标题： 基于学习的模型稀疏性通过投影梯度下降法 显示英文标题

标题： Learning Model-Based Sparsity via Projected Gradient Descent

摘要： 之前已经提出了几种用于结构化稀疏先验的统计估计的凸公式方法。 这些方法通常需要仔细调整正则化参数，这往往是一项繁琐或启发式的任务。 此外，这些方法产生的估计可能不属于所需的稀疏模型，尽管能够准确地近似真实参数。 因此，在估计结构化稀疏参数时，贪心型算法常常更为可取。 到目前为止，这些贪心方法大多集中在线性统计模型上。 本文研究了具有非凸结构化稀疏参数模型作为约束集的投影梯度下降法。 如果代价函数具有稳定的模型受限Hessian，则该算法可以产生所需最小值的近似值。 作为一个例子，我们详细阐述了主要结果在广义线性模型中的应用。 显示英文摘要

摘要： Several convex formulation methods have been proposed previously for statistical estimation with structured sparsity as the prior. These methods often require a carefully tuned regularization parameter, often a cumbersome or heuristic exercise. Furthermore, the estimate that these methods produce might not belong to the desired sparsity model, albeit accurately approximating the true parameter. Therefore, greedy-type algorithms could often be more desirable in estimating structured-sparse parameters. So far, these greedy methods have mostly focused on linear statistical models. In this paper we study the projected gradient descent with non-convex structured-sparse parameter model as the constraint set. Should the cost function have a Stable Model-Restricted Hessian the algorithm produces an approximation for the desired minimizer. As an example we elaborate on application of the main results to estimation in Generalized Linear Model.