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The local power of the gradient test

Lemonte, Artur José; Ferrari, Silvia Lopes de Paula
Fonte: SPRINGER HEIDELBERG; HEIDELBERG Publicador: SPRINGER HEIDELBERG; HEIDELBERG
Tipo: Artigo de Revista Científica
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The asymptotic expansion of the distribution of the gradient test statistic is derived for a composite hypothesis under a sequence of Pitman alternative hypotheses converging to the null hypothesis at rate n(-1/2), n being the sample size. Comparisons of the local powers of the gradient, likelihood ratio, Wald and score tests reveal no uniform superiority property. The power performance of all four criteria in one-parameter exponential family is examined.; FAPESP; CNPq (Brazil)

Modelagem e controle linear de um sistema de levitação de imã permanente.; Modeling and linear control of a permanent magnet levitation system.

Botelho, Izaias José
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 08/02/2008 Português
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O objetivo deste trabalho é apresentar um novo tipo de sistema de levitação baseado na força de interação magnética entre uma bobina de núcleo não-magnético e um imã permanente, em casos de simetria axial entre os dispositivos, nos moldes do problema 23 proposto no TEAM Workshop. Este tema é bastante atual e vários métodos têm sido estudados e propostos em razão da complexidade na determinação precisa das forças sobre os imãs permanentes imersos em um campo magnético em um circuito magnético aberto. O primeiro grande desafio deste trabalho é obter uma expressão analítica para esta força de interação magnética em casos de simetria axial usando o método de cargas magnéticas ligadas. Para tal, algumas hipóteses simplificadoras foram adotadas como considerar o campo magnético gerado pela bobina aproximadamente uniforme em toda a face do imã permanente e assumir que a magnetização do imã é constante e independente da variação de sua distância para a bobina. Pretende-se aproveitar o sistema implementado neste trabalho como bancada experimental no Laboratório de Controle da Universidade de São Paulo. Foi projetado um controlador PID através de ferramentas gráficas obedecendo a alguns critérios de desempenho...

Rastreador linear quadrático com custo médio de longo prazo para sistemas lineares com saltos markovianos; Reference tracking controller with long run average cost for Markov jump linear system

Bertolucci, Luiz Henrique Barchi
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 08/04/2011 Português
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Neste trabalho estudamos um controlador denominado rastreador linear quadrático (RLQ) com custo médio de longo prazo (CMLP) para sistemas lineares com saltos markovianos (SLSM). Mostramos que o conceito de detetabilidade uniforme, juntamente com a hipótese de que o regulador linear quadrático associado ao RLQ tenha custo uniformemente limitado, são suficientes para que o controle obtido seja estabilizante em um certo sentido. A partir deste resultado, e considerando as mesmas hipóteses, demonstramos a existência do CMLP. Com isto, estendemos os resultados dispostos na literatura desde que consideramos um sistema variante no tempo e uma estrutura mais geral para a cadeia deMarkov. Além disto, avaliamos a aplicação deste controlador no planejamento da operação de um sistema hidrotérmico. Para isto, utilizamos o sistema de usinas do rio São Francisco, em dois casos de estudo, para comparar o desempenho do controlador estudado em relação à solução ótima para o problema, encontrada com o uso da programação dinâmica estocástica, e em relação à solução obtida via programação dinâmica determinística. Os resultados sugerem que o RLQ pode representar uma alternativa interessante para o problema de planejamento hidrotérmico; In the present work we study the reference tracking controller (RTC) for the long run average cost (LRAC) problem for Markov jump linear systems. We show that uniform detectability and an hypothesis that the linear quadratic regulator associated with the RTC has uniformly bounded cost...

Non-linear finite element simulations of injuries with free boundaries: application to surgical wounds

Valero, C.; Javierre, E.; García-Aznar, J. M.; Gómez-Benito, M. J.
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
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Wound healing is a process driven by biochemical and mechanical variables in which new tissue is synthesised to recover original tissue functionality. Wound morphology plays a crucial role in this process, as the skin behaviour is not uniform along different directions. In this work we simulate the contraction of surgical wounds, which can be characterised as elongated and deep wounds. Due to the regularity of this morphology, we approximate the evolution of the wound through its cross-section, adopting a plane strain hypothesis. This simplification reduces the complexity of the computational problem while maintaining allows for a thorough analysis of the role of wound depth in the healing process, an aspect of medical and computational relevance that has not yet been addressed. To reproduce wound contraction we consider the role of fibroblasts, myofibroblasts, collagen and a generic growth factor. The contraction phenomenon is driven by cell-generated forces. We postulate that these forces are adjusted to the mechanical environment of the tissue where cells are embedded through a mechanosensing and mechanotransduction mechanism. To solve the non-linear problem we use the Finite Element Method and an updated Lagrangian approach to represent the change in the geometry. To elucidate the role of wound depth and width on the contraction pattern and evolution of the involved species...

