Statistical Inference with Ensemble of Clustered Desparsified Lasso

TL;DR

This paper introduces a scalable statistical inference method for high-dimensional imaging data, combining desparsified Lasso, feature clustering, and ensembling to improve confidence in model parameters.

Contribution

The paper presents a novel algorithm that scales to ultra-high-dimensional data by integrating clustering and ensembling with desparsified Lasso for reliable inference.

Findings

Ensemble of clustering and desparsified Lasso improves inference accuracy.

The method controls specificity in high-dimensional settings.

Demonstrated stability on neuroimaging datasets.

Abstract

Medical imaging involves high-dimensional data, yet their acquisition is obtained for limited samples. Multivariate predictive models have become popular in the last decades to fit some external variables from imaging data, and standard algorithms yield point estimates of the model parameters. It is however challenging to attribute confidence to these parameter estimates, which makes solutions hardly trustworthy. In this paper we present a new algorithm that assesses parameters statistical significance and that can scale even when the number of predictors p $\ge$ 10^5 is much higher than the number of samples n $\le$ 10^3 , by lever-aging structure among features. Our algorithm combines three main ingredients: a powerful inference procedure for linear models --the so-called Desparsified Lasso-- feature clustering and an ensembling step. We first establish that Desparsified Lasso alone cannot handle n p regimes; then we demonstrate that the combination of clustering and ensembling provides an accurate solution, whose specificity is controlled. We also demonstrate stability improvements on two neuroimaging datasets.