A note on the minimax risk of sparse linear regression

Understand

Sparse linear regression is one of the classical and extensively studied problems in high-dimensional statistics and compressed sensing.

• Despite the substantial body of literature dedicated to this problem, the precise determination of its minimax risk remains elusive.
• This paper aims to fill this gap by deriving asymptotically constant-sharp characterization for the minimax risk of sparse linear regression.
• More specifically, the paper focuses on scenarios where the sparsity level, denoted as k, satisfies the condition $(k \log p)/n {\to} 0$, with p and n representing the number of features and observations respectively.