Generalized High-Dimensional Trace Regression via Nuclear Norm Regularization
核范数正则化的广义高维迹回归
We study the generalized trace regression with a near low-rank regression coefficient matrix, which extends notion of sparsity for regression coefficient vectors. Specifically, given a matrix covariate $X$, the probability density function $f(Y\vert X)=c(Y)\exp{(φ^{-1}\left[-Yη^* + b(η^*)\right])}$, where $η^*=tr({Θ^*}^TX)$. This model accommodates various types of responses and embraces many important problem setups such as reduced-rank regression, matrix regression that…