Sparse high-dimensional linear regression. Estimating squared error and a phase transition
稀疏高维线性回归：平方误差估计与相变
We consider a sparse high-dimensional regression model where the goal is to recover a k-sparse unknown binary vector β∗ from n noisy linear observations of the form Y=Xβ∗+W∈Rn where X∈Rn×p has i.i.d. N(0,1) entries and W∈Rn has i.i.d. N(0,σ2) entries. In the high signal-to-noise ratio regime and sublinear sparsity regime, while the order of the sample size needed to recover the unknown vector information-theoretically is known to be n∗:=2klogp/log(k/σ2+1), no polynomial-time…