稀疏估计的凸与非凸方法：GLasso，多核学习和超参数GLasso
Convex vs nonconvex approaches for sparse estimation: GLasso, Multiple Kernel Learning and Hyperparameter GLasso
摘要：
稀疏估计的流行Lasso方法可以通过与特定随机模型相关联的联合密度的边缘化来导出。相同概率模型的不同边缘化导致不同的非凸估计，其中超参数被优化。扩展这些参数的问题，其中组的变量估计，我们研究了稀疏估计的计算方案，不同于组套索。虽然基本的优化问题定义这个估计是非凸的，初始化策略的基础上，一个单变量贝叶斯前向选择方案。这也使我们能够定义一个有效的非凸估计，其中只有一个标量变量参与优化过程。理论参数，独立于进入稀疏模型的先验的正确性，包括澄清与其他凸估计相比，这种非凸技术的优点。数值实验也被用来比较这些方法的性能。
英文摘要：
The popular Lasso approach for sparse estimation can be derived via marginalization of a joint density associated with a particular stochastic model. A different marginalization of the same probabilistic model leads to a different non-convex estimator where hyperparameters are optimized. Extending these arguments to problems where groups of variables have to be estimated, we study a computational scheme for sparse estimation that differs from the Group Lasso. Although the underlying optimization problem defining this estimator is non-convex, an initialization strategy based on a univariate Bayesian forward selection scheme is presented. This also allows us to define an effective non-convex estimator where only one scalar variable is involved in the optimization process. Theoretical arguments, independent of the correctness of the priors entering the sparse model, are included to clarify the advantages of this non-convex technique in comparison with other convex estimators. Numerical experiments are also used to compare the performance of these approaches.
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