L1 Regularization Paths in Linear Models by Parametric Gaussian Message Passing
Provides a unified message-passing framework for L1 regularization in state space models, but the practical advantage over existing methods is not clearly demonstrated with concrete performance numbers.
The paper proposes two new algorithms for computing L1 regularization paths in state space models (including LASSO, SVM, Kalman smoothing) using parametric Gaussian message passing, achieving competitive complexity with prior methods in some cases.
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.