Countless signal processing applications include the reconstruction of signals from few indirect linear measurements. The design of effective measurement operators is typically constrained by the underlying hardware and physics, posing a challenging and often even discrete optimization task. While the potential of gradient-based learning via the unrolling of iterative recovery algorithms has been demonstrated, it has remained unclear how to leverage this technique when the set of admissible measurement operators is structured and discrete. We tackle this problem by combining unrolled optimization with Gumbel reparametrizations, which enable the computation of low-variance gradient estimates of categorical random variables. Our approach is formalized by GLODISMO (Gradient-based Learning of DIscrete Structured Measurement Operators). This novel method is easy-to-implement, computationally efficient, and extendable due to its compatibility with automatic differentiation. We empirically demonstrate the performance and flexibility of GLODISMO in several prototypical signal recovery applications, verifying that the learned measurement matrices outperform conventional designs based on randomization as well as discrete optimization baselines.
Accelerated Structured Alternating Projections for Robust Spectrally Sparse Signal Recovery
University of California, Los Angeles（加州大学洛杉矶分校）；Hong Kong University of Science and Technology（香港科技大学）；Southwestern University of Finance and Economics（西南财经大学）；Shenzhen University（深圳大学）
Accelerating Ill-conditioned Hankel Matrix Recovery via Structured Newton-like Descent
Department of Statistics and Data Science and Department of Computer Science, University of Central Florida（统计与数据科学系和计算机科学系，中央佛罗里达大学）；Department of Computational Mathematics, Science and Engineering and Department of Mathematics, Michigan State University（计算数学、科学与工程系和数学系，密歇根州立大学）；School of Mathematics and Statistics, and Hubei Key Laboratory of Computational Science, Wuhan University（数学与统计学系，和湖北计算科学重点实验室，武汉大学）；School of Artificial Intelligence, Wuhan University, National Center for Applied Mathematics in Hubei, and Hubei Key Laboratory of Computational Science, Wuhan, China（人工智能学院，武汉大学，湖北应用数学中心，和湖北计算科学重点实验室，中国武汉）；Institute for Advanced Study, Shenzhen University（先进研究学院，深圳大学）
A Scalable Factorization Approach for High-Order Structured Tensor Recovery
Department of Computer Science and Engineering, the Ohio State University（计算机科学与工程系，俄亥俄州立大学）；Department of Electrical Engineering, Colorado School of Mines（电气工程系，科罗拉多矿学院）
SGA: A Robust Algorithm for Partial Recovery of Tree-Structured Graphical Models with Noisy Samples
National University of Singapore（新加坡国立大学）
我们考虑学习伊辛树模型时，从节点的观察是由独立的，但不相同分布的噪声与未知的统计损坏。Katiyar等人（2020）表明，虽然无法恢复精确的树结构，但可以恢复部分树结构;即属于包含真树的等价类的结构。本文对Katiyar et al.（2020）进行了系统的改进。首先，我们提出了一个新的不可能的结果，通过推导出的部分恢复所需的样本数的界限。第二，我们推导出一个显着改善的样本复杂度的结果，其中的最小相关$ρ_{\min}$的依赖是$ρ_{\min}^{-8}$，而不是$ρ_{\min}^{-24}$。最后，我们提出了对称几何平均（SGA），一个更强大的统计算法的部分树恢复。我们提供了各种树的误差指数分析和广泛的数值结果，以表明SGA的样本复杂度明显优于Katiyar等人的算法。SGA可以很容易地扩展到高斯模型，并通过数值实验表明，同样优越。
On the stable recovery of deep structured linear networks under sparsity constraints
Institut de Mathématiques de Toulouse（图卢兹数学研究所）；Université de Toulouse（图卢兹大学）；CNRS（法国国家科学研究中心）；UPS IMT（图卢兹第三大学数学研究所）；Institut de Recherche Technologique Saint-Exupéry（圣埃克苏佩里技术研究所）
Tensor Network Moral Graph Recovery of Discrete Probability Distributions
Heisenberg Research Center（海森堡研究中心）；Huawei Technologies Duesseldorf GmbH（华为技术杜塞尔多夫有限公司）；Center for Computational Simulation, Universidad Politécnica de Madrid（马德里理工大学计算模拟中心）
