A Unified Dynamic Approach to Sparse Model Selection
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Proceedings of the TwentyFirst International Conference on Artificial Intelligence and Statistics, PMLR 84:20472055, 2018.
Abstract
Sparse model selection is ubiquitous from linear regression to graphical models where regularization paths, as a family of estimators upon the regularization parameter varying, are computed when the regularization parameter is unknown or decided dataadaptively. Traditional computational methods rely on solving a set of optimization problems where the regularization parameters are fixed on a grid that might be inefficient. In this paper, we introduce a simple iterative regularization path, which follows the dynamics of a sparse Mirror Descent algorithm or a generalization of Linearized Bregman Iterations with nonlinear loss. Its performance is competitive to glmnet with a further bias reduction. A path consistency theory is presented that under the Restricted Strong Convexity and the Irrepresentable Condition, the path will first evolve in a subspace with no false positives and reach an estimator that is signconsistent or of minimax optimal $\ell_2$ error rate. Early stopping regularization is required to prevent overfitting. Application examples are given in sparse logistic regression and Ising models for NIPS coauthorship.
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