提出两种新算法，高效计算线性模型的L1正则化路径。
L1 Regularization Paths in Linear Models by Parametric Gaussian Message Passing
- 基于参数化高斯消息传递的递归算法
- 仅需矩阵乘法，复杂度可优于已有方法
- 适用于卡尔曼平滑、LASSO等场景
本文研究在状态空间框架下计算L1正则化路径的问题，涵盖L1正则化卡尔曼平滑、线性SVM、LASSO等。提出两种互为对偶的新算法：第一种用于独立变量的L1正则化，第二种用于依赖变量的L1正则化。核心是相关因子图中的参数化高斯消息传递（即卡尔曼型前向-后向递推）。所提方法应用广泛，通常仅需矩阵乘法，其复杂度在某些情况下可与现有方法竞争。
原文摘要 · Abstract (English)
The paper considers the computation of L1 regularization paths in a state space setting, which includes L1 regularized Kalman smoothing, linear SVM, LASSO, and more. The paper proposes two new algorithms, which are duals of each other; the first algorithm applies to L1 regularization of independent variables while the second applies to L1 regularization of dependent variables. The heart of the proposed algorithms is parametric Gaussian message passing (i.e., Kalman-type forward-backward recursions) in the pertinent factor graphs. The proposed methods are broadly applicable, they (usually) require only matrix multiplications, and their complexity can be competitive with prior methods in some cases.
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