标题： 一种通过邻近优化进行结构化稀疏性的通用框架 显示英文标题

标题： A General Framework for Structured Sparsity via Proximal Optimization

摘要： 我们研究了一个结构化稀疏性的广义框架。 它通过将额外的变量约束纳入凸优化问题中，扩展了众所周知的Lasso和组Lasso方法。 该框架提供了一种直接的方法来偏好预定的稀疏模式，如排序、连续区域和重叠组等。 现有的优化方法仅限于特定的约束集，并且在样本量和维度上难以扩展。 我们提出了一种新颖的一阶邻近方法，该方法建立在固定点和连续逼近的结果之上。 该算法可以应用于一般的锥形和范数约束集，并依赖于一个可以显式计算的邻近算子子问题。 在不同回归问题上的实验表明了优化算法的效率及其与问题规模的可扩展性。 它们还展示了最先进的统计性能，优于Lasso和StructOMP。 显示英文摘要

摘要： We study a generalized framework for structured sparsity. It extends the well-known methods of Lasso and Group Lasso by incorporating additional constraints on the variables as part of a convex optimization problem. This framework provides a straightforward way of favouring prescribed sparsity patterns, such as orderings, contiguous regions and overlapping groups, among others. Existing optimization methods are limited to specific constraint sets and tend to not scale well with sample size and dimensionality. We propose a novel first order proximal method, which builds upon results on fixed points and successive approximations. The algorithm can be applied to a general class of conic and norm constraints sets and relies on a proximity operator subproblem which can be computed explicitly. Experiments on different regression problems demonstrate the efficiency of the optimization algorithm and its scalability with the size of the problem. They also demonstrate state of the art statistical performance, which improves over Lasso and StructOMP.