Statistical Agnostic Mapping: A framework in neuroimaging based on concentration inequalities
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AuthorGorriz Sáez, Juan Manuel; Jiménez Mesa, Carmen; Segovia, Fermín; Castillo Barnes, Diego; Martínez Murcia, Francisco J.; Salas-González, Diego; Illan, Ignacio A.; García Puntonet, Carlos; López García, David
Hypothesis testsUpper boundsActual and empirical risksFinite class lemmaRademacher averagesCross-validation
Gorriz, J. M., Jimenez-Mesa, C., Romero-Garcia, R., Segovia, F., Ramirez, J., Castillo-Barnes, D., ... & Suckling, J. (2021). Statistical Agnostic Mapping: A framework in neuroimaging based on concentration inequalities. Information Fusion, 66, 198-212. [doi: 10.1016/j.inffus.2020.09.008]
SponsorshipMINECO/ FEDER, Spain RTI2018-098913-B100 CV20-45250 A-TIC-080-UGR18; Ministerio de Universidades, Spain under the FPU Predoctoral Grant FPU 18/04902; United States Department of Health & Human Services National Institutes of Health (NIH) - USA U01 AG024904; DOD ADNI, Spain (Department of Defense) W81-XWH-12-2-0012; United States Department of Health & Human Services National Institutes of Health (NIH) - USA NIH National Institute on Aging (NIA); United States Department of Health & Human Services National Institutes of Health (NIH) - USA NIH National Institute of Biomedical Imaging & Bioengineering (NIBIB); AbbVie; Alzheimer's Association; Alzheimer's Drug Discovery Foundation; Araclon Biotech; BioClinica, Inc.; Biogen; Bristol-Myers Squibb; CereSpir, Inc.; Cogstate; Eisai Co Ltd; Elan Pharmaceuticals, Inc.; Eli Lilly; EuroImmun; F. Hoffmann-La Roche Ltd and its affiliated company Genentech, Inc.; Fujirebio; GE Healthcare; IXICO Ltd.; Janssen Alzheimer Immunotherapy Research & Development, LLC.; Johnson & Johnson USA; Lumosity; Lundbeck Corporation; Merck & Company; Meso Scale Diagnostics, LLC.; NeuroRx Research; Neurotrack Technologies; Novartis; Pfizer; Piramal Imaging; Servier; Takeda Pharmaceutical Company Ltd; Transition Therapeutics; Canadian Institutes of Health Research (CIHR)
In the 1970s a novel branch of statistics emerged focusing its effort on the selection of a function for the pattern recognition problem that would fulfill a relationship between the quality of the approximation and its complexity. This theory is mainly devoted to problems of estimating dependencies in the case of limited sample sizes, and comprise all the empirical out-of sample generalization approaches; e.g. cross validation (CV). In this paper a data-driven approach based on concentration inequalities is designed for testing competing hypothesis or comparing different models. In this sense we derive a Statistical Agnostic (non-parametric) Mapping (SAM) for neuroimages at voxel or regional levels which is able to: (i) relieve the problem of instability with limited sample sizes when estimating the actual risk via CV; and (ii) provide an alternative way of Family-wise-error (FWE) corrected p-value maps in inferential statistics for hypothesis testing. Using several neuroimaging datasets (containing large and small effects) and random task group analyses to compute empirical familywise error rates, this novel framework resulted in a model validation method for small samples over dimension ratios, and a less-conservative procedure than FWE..-value correction to determine the significance maps from the inferences made using small upper bounds of the actual risk.