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

Statistical Inference with Ensemble of Clustered Desparsified Lasso