A closed-form proximal operator for jointly updating coefficients and their adaptive Lasso penalties enables debiased variable selection with arbitrary sparsity structure in nonlinear models.
Convex Relaxation for Combinatorial Penalties
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abstract
In this paper, we propose an unifying view of several recently proposed structured sparsity-inducing norms. We consider the situation of a model simultaneously (a) penalized by a set- function de ned on the support of the unknown parameter vector which represents prior knowledge on supports, and (b) regularized in Lp-norm. We show that the natural combinatorial optimization problems obtained may be relaxed into convex optimization problems and introduce a notion, the lower combinatorial envelope of a set-function, that characterizes the tightness of our relaxations. We moreover establish links with norms based on latent representations including the latent group Lasso and block-coding, and with norms obtained from submodular functions.
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Proximal Iteration for Nonlinear Adaptive Lasso
A closed-form proximal operator for jointly updating coefficients and their adaptive Lasso penalties enables debiased variable selection with arbitrary sparsity structure in nonlinear models.