Ecologia e comportamento della lontra eurasiatica (Lutra lutra) in un'area mediterranea (Alentejo, Portugal); ECOLOGY AND BEHAVIOUR OF THE EURASIAN OTTER (Lutra lutra) IN A MEDITERRANEAN AREA (ALENTEJO, PORTUGAL)

QUAGLIETTA, LORENZO
Fonte: La Sapienza Universidade de Roma Publicador: La Sapienza Universidade de Roma
Tipo: Tese de Doutorado
Português
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Despite being a highly studied carnivore, the Eurasian otter (Lutra lutra) still offers the opportunity to explore many aspects of its ecology and behaviour that are poorly known or have only been investigated in temperate areas. From April 2007 to October 2010, the OPA research project (Otter Project in Alentejo) was conducted in the south-central Alentejo region of Portugal, in an area of roughly 800 km2. Through the capture and subsequent radio-tracking of 16 wild Lutra lutra individuals (9 males and 7 females) for an average of 139 radio-locations per animal (about 126 days), together with the genotyping of 51 individual otters, the project aimed to provide a set of basic data on the biology and ecology of the species that were missing or limited throughout its extent of occurrence or in the Mediterranean environment. This thesis focus on some of the aspects of the referred project, such as: (1) extent of home ranges (HR) and movement patterns, including their relationships to seasonality and the availability (and its variability) of water resources; (2) genetic spatial structure, dispersal and social interactions; (3) activity rhythms; (4) habitat selection, with particular focus on the modality and frequency of use of reservoirs; (5) testing of a GPS GSM/GPRS telemetry system in riparian habitats and on free-ranging wild otters. Concerning point (1)...

Testing Mean-Variance Efficiency in CAPM with Possibly Non-Gaussian Errors : An Exact Simulation-Based Approach

BEAULIEU, Marie-Claude; DUFOUR, Jean-Marie; KHALAF, Lynda
Fonte: Université de Montréal Publicador: Université de Montréal
Tipo: Artigo de Revista Científica Formato: 400691 bytes; application/pdf
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In this paper we propose exact likelihood-based mean-variance efficiency tests of the market portfolio in the context of Capital Asset Pricing Model (CAPM), allowing for a wide class of error distributions which include normality as a special case. These tests are developed in the frame-work of multivariate linear regressions (MLR). It is well known however that despite their simple statistical structure, standard asymptotically justified MLR-based tests are unreliable. In financial econometrics, exact tests have been proposed for a few specific hypotheses [Jobson and Korkie (Journal of Financial Economics, 1982), MacKinlay (Journal of Financial Economics, 1987), Gib-bons, Ross and Shanken (Econometrica, 1989), Zhou (Journal of Finance 1993)], most of which depend on normality. For the gaussian model, our tests correspond to Gibbons, Ross and Shanken’s mean-variance efficiency tests. In non-gaussian contexts, we reconsider mean-variance efficiency tests allowing for multivariate Student-t and gaussian mixture errors. Our framework allows to cast more evidence on whether the normality assumption is too restrictive when testing the CAPM. We also propose exact multivariate diagnostic checks (including tests for multivariate GARCH and mul-tivariate generalization of the well known variance ratio tests) and goodness of fit tests as well as a set estimate for the intervening nuisance parameters. Our results [over five-year subperiods] show the following: (i) multivariate normality is rejected in most subperiods...

Finite-Sample Diagnostics for Multivariate Regressions with Applications to Linear Asset Pricing Models

