Gaussian Mean Testing under Truncation

Clement Louis Canonne, Themis Gouleakis, Yuhao Wang, Qiping Yang
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:4879-4887, 2025.

Abstract

We consider the task of Gaussian mean testing, that is, of testing whether a high-dimensional vector perturbed by white noise has large magnitude, or is the zero vector. This question, originating from the signal processing community, has recently seen a surge of interest from the machine learning and theoretical computer science community, and is by now fairly well understood. What is much less understood, and the focus of our work, is how to perform this task under \emph{truncation}: that is, when the observations (i.i.d. samples from the underlying high-dimensional Gaussian) are only observed when they fall in an given subset of the domain $\mathbb{R}^d$. This truncation model, previously studied in the context of \emph{learning} (instead of \emph{testing}) the mean vector, has a range of applications, in particular in Economics and Social Sciences. As our work shows, sample truncations affect the complexity of the testing task in a rather subtle and surprising way.

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-canonne25a, title = {Gaussian Mean Testing under Truncation}, author = {Canonne, Clement Louis and Gouleakis, Themis and Wang, Yuhao and Yang, Qiping}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {4879--4887}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/canonne25a/canonne25a.pdf}, url = {https://proceedings.mlr.press/v258/canonne25a.html}, abstract = {We consider the task of Gaussian mean testing, that is, of testing whether a high-dimensional vector perturbed by white noise has large magnitude, or is the zero vector. This question, originating from the signal processing community, has recently seen a surge of interest from the machine learning and theoretical computer science community, and is by now fairly well understood. What is much less understood, and the focus of our work, is how to perform this task under \emph{truncation}: that is, when the observations (i.i.d. samples from the underlying high-dimensional Gaussian) are only observed when they fall in an given subset of the domain $\mathbb{R}^d$. This truncation model, previously studied in the context of \emph{learning} (instead of \emph{testing}) the mean vector, has a range of applications, in particular in Economics and Social Sciences. As our work shows, sample truncations affect the complexity of the testing task in a rather subtle and surprising way.} }
Endnote
%0 Conference Paper %T Gaussian Mean Testing under Truncation %A Clement Louis Canonne %A Themis Gouleakis %A Yuhao Wang %A Qiping Yang %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-canonne25a %I PMLR %P 4879--4887 %U https://proceedings.mlr.press/v258/canonne25a.html %V 258 %X We consider the task of Gaussian mean testing, that is, of testing whether a high-dimensional vector perturbed by white noise has large magnitude, or is the zero vector. This question, originating from the signal processing community, has recently seen a surge of interest from the machine learning and theoretical computer science community, and is by now fairly well understood. What is much less understood, and the focus of our work, is how to perform this task under \emph{truncation}: that is, when the observations (i.i.d. samples from the underlying high-dimensional Gaussian) are only observed when they fall in an given subset of the domain $\mathbb{R}^d$. This truncation model, previously studied in the context of \emph{learning} (instead of \emph{testing}) the mean vector, has a range of applications, in particular in Economics and Social Sciences. As our work shows, sample truncations affect the complexity of the testing task in a rather subtle and surprising way.
APA
Canonne, C.L., Gouleakis, T., Wang, Y. & Yang, Q.. (2025). Gaussian Mean Testing under Truncation. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:4879-4887 Available from https://proceedings.mlr.press/v258/canonne25a.html.

Related Material