CoSaMP: Iterative signal recovery from incomplete and inaccurate samples

Compressive sampling offers a new paradigm for acquiring signals that are compressible with respect to an orthonormal basis. The major algorithmic challenge in compressive sampling is to approximate a compressible signal from noisy samples. This paper describes a new iterative recovery algorithm called CoSaMP that delivers the same guarantees as the best optimization-based approaches. Moreover, this algorithm offers rigorous bounds on computational cost and storage. It is likely to be extremely efficient for practical problems because it requires only matrix-vector multiplies with the sampling matrix. For many cases of interest, the running time is just O(N*log^2(N)), where N is the length of the signal.Comment: 30 pages. Revised. Presented at Information Theory and Applications, 31 January 2008, San Dieg

Greedy Signal Recovery Review

The two major approaches to sparse recovery are L1-minimization and greedy methods. Recently, Needell and Vershynin developed Regularized Orthogonal Matching Pursuit (ROMP) that has bridged the gap between these two approaches. ROMP is the first stable greedy algorithm providing uniform guarantees. Even more recently, Needell and Tropp developed the stable greedy algorithm Compressive Sampling Matching Pursuit (CoSaMP). CoSaMP provides uniform guarantees and improves upon the stability bounds and RIC requirements of ROMP. CoSaMP offers rigorous bounds on computational cost and storage. In many cases, the running time is just O(NlogN), where N is the ambient dimension of the signal. This review summarizes these major advances

CoSaMP: Iterative Signal Recovery from Incomplete and Inaccurate Samples

Compressive sampling offers a new paradigm for acquiring signals that are compressible with respect to an orthonormal basis. The major algorithmic challenge in compressive sampling is to approximate a compressible signal from noisy samples. This paper describes a new iterative recovery algorithm called CoSaMP that delivers the same guarantees as the best optimization-based approaches. Moreover, this algorithm offers rigorous bounds on computational cost and storage. It is likely to be extremely efficient for practical problems because it requires only matrix-vector multiplies with the sampling matrix. For compressible signals, the running time is just O(N log^2 N), where N is the length of the signal

Reconstruction of Demand Shocks in Input-Output Networks

Input-Output analysis describes the dependence of production, demand and trade between sectors and regions and allows to understand the propagation of economic shocks through economic networks. A central challenge in practical applications is the availability of data. Observations may be limited to the impact of the shocks in few sectors, but a complete picture of the origin and impacts would be highly desirable to guide political countermeasures. In this article we demonstrate that a shock in the final demand in few sectors can be fully reconstructed from limited observations of production changes. We adapt three algorithms from sparse signal recovery and evaluate their performance and their robustness to observation uncertainties.Comment: 10 pages, 4 figures, conference proceeding for CompleNet 202

Structured Sparsity: Discrete and Convex approaches

Compressive sensing (CS) exploits sparsity to recover sparse or compressible signals from dimensionality reducing, non-adaptive sensing mechanisms. Sparsity is also used to enhance interpretability in machine learning and statistics applications: While the ambient dimension is vast in modern data analysis problems, the relevant information therein typically resides in a much lower dimensional space. However, many solutions proposed nowadays do not leverage the true underlying structure. Recent results in CS extend the simple sparsity idea to more sophisticated {\em structured} sparsity models, which describe the interdependency between the nonzero components of a signal, allowing to increase the interpretability of the results and lead to better recovery performance. In order to better understand the impact of structured sparsity, in this chapter we analyze the connections between the discrete models and their convex relaxations, highlighting their relative advantages. We start with the general group sparse model and then elaborate on two important special cases: the dispersive and the hierarchical models. For each, we present the models in their discrete nature, discuss how to solve the ensuing discrete problems and then describe convex relaxations. We also consider more general structures as defined by set functions and present their convex proxies. Further, we discuss efficient optimization solutions for structured sparsity problems and illustrate structured sparsity in action via three applications.Comment: 30 pages, 18 figure

Understanding and measuring child welfare outcomes

The new Children\u27s and Family Services Reviews (CFSR) process focuses on the effectiveness of services to children and families by measuring client outcomes. This article reviews the research literature related to child welfare outcomes in order to provide a context for federal accountability efforts. It also summarizes the 2001 federal mandate to hold states accountable for child welfare outcomes and describes California\u27s response to this mandate. Implications of the outcomes literature review and measurement problems in the CFSR process suggest CSFR measures do not always capture meaningful outcomes. Recommendations for change are made

Reunifying from behind bars: A quantitative study of the relationship between parental incarceration, service use, and foster care reunification

Incarcerated parents attempting to reunify with their children in foster care can find it difficult to complete the activities on their court-ordered case plans, such as drug treatment services and visitation with children. Although much has been written regarding the obstacles that are likely to interfere with reunification for incarcerated parents, very little quantitative research has examined the topic. This study uses secondary data to examine the incarceration experiences and reunification outcomes of a sample of 225 parents in one large urban California county. In multivariate analysis controlling for problems and demographics, incarcerated parents were less likely to reunify with their children; however, service use appeared to mediate this relationship, as the negative association between incarceration and reunification did not persist when service use was included as a variable in the model. Suggestions are made for policy and practice changes to improve reunification outcomes for this population of parents.