Damian Brzyski

Title:
Using machine learning techniques in discovering response-related communities in the brain/

Abstract: 
Classical regression methods treat covariates as a vector and estimate a corresponding vector of regression coefficients. In medical applications, however, regressors in a form of multidimensional arrays can be often met. For example, one may be interested in identifying regions of the brain associated with an outcome of interest based on MRI images. Turning such image array into a vector is an unsatisfactory solution, since it destroys the inherent spatial structure of the image and could be very challenging from the computational point of view. In my talk, I will present an alternative approach - the regularized matrix regression - where the matrix of regression coefficients is defined as a solution to the specific optimization problem. The method, called Sparsity Inducing Nuclear Norm Estimator (SpINNEr), simultaneously imposes two types of penalties on the matrix -- the nuclear and the LASSO-type norm -- to encourage the low rank of the solution and its entry-wise sparsity. Our software allows for the automatic selection of the weights defining the optimal trade-off between two considered types of penalties and the alternating direction method of multipliers (ADMM) was used to build the fast and efficient numerical solver. SPINNER has been applied to investigate associations between brain's structural connections and HIV disease-related outcomes. Our approach outperforms others methods in the estimation accuracy in the considered situation -- when the response-related entries (representing brain's connections) are arranged in well-connected communities.