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.

翻译：本文考虑了状态空间设置下的L1正则化路径计算问题，涵盖L1正则化的卡尔曼平滑、线性支持向量机、LASSO等方法。论文提出了两种互为对偶的新算法：第一种算法适用于独立变量的L1正则化，第二种算法适用于相依变量的L1正则化。所提算法的核心是在相关因子图中进行参数化高斯消息传递（即卡尔曼式前向-后向递归）。本文方法具有广泛适用性，通常仅需矩阵乘法运算，且其复杂度在某些情况下可与现有方法相媲美。