“Statistics Meets Statistical Mechanics” 微型研讨会日程 （2021年12月30日，14:00 - 18:00） 

　　中国科学院理论物理研究所南楼6层，6620 会议室 

　　组织者：周海军 （zhouhj@itp.ac.cn） 

　　这是一个统计物理与数据科学的交叉学科微型研讨会，为期半天，邀请了北京地区几位实验、算法和理论方面从事研究工作的学者作邀请报告，希望促进研究团队之间的交流和合作。 

　　研讨会不收注册费，不用提前注册登记。欢迎感兴趣的老师和同学们参加，期待一起交流探讨。 

　　——————————————————————————————————————————— 

　　14:00 - 14:50       吴令安（中科院物理研究所）及研究团队 

　　压缩感知在计算关联成像中的应用 

　　将压缩感知理论引入计算关联成像，给计算关联成像技术水平带来了大幅提升，包括关联成像的测量速度、重建图像质量和成像分辨率等方面的性能提升。本报告主要针对计算关联成像方案，也称为单像素成像，通过实验数据证实压缩感知算法的有效性和局限性，介绍压缩感知算法在用于计算关联成像过程中所面临的问题与挑战。报告的内容主要侧重于从测量基矩阵构造角度出发，通过具体的案例讨论包括TVAL3、GPSR，Walsh-Hadamard变换和Deep learning 等算法在计算关联成像中的应用，并提出一些具体的优化方案。 

　　14:50 - 15:00       提问讨论 

　　——————————————————————————————————————————— 

　　15:00 - 15:30       马俊杰（中科院数学与系统科学院） 

　　On spectral method for phase retrieval with random orthogonal matrices 

　　Phase retrieval refers to algorithmic methods for recovering a signal from its phaseless measurements. Local search algorithms that work directly on the non-convex formulation of the problem have been very popular recently. Due to the nonconvexity of the problem, the success of these local search algorithms depends heavily on their starting points. The most widely used initialization scheme is the spectral method, in which the leading eigenvector of a data-dependent matrix is used as a starting point. Recently, the performance of the spectral initialization was characterized accurately for measurement matrices with independent and identically distributed entries. Our aim is to obtain the same level of knowledge for isotropically random column-orthogonal matrices, which are substantially better models for practical phase retrieval systems. Towards this goal, we consider the asymptotic setting in which the number of measurements and the dimension of the signal diverge to infinity with a fixed ratio, and obtain a simple expression for the overlap between the spectral estimator and the true signal vector using tools from random matrix theory. I will also talk about a linearized approximate message passing (L-AMP) iteration, which is a useful tool to derive accurate asymptotic predictions and study the universality phenomenon.  

　　15:30 - 15:40      提问讨论 

　　15:40 - 16:00       茶歇 

　　——————————————————————————————————————————— 

　　15:60 - 16:30       孙怡帆（人民大学统计学院） 

　　Biomarker-guided heterogeneity analysis of genetic regulations via multivariate sparse fusion 

　　Heterogeneity is a hallmark of many complex diseases. There are multiple ways of defining heterogeneity, among which the heterogeneity in genetic regulations, for example GEs (gene expressions) by CNVs (copy number variations) and methylation, has been suggested but little investigated. The heterogeneity in genetic regulations can be linked with disease severity, progression, and other traits and is biologically highly important. However, the analysis can be very challenging with the high dimensionality of both sides of regulation and sparse and weak signals. In this article, we consider the scenario where subjects form unknown subgroups, and each subgroup has unique genetic regulation relationships. Further, such heterogeneity is “guided" by a known biomarker. We develop an MSF (Multivariate Sparse Fusion) approach, which innovatively applies the penalized fusion technique to simultaneously determine the number and structure of subgroups and regulation relationships within each subgroup. An effective computational algorithm is developed, and extensive simulations are conducted. The analysis of heterogeneity in the GE-CNV regulations in melanoma and GE-methylation regulations in stomach cancer using the TCGA (The Cancer Genome Atlas) data leads to interesting findings.   

　　16:30 - 16:40       提问讨论 

　　——————————————————————————————————————————— 

　　16:40 - 17:05       于雪（中国人民大学统计学院） 

　　Clustered Federated Learning with Concave Fusion 

　　17:05 - 17:10      提问讨论 

　　——————————————————————————————————————————— 

　　17:10 - 17:40       王闯（中科院自动化所） 

　　TBA 

　　17:40 - 17:50       提问讨论 

　　——————————————————————————————————————————— 

　　17:50 - 18:00       周海军（中科院理论物理所） 

　　Shortest-solution guided Decimation (SSD) for Compressed Sensing 

　　Compressed sensing is an important problem in many fields of science and engineering. It reconstructs signals by finding sparse solutions to underdetermined linear equations. Here I briefly describe a deterministic and non-parametric algorithm, shortest-solution guided decimation (SSD), to construct support of the sparse solution under the guidance of the dense least-squares solution of the recursively decimated linear equation [Shen et al., IEEE Access 6: 5564 (2018)]. The most significant feature of SSD is its insensitivity to correlations in the sampling matrix. The algorithm can  also be adapted to consider the effect of measurement noise, and it showed competitive results in comparison with several other representative heuristic algorithms [Yu et al., Scientific Reports 11: 24034 (2021)]. It may be interesting to explore real-world applications.