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Title: Tensor quantile regression with application to association between neuroimages and human intelligence Authors:  Cai Li - St. Jude Children's Research Hospital (United States) [presenting]
Heping Zhang - Yale University (United States)
Abstract: Human intelligence is usually measured by well-established psychometric tests through a series of problem-solving. The recorded cognitive scores are continuous but usually heavy-tailed with potential outliers and violating the normality assumption. Motivated by association studies between MRI images and human intelligence, we propose a tensor quantile regression model, which is a general and robust alternative to the commonly used scalar-on-image linear regression. Moreover, we take into account rich spatial information of brain structures, incorporating low-rankness and piecewise smoothness of imaging coefficients into a regularized regression framework. We formulate the optimization problem as a sequence of penalized quantile regressions with a generalized Lasso penalty, based on tensor decomposition, and develop a computationally efficient algorithm to estimate the model components. Extensive numerical studies are conducted to examine the empirical performance of the proposed method and its competitors. Finally, we apply the proposed method to a large-scale important dataset, the Human Connectome Project. We are able to identify the most activated brain subregions associated with quantiles of human intelligence. The prefrontal and anterior cingulate cortex are found to be mostly associated with lower and upper quantiles of fluid intelligence. The insular cortex associated with the median of fluid intelligence is a rarely reported region.