Minimax estimation in multi-task regression under low-rank structures

This study investigates the minimaxity of a multi-task nonparametric regression problem. We formulate simultaneous function estimation problem based on information pooling across multiple experiments under low-dimensional structure. A reduced rank estimator nuclear norm penalisation scheme is proposed to incorporate structure in process. set functions defined terms their Fourier coefficients formally characterise dependence among functions. Minimax upper and lower bounds are established various asymptotic scenarios examine role low-rank determining optimal rates convergence. The results confirm that exploiting can significantly improve convergence rate for also imply minimax sense rank-constraint Sobolev class vector-valued