Implementation of Functional Tensor Regression

Data

ADHD data from http://fcon_1000.projects.nitrc.org/indi/adhd200/ was used for this work. The file "ADHD_prep.RData" was obtained after pre-processing by "real_prep.R".

Code

• "func.R": Build functions to implement the Riemannian Gauss--Newton algorithm for functional tensor regression (FTReg).
• "simu_begin.R": Generate the simulation setting.
• "simu_rho.R": Perform FTReg on simulated data under different tuning parameters, with coefficient rank and sample size fixed.
• "simu_r.R": Perform FTReg on simulated data under different coefficient ranks, with tuning parameter selected to be optimal and sample size fixed.
• "simu_sigma.R": Perform FTReg on simulated data under different signal-to-noise ratios, with coefficient rank and sample size fixed.
• "simu_n.R": Perform FTReg on simulated data under different sample sizes, with tuning parameter selected to be optimal and coefficient rank fixed.
• "simu_p.R": Perform FTReg on simulated data under different sampling frequencies, with coefficient rank and sample size fixed.
• "real.R": Perform FTReg on ADHD data, with coefficient rank and tuning parameter selected to be optimal.
• "simu_irr.R": Perform FTReg on simulated data generated on a non-uniform grid, similar to "simu_begin.R" + "simu_rho.R".

Workflow

First of all, make sure that "func.R" is in the working directory.

• Simulation: Run "simu_begin.R" and then any of "simu_rho.R", "simu_r.R", "simu_sigma.R", "simu_n.R" and "simu_p.R". Besides, run "simu_irr.R".
• Real data example: Make sure that "ADHD_prep.RData" is in the working directory. Run "real.R".