Tensor Quantile Regression for Neuroimage Study of Human Intelligence
Susan Dwight Bliss Professor of Biostatistics, Yale University School of Public Health
Date: Friday, October 15, 2021
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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. Meanwhile, magnetic resonance imaging provides an unparalleled opportunity to study brain structures and cognitive ability. 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 piece-wise 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 alternating direction method of multipliers algorithm 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 find that the tensor quantile regression can serve as a prognostic tool to assess future risk of cognitive impairment progression. More importantly, with the proposed method, 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 quantile of fluid intelligence. The insular cortex associated with median of fluid intelligence is a rarely reported region.
This is a joint work with Cai Li, currently a postdoctoral associate at Department of Biostatistics, Yale University School of Public Health.
About the speaker
Dr. Zhang published over 340 research articles and monographs in theory and applications of statistical methods and in several areas of biomedical research including epidemiology, genetics, child and women health, mental health, substance use, and reproductive medicine. He directed a training program in mental health research that was funded by the NIMH. He directs the Collaborative Center for Statistics in Science that coordinates the Reproductive Medicine Network to evaluate treatment effectiveness for infertility. He is a fellow of the American Statistical Association and a fellow of the Institute of Mathematical Statistics. He was named the 2008 Myrto Lefokopoulou distinguished lecturer by Harvard School of Public Health and a Medallion Lecturer by the Institute of Mathematical Statistics. In 2011, he received the Royan International Award on Reproductive Health. Dr. Zhang was the president of the International Chinese Statistical Association in 2019. He serves as the editor of the Journal of the American Statistical Association - Applications and Case Studies. He was selected to deliver 2022 Neyman lecture by the Institute of Mathematical Statistics.