Using Copula distributions to support more accurate imaging-based diagnostic classifiers for neuropsychiatric disorders

Abstract

Many investigators have tried to apply machine learning techniques to magnetic resonance images (MRIs) of the brain in order to diagnose neuropsychiatric disorders. Usually the number of brain imaging measures (such as measures of cortical thickness and measures of local surface morphology) derived from the MRIs (i.e., their dimensionality) has been large (e.g. >10) relative to the number of participants who provide the MRI data (<100). Sparse data in a high dimensional space increases the variability of the classification rules that machine learning algorithms generate, thereby limiting the validity, reproducibility, and generalizability of those classifiers. The accuracy and stability of the classifiers can improve significantly if the multivariate distributions of the imaging measures can be estimated accurately. To accurately estimate the multivariate distributions using sparse data, we propose to estimate first the univariate distributions of imaging data and then combine them using a Copula to generate more accurate estimates of their multivariate distributions. We then sample the estimated Copula distributions to generate dense sets of imaging measures and use those measures to train classifiers. We hypothesize that the dense sets of brain imaging measures will generate classifiers that are stable to variations in brain imaging measures, thereby improving the reproducibility, validity, and generalizability of diagnostic classification algorithms in imaging datasets from clinical populations. In our experiments, we used both computer-generated and real-world brain imaging datasets to assess the accuracy of multivariate Copula distributions in estimating the corresponding multivariate distributions of real-world imaging data. Our experiments showed that diagnostic classifiers generated using imaging measures sampled from the Copula were significantly more accurate and more reproducible than were the classifiers generated using either the real-world imaging measures or their multivariate Gaussian distributions. Thus, our findings demonstrate that estimated multivariate Copula distributions can generate dense sets of brain imaging measures that can in turn be used to train classifiers, and those classifiers are significantly more accurate and more reproducible than are those generated using real-world imaging measures alone.

Voronoi Decomposition of Cardiovascular Dependency Structures in Different Ambient Conditions: An Entropy Study

“…The copula has been intensively used for the analysis and prediction of financial time series and the prediction of insurance risk [ 36 , 37 , 38 , 39 ], in hydrology and climate analysis [ 40 , 41 , 42 ] and communications [ 43 ]. Medical applications include aortic regurgitation study [ 44 ] and diagnostic classifiers for neuropsychiatric disorders [ 45 ]. A possibility to use a bivariate copula to analyze the cardiovascular dependency structures was introduced in [ 46 ] and pharmacologically validated by blocking the feedback paths using Scopolamine, Atenolol, Prazosin, and Hexamethonium.…”

Dependency Structures in Differentially Coded Cardiovascular Time Series

“…Its release in [37] initiated an extensive implementation within the various fields, but the applications in biomedical studies are rare, including imaging-based diagnostic classifiers for neuropsychiatric disorders [38], the aortic regurgitation [39], and a drug sensitivity prediction [40]. The possibility of applying a copula for cardiovascular signals is pointed out in [41], while its pharmacological validation is performed in [31].…”

Biomarkers in Child Mental Health: a bio-psycho-social perspective is needed

“…Similarly, others work on learning (vector) machine approaches and feature reduction techniques in neuroimaging to generate clinical useful biomarkers [ 16 , 17 ] or try to find “more accurate imaging-based classifiers for neuropsychiatric disorders” which e.g. may identify “neural pathways with aberrant morphological features associated with Tourette Syndrome in children and adults” [ 18 , 19 ]. Also, the validity of the RDoC domains during child development (as well as DSM/ICD psychopathological clusters/profiles) need further investigations in order to better verify on which basis the biomarker in question is grounded and tested.…”