General performance metrics for the LASSO
General performance metrics for the LASSO
复制标题
LASSO 的一般性能指标
DOI：
--
复制
发表时间：
2016
期刊：
影响因子：
--
通讯作者：
B. Hassibi
中科院分区：
文献类型：
--
作者：
Ehsan Abbasi;Christos Thrampoulidis;B. Hassibi
最新的工作已经确定了从噪声线性（和可能的压缩）观察值中恢复结构化信号（例如稀疏，低阶）时，对非平滑凸优化方法的平均平方错误（MSE）性能进行了准确的预测。具体来说，在最近的论文中[15]，我们使用基于高斯工艺方法的框架仔细地表征了一般的正规M估计器的MSE性能。分析一类Lipschitz性能指标的框架（除了标准MSE之外，还包括ℓ1重建误差，成功识别元素是否属于稀疏信号的支持的概率，对于具体性，我们主要集中于ℓ1的最小二乘（又称套索）下的稀疏恢复问题。数值模拟和讨论其精确性在最佳调整重建方法的参数方面的重要性。
A recent line of work has established accurate predictions of the mean squared-error (MSE) performance of non-smooth convex optimization methods when used to recover structured signals (e.g. sparse, low-rank) from noisy linear (and possibly compressed) observations. Specifically, in a recent paper [15] we precisely characterized the MSE performance of a general class of regularized M-estimators using a framework that is based on Gaussian process methods. Here, we extend the framework to the analysis of a general class of Lipschitz performance metrics, which in addition to the standard MSE, includes the ℓ1-reconstruction error, the probability of successfully identifying whether an element belongs to the support of a sparse signal, the empirical distribution of the error, etc. For concreteness, we primarily focus on the problem of sparse recovery under ℓ1-regularized least-squares (aka LASSO). We illustrate the validity of the theoretical predictions through numerical simulations and discuss the importance of their precise nature in optimally tuning the involved parameters of the reconstruction method.