Abstract
In brain imaging, decoding is widely used to infer relationships between brain and cognition, or to craft brain-imaging biomarkers of pathologies. Yet, standard decoding procedures do not come with statistical guarantees, and thus do not give confidence bounds to interpret the pattern maps that they produce. Indeed, in whole-brain decoding settings, the number of explanatory variables is much greater than the number of samples, hence classical statistical inference methodology cannot be applied. Specifically, the standard practice that consists in thresholding decoding maps is not a correct inference procedure. We contribute a new statistical-testing framework for this type of inference. To overcome the statistical inefficiency of voxel-level control, we generalize the Family Wise Error Rate (FWER) to account for a spatial tolerance δ, introducing the δ-Family Wise Error Rate (δ-FWER). Then, we present a decoding procedure that can control the δ-FWER: the Ensemble of Clustered Desparsified Lasso (EnCluDL), a procedure for multivariate statistical inference on high-dimensional structured data. We evaluate the statistical properties of EnCluDL with a thorough empirical study, along with three alternative procedures including decoder map thresholding. We show that EnCluDL exhibits the best recovery properties while ensuring the expected statistical control.
Highlights
Predicting behavior or diseases status from brain images is an important analytical approach for imaging neurosciences, as it provides an effective evaluation of the infor[32] mation carried by brain images
Decoding models are fundamental for causal interpretation of the implication of brain regions for an outcome of interest, mental process or disease status [Weichwald et al, 2015]
Et al, 2018], and as a result comes with theoretical statistical guarantees: it controls the δ-Family Wise Error Rate (FWER) for a predetermined tolerance parameter δ equal to the largest diameter of the clusters, assuming that the observed samples are i.i.d. and that the weight maps are homogeneous and sparse
Summary
Predicting behavior or diseases status from brain images is an important analytical approach for imaging neurosciences, as it provides an effective evaluation of the infor[32] mation carried by brain images. Another method proposed by Gaonkar and Davatzikos [2012], designed for neuroimaging settings, relies on the analytic approxima[180] tion of a permutation test performed over a linear SVM/SVR estimator. The recently proposed Ensemble of Clustered Desparsified Lasso (EnCluDL) [Chevalier et al, 2018] combines three steps: a clustering procedure that reduces the problem dimension but preserves data structure, the Desparsified Lasso procedure that is tractable on the compressed problem, and an ensembling method intro[230] duced by Meinshausen et al [2009] that aggregates several solutions of the compressed problem We defer the extension of EnCluDL to FDR-controlling procedures and the benchmarking with alternatives to future work
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