Spatially relaxed inference on high-dimensional linear models

We consider the inference problem for high-dimensional linear models, when covariates have an underlying spatial organization reflected in their correlation. A typical example of such a setting is high-resolution imaging, in which neighboring pixels are usually very similar. Accurate point and confidence intervals estimation is not possible in this context with many more covariates than samples, furthermore with high correlation between covariates. This calls for a reformulation of the statistical inference problem, that takes into account the underlying spatial structure: if covariates are locally correlated, it is acceptable to detect them up to a given spatial uncertainty. We thus propose to rely on the δ-FWER, that is the probability of making a false discovery at a distance greater than δ from any true positive. With this target measure in mind, we study the properties of ensembled clustered inference algorithms which combine three techniques: spatially constrained clustering, statistical inference, and ensembling to aggregate several clustered inference solutions. We show that ensembled clustered inference algorithms control the δ-FWER under standard assumptions for δ equal to the largest cluster diameter. We complement the theoretical analysis with empirical results, demonstrating accurate δ-FWER control and decent power achieved by such inference algorithms.

READ FULL TEXT

page 11

page 15

research
07/14/2023

Sparsified Simultaneous Confidence Intervals for High-Dimensional Linear Models

Statistical inference of the high-dimensional regression coefficients is...
research
01/29/2020

Adaptive Estimation and Statistical Inference for High-Dimensional Graph-Based Linear Models

We consider adaptive estimation and statistical inference for high-dimen...
research
05/28/2023

Statistical Inference in High-Dimensional Generalized Linear Models with Asymmetric Link Functions

We have developed a statistical inference method applicable to a broad r...
research
06/15/2018

Statistical Inference with Ensemble of Clustered Desparsified Lasso

Medical imaging involves high-dimensional data, yet their acquisition is...
research
01/18/2022

Statistical Inference on Explained Variation in High-dimensional Linear Model with Dense Effects

Statistical inference on the explained variation of an outcome by a set ...
research
09/29/2020

Statistical control for spatio-temporal MEG/EEG source imaging with desparsified multi-task Lasso

Detecting where and when brain regions activate in a cognitive task or i...
research
03/12/2019

ECKO: Ensemble of Clustered Knockoffs for multivariate inference on fMRI data

Continuous improvement in medical imaging techniques allows the acquisit...

Please sign up or login with your details

Forgot password? Click here to reset