DUFOUR, Jean-Marie; KHALAF, Lynda; BEAULIEU, Marie-Claude
Fonte: Université de Montréal Publicador: Université de Montréal
Tipo: Artigo de Revista Científica Formato: 219916 bytes; application/pdf
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In this paper, we propose several finite-sample specification tests for multivariate linear regressions (MLR) with applications to asset pricing models. We focus on departures from the assumption of i.i.d. errors assumption, at univariate and multivariate levels, with Gaussian and non-Gaussian (including Student t) errors. The univariate tests studied extend existing exact procedures by allowing for unspecified parameters in the error distributions (e.g., the degrees of freedom in the case of the Student t distribution). The multivariate tests are based on properly standardized multivariate residuals to ensure invariance to MLR coefficients and error covariances. We consider tests for serial correlation, tests for multivariate GARCH and sign-type tests against general dependencies and asymmetries. The procedures proposed provide exact versions of those applied in Shanken (1990) which consist in combining univariate specification tests. Specifically, we combine tests across equations using the MC test procedure to avoid Bonferroni-type bounds. Since non-Gaussian based tests are not pivotal, we apply the “maximized MC” (MMC) test method [Dufour (2002)], where the MC p-value for the tested hypothesis (which depends on nuisance parameters) is maximized (with respect to these nuisance parameters) to control the test’s significance level. The tests proposed are applied to an asset pricing model with observable risk-free rates...

Simulation-Based Finite and Large Sample Tests in Multivariate Regressions.

DUFOUR, Jean-Marie; KHALAF, Lynda
Fonte: Université de Montréal Publicador: Université de Montréal
Tipo: Artigo de Revista Científica Formato: 762828 bytes; application/pdf
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In the context of multivariate linear regression (MLR) models, it is well known that commonly employed asymptotic test criteria are seriously biased towards overrejection. In this paper, we propose a general method for constructing exact tests of possibly nonlinear hypotheses on the coefficients of MLR systems. For the case of uniform linear hypotheses, we present exact distributional invariance results concerning several standard test criteria. These include Wilks' likelihood ratio (LR) criterion as well as trace and maximum root criteria. The normality assumption is not necessary for most of the results to hold. Implications for inference are two-fold. First, invariance to nuisance parameters entails that the technique of Monte Carlo tests can be applied on all these statistics to obtain exact tests of uniform linear hypotheses. Second, the invariance property of the latter statistic is exploited to derive general nuisance-parameter-free bounds on the distribution of the LR statistic for arbitrary hypotheses. Even though it may be difficult to compute these bounds analytically, they can easily be simulated, hence yielding exact bounds Monte Carlo tests. Illustrative simulation experiments show that the bounds are sufficiently tight to provide conclusive results with a high probability. Our findings illustrate the value of the bounds as a tool to be used in conjunction with more traditional simulation-based test methods (e.g....

Exact Multivariate Tests of Asset Pricing Models with Stable Asymmetric Distributions

BEAULIEU, Marie-Claude; DUFOUR, Jean-Marie; KHALAF, Lynda
Fonte: Université de Montréal Publicador: Université de Montréal
Tipo: Artigo de Revista Científica Formato: 204421 bytes; application/pdf
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In this paper, we propose exact inference procedures for asset pricing models that can be formulated in the framework of a multivariate linear regression (CAPM), allowing for stable error distributions. The normality assumption on the distribution of stock returns is usually rejected in empirical studies, due to excess kurtosis and asymmetry. To model such data, we propose a comprehensive statistical approach which allows for alternative - possibly asymmetric - heavy tailed distributions without the use of large-sample approximations. The methods suggested are based on Monte Carlo test techniques. Goodness-of-fit tests are formally incorporated to ensure that the error distributions considered are empirically sustainable, from which exact confidence sets for the unknown tail area and asymmetry parameters of the stable error distribution are derived. Tests for the efficiency of the market portfolio (zero intercepts) which explicitly allow for the presence of (unknown) nuisance parameter in the stable error distribution are derived. The methods proposed are applied to monthly returns on 12 portfolios of the New York Stock Exchange over the period 1926-1995 (5 year subperiods). We find that stable possibly skewed distributions provide statistically significant improvement in goodness-of-fit and lead to fewer rejections of the efficiency hypothesis.

Non-linear relationship of cell hit and transformation probabilities in low dose of inhaled radon progenies

Balásházy, Imre; Farkas, Árpád; Madas, Balázs Gergely; Hofmann, Werner
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 12/06/2013 Português
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Cellular hit probabilities of alpha particles emitted by inhaled radon progenies in sensitive bronchial epithelial cell nuclei were simulated at low exposure levels to obtain useful data for the rejection or in support of the linear-non-threshold (LNT) hypothesis. In this study, local distributions of deposited inhaled radon progenies in airway bifurcation models were computed at exposure conditions, which are characteristic of homes and uranium mines. Then, maximum local deposition enhancement factors at bronchial airway bifurcations, expressed as the ratio of local to average deposition densities, were determined to characterize the inhomogeneity of deposition and to elucidate their effect on resulting hit probabilities. The results obtained suggest that in the vicinity of the carinal regions of the central airways the probability of multiple hits can be quite high even at low average doses. Assuming a uniform distribution of activity there are practically no multiple hits and the hit probability as a function of dose exhibits a linear shape in the low dose range. The results are quite the opposite in the case of hot spots revealed by realistic deposition calculations, where practically all cells receive multiple hits and the hit probability as a function of dose is non-linear in the average dose range of 10-100 mGy.; Comment: Copyright 2009 IOP Publishing Ltd...

Active and passive learning of linear separators under log-concave distributions

Balcan, Maria Florina; Long, Philip M.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
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We provide new results concerning label efficient, polynomial time, passive and active learning of linear separators. We prove that active learning provides an exponential improvement over PAC (passive) learning of homogeneous linear separators under nearly log-concave distributions. Building on this, we provide a computationally efficient PAC algorithm with optimal (up to a constant factor) sample complexity for such problems. This resolves an open question concerning the sample complexity of efficient PAC algorithms under the uniform distribution in the unit ball. Moreover, it provides the first bound for a polynomial-time PAC algorithm that is tight for an interesting infinite class of hypothesis functions under a general and natural class of data-distributions, providing significant progress towards a longstanding open question. We also provide new bounds for active and passive learning in the case that the data might not be linearly separable, both in the agnostic case and and under the Tsybakov low-noise condition. To derive our results, we provide new structural results for (nearly) log-concave distributions, which might be of independent interest as well.

Testing Gaussian random hypothesis with the cosmic microwave background temperature anisotropies in the three-year WMAP data

Chiang, Lung-Yih; Naselsky, Pavel D.; Coles, Peter
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
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We test the hypothesis that the temperature of the cosmic microwave background is consistent with a Gaussian random field defined on the celestial sphere, using de-biased internal linear combination (DILC) map produced from the 3-year WMAP data. We test the phases for spherical harmonic modes with l <= 10 (which should be the cleanest) for their uniformity, randomness, and correlation with those of the foreground templates. The phases themselves are consistent with a uniform distribution, but not for l <= 5, and the differences between phases are not consistent with uniformity. For l=3 and l=6, the phases of the CMB maps cross-correlate with the foregrounds, suggestion the presence of residual contamination in the DLC map even on these large scales. We also use a one-dimensional Fourier representation to assemble a_lm into the \Delta T_l(\phi) for each l mode, and test the positions of the resulting maxima and minima for consistency with uniformity randomness on the unit circle. The results show significant departures at the 0.5% level, with the one-dimensional peaks being concentrated around \phi=180 degs. This strongly significant alignment with the Galactic meridian, together with the cross-correlation of DILC phases with the foreground maps...

Distance Maps and Plant Development #2: Facilitated Transport and Uniform Gradient

Dimitrov, Pavel; Zucker, Steven W.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 28/05/2009 Português
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The principles underlying plant development are extended to allow a more molecular mechanism to elaborate the schema by which ground cells differentiate into vascular cells. Biophysical considerations dictate that linear dynamics are not sufficent to capture facilitated auxin transport (e.g., through PIN). We group these transport facilitators into a non-linear model under the assumption that they attempt to minimize certain {\em differences} of auxin concentration. This Constant Gradient Hypothesis greatly increases the descriptive power of our model to include complex dynamical behaviour. Specifically, we show how the early pattern of PIN1 expression appears in the embryo, how the leaf primordium emerges, how convergence points arise on the leaf margin, how the first loop is formed, and how the intricate pattern of PIN shifts during the early establishment of vein patterns in incipient leaves of Arabidopsis. Given our results, we submit that the model provides evidence that many of the salient structural characteristics that have been described at various stages of plant development can arise from the uniform application of a small number of abstract principles.

Coupling Linear Sloshing with Six Degrees of Freedom Rigid Body Dynamics

Dubois, François; Stoliaroff, Dimitri
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 06/07/2014 Português
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Fluid motion in tanks is usually described in space industry with the so-called Lomen hypothesis which assumes the vorticity is null in the moving frame. We establish in this contribution that this hypothesis is valid only for uniform rotational motions. We give a more general formulation of this coupling problem, with a compact formulation. We consider the mechanical modelling of a rigid body with a motion of small amplitude, containing an incompressible fluid in the linearized regime. We first establish that the fluid motion remains irrotational in a Galilean referential if it is true at the initial time. When continuity of normal velocity and pressure are prescribed on the free surface, we establish that the global coupled problem conserve an energy functional composed by three terms. We introduce the Stokes - Zhukovsky vector fields, solving Neumann problems for the Laplