稀疏估计广义自由度的估计
Evaluation of Generalized Degrees of Freedom for Sparse Estimation by Replica Method
摘要：
我们开发了一种方法来评估广义自由度（GDF），这是一个模型选择标准的关键量，线性回归稀疏正则化。使用副本方法，GDF表示的变量，表征鞍点的自由能，而不依赖于形式的正则化。在副本对称（RS）分析的框架内，GDF提供了一个物理意义的非零组件的有效密度。我们的方法在RS阶段的有效性支持我们的结果与以前的数学结果的一致性。在RS阶段的分析结果的数值实现的信念传播算法。
英文摘要：
We develop a method to evaluate the generalized degrees of freedom (GDF), which is a key quantity of a model selection criterion, for linear regression with sparse regularization. Using the replica method, GDF is expressed by the variables that characterize the saddle point of the free energy without depending on the form of the regularization. Within the framework of replica symmetric (RS) analysis, GDF is provided with a physical meaning as the effective density of non-zero components. The validity of our method in the RS phase is supported by the consistency of our results with previous mathematical results. The analytical results in the RS phase are numerically achieved by the belief propagation algorithm.
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