constrained least square estimator coupled with hypothesis tests to infer the serial correlation in the presence of unknown and unstructured dynamic background. The TV constraint on the dynamic background encourages a piecewise constant structure, which can approximate a wide range of dynamic backgrounds. The tuning parameter is selected via the Ljung-Box test to control the bias-variance trade-off. We establish a non-asymptotic upper bound for the estimation error through variational inequalities. We also derive a lower error bound via Fano’s method and show the proposed method is near-optimal. Numerical simulation and a real study in psychology demonstrate the excellent performance of our proposed method compared with the state-of-the-art.

Cite this Paper

BibTeX
@InProceedings{pmlr-v139-wei21b, title = {Inferring serial correlation with dynamic backgrounds}, author = {Wei, Song and Xie, Yao and Rahnev, Dobromir}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {11047--11057}, year = {2021}, editor = {Meila, Marina and Zhang, Tong}, volume = {139}, series = {Proceedings of Machine Learning Research}, month = {18--24 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v139/wei21b/wei21b.pdf}, url = {https://proceedings.mlr.press/v139/wei21b.html}, abstract = {Sequential data with serial correlation and an unknown, unstructured, and dynamic background is ubiquitous in neuroscience, psychology, and econometrics. Inferring serial correlation for such data is a fundamental challenge in statistics. We propose a Total Variation (TV) constrained least square estimator coupled with hypothesis tests to infer the serial correlation in the presence of unknown and unstructured dynamic background. The TV constraint on the dynamic background encourages a piecewise constant structure, which can approximate a wide range of dynamic backgrounds. The tuning parameter is selected via the Ljung-Box test to control the bias-variance trade-off. We establish a non-asymptotic upper bound for the estimation error through variational inequalities. We also derive a lower error bound via Fano’s method and show the proposed method is near-optimal. Numerical simulation and a real study in psychology demonstrate the excellent performance of our proposed method compared with the state-of-the-art.} }
Endnote
%0 Conference Paper %T Inferring serial correlation with dynamic backgrounds %A Song Wei %A Yao Xie %A Dobromir Rahnev %B Proceedings of the 38th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Marina Meila %E Tong Zhang %F pmlr-v139-wei21b %I PMLR %P 11047--11057 %U https://proceedings.mlr.press/v139/wei21b.html %V 139 %X Sequential data with serial correlation and an unknown, unstructured, and dynamic background is ubiquitous in neuroscience, psychology, and econometrics. Inferring serial correlation for such data is a fundamental challenge in statistics. We propose a Total Variation (TV) constrained least square estimator coupled with hypothesis tests to infer the serial correlation in the presence of unknown and unstructured dynamic background. The TV constraint on the dynamic background encourages a piecewise constant structure, which can approximate a wide range of dynamic backgrounds. The tuning parameter is selected via the Ljung-Box test to control the bias-variance trade-off. We establish a non-asymptotic upper bound for the estimation error through variational inequalities. We also derive a lower error bound via Fano’s method and show the proposed method is near-optimal. Numerical simulation and a real study in psychology demonstrate the excellent performance of our proposed method compared with the state-of-the-art.
APA
Wei, S., Xie, Y. & Rahnev, D.. (2021). Inferring serial correlation with dynamic backgrounds. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:11047-11057 Available from https://proceedings.mlr.press/v139/wei21b.html.

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