Signal Space CoSaMP for Sparse Recovery with Redundant Dictionaries

Compressive sensing (CS) has recently emerged as a powerful framework for acquiring sparse signals. The bulk of the CS literature has focused on the case where the acquired signal has a sparse or compressible representation in an orthonormal basis. In practice, however, there are many signals that cannot be sparsely represented or approximated using an orthonormal basis, but that do have sparse representations in a redundant dictionary. Standard results in CS can sometimes be extended to handle this case provided that the dictionary is sufficiently incoherent or well-conditioned, but these approaches fail to address the case of a truly redundant or overcomplete dictionary. In this paper we describe a variant of the iterative recovery algorithm CoSaMP for this more challenging setting. We utilize the D-RIP, a condition on the sensing matrix analogous to the well-known restricted isometry property. In contrast to prior work, the method and analysis are "signal-focused"; that is, they are oriented around recovering the signal rather than its dictionary coefficients. Under the assumption that we have a near-optimal scheme for projecting vectors in signal space onto the model family of candidate sparse signals, we provide provable recovery guarantees. Developing a practical algorithm that can provably compute the required near-optimal projections remains a significant open problem, but we include simulation results using various heuristics that empirically exhibit superior performance to traditional recovery algorithms

Spectral Clustering: An Empirical Study of Approximation Algorithms and its Application to the Attrition Problem

Clustering is the problem of separating a set of objects into groups (called clusters) so that objects within the same cluster are more similar to each other than to those in different clusters. Spectral clustering is a now well-known method for clustering which utilizes the spectrum of the data similarity matrix to perform this separation. Since the method relies on solving an eigenvector problem, it is computationally expensive for large datasets. To overcome this constraint, approximation methods have been developed which aim to reduce running time while maintaining accurate classification. In this article, we summarize and experimentally evaluate several approximation methods for spectral clustering. From an applications standpoint, we employ spectral clustering to solve the so-called attrition problem, where one aims to identify from a set of employees those who are likely to voluntarily leave the company from those who are not. Our study sheds light on the empirical performance of existing approximate spectral clustering methods and shows the applicability of these methods in an important business optimization related problem

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

Dismissive and deceptive car dealerships create barriers to electric vehicle adoption at the point of sale

This study investigates the role of car dealerships in the electrification of passenger transport, namely their sales advice about the purchase and use of electric vehicles (EVs). Because most consumers do not have pre-existing knowledge of EVs, and current market conditions favour petrol and diesel vehicles, car dealership experiences may strongly influence EV purchasing decisions. Here we show that car dealerships pose a significant barrier at the point of sale due to a perceived lack of business case viability in relation to petrol and diesel vehicles. In 126 shopping experiences at 82 car dealerships across Denmark, Finland, Iceland, Norway, and Sweden, we find dealers were dismissive of EVs, misinformed shoppers on vehicle specifications, omitted EVs from the sales conversation and strongly oriented customers towards petrol and diesel vehicle options. Dealer’s technological orientation, willingness to sell, and displayed knowledge of EVs were the main contributors to likely purchase intentions. These findings combined with expert interviews suggest that government and industry signalling affect sales strategies and purchasing trends. Policy and business strategies that address barriers at the point of sale are needed to accelerate EV adoption

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.

Efficient Sparse Coding in Early Sensory Processing: Lessons from Signal Recovery

Sensory representations are not only sparse, but often overcomplete: coding units significantly outnumber the input units. For models of neural coding this overcompleteness poses a computational challenge for shaping the signal processing channels as well as for using the large and sparse representations in an efficient way. We argue that higher level overcompleteness becomes computationally tractable by imposing sparsity on synaptic activity and we also show that such structural sparsity can be facilitated by statistics based decomposition of the stimuli into typical and atypical parts prior to sparse coding. Typical parts represent large-scale correlations, thus they can be significantly compressed. Atypical parts, on the other hand, represent local features and are the subjects of actual sparse coding. When applied on natural images, our decomposition based sparse coding model can efficiently form overcomplete codes and both center-surround and oriented filters are obtained similar to those observed in the retina and the primary visual cortex, respectively. Therefore we hypothesize that the proposed computational architecture can be seen as a coherent functional model of the first stages of sensory coding in early vision

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

Precision Tests of the Standard Model

30 páginas, 11 figuras, 11 tablas.-- Comunicación presentada al 25º Winter Meeting on Fundamental Physics celebrado del 3 al 8 de MArzo de 1997 en Formigal (España).Precision measurements of electroweak observables provide stringent tests of the Standard Model structure and an accurate determination of its parameters. An overview of the present experimental status is presented.This work has been supported in part by CICYT (Spain) under grant No. AEN-96-1718.Peer reviewe

Low Complexity Regularization of Linear Inverse Problems

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for recovering the unknown signal is to solve a convex optimization problem that enforces some prior knowledge about its structure. This has proved efficient in many problems routinely encountered in imaging sciences, statistics and machine learning. This chapter delivers a review of recent advances in the field where the regularization prior promotes solutions conforming to some notion of simplicity/low-complexity. These priors encompass as popular examples sparsity and group sparsity (to capture the compressibility of natural signals and images), total variation and analysis sparsity (to promote piecewise regularity), and low-rank (as natural extension of sparsity to matrix-valued data). Our aim is to provide a unified treatment of all these regularizations under a single umbrella, namely the theory of partial smoothness. This framework is very general and accommodates all low-complexity regularizers just mentioned, as well as many others. Partial smoothness turns out to be the canonical way to encode low-dimensional models that can be linear spaces or more general smooth manifolds. This review is intended to serve as a one stop shop toward the understanding of the theoretical properties of the so-regularized solutions. It covers a large spectrum including: (i) recovery guarantees and stability to noise, both in terms of $\ell^2$-stability and model (manifold) identification; (ii) sensitivity analysis to perturbations of the parameters involved (in particular the observations), with applications to unbiased risk estimation ; (iii) convergence properties of the forward-backward proximal splitting scheme, that is particularly well suited to solve the corresponding large-scale regularized optimization problem

Brazil in the Era of Fascism: The “New State” of Getúlio Vargas

The New State established in Brazil by Getúlio Vargas (1937–1945) is the most important case of the institutionalisation of a dictatorship of the fascism era in Latin America. During this time, an impressive spectrum of authoritarian regimes was established, some of which were very instable and poorly institutionalised, while others were more consolidated. Roger Griffin coined the concept of para-fascism for some of them, and the “New State” of Getúlio Vargas in Brazil is a paradigmatic case. In this essay, we analyse the processes of institutional reform in 1930s Brazil paying particular attention to how domestic political actors look at institutional models of fascism and corporatism.info:eu-repo/semantics/publishedVersio