论文标题
随机聚集的最小二乘以支持恢复
Randomly Aggregated Least Squares for Support Recovery
论文作者
论文摘要
我们研究了确切支持恢复的问题：给定（未知的）矢量$θ\ in \ weft \ { - 1,0,1 \ right \}^d $，我们可以访问噪声的测量$$ y =xθ+ω，$xθ+ω，$ x \ in $ x \ where $ x \ in \ mathbbbb {r}^n \ time n \ time n is soing s a noise a noise a so（ \ mathbb {r}^n $是（未知）高斯向量。我们可以选择$ n $有多小，并且仍然可靠地恢复了$θ$的支持？我们提出RAWLS（随机汇总的未加权最小二乘支持恢复）：主要思想是采用$ n $方程的随机子集，对减少的信息进行最小二乘恢复，然后在许多随机子集中平均。我们表明，所提出的过程可以证明可以恢复$θ$的近似值，并通过数值示例证明其在支持恢复中的使用。
We study the problem of exact support recovery: given an (unknown) vector $θ\in \left\{-1,0,1\right\}^D$, we are given access to the noisy measurement $$ y = Xθ+ ω,$$ where $X \in \mathbb{R}^{N \times D}$ is a (known) Gaussian matrix and the noise $ω\in \mathbb{R}^N$ is an (unknown) Gaussian vector. How small we can choose $N$ and still reliably recover the support of $θ$? We present RAWLS (Randomly Aggregated UnWeighted Least Squares Support Recovery): the main idea is to take random subsets of the $N$ equations, perform a least squares recovery over this reduced bit of information and then average over many random subsets. We show that the proposed procedure can provably recover an approximation of $θ$ and demonstrate its use in support recovery through numerical examples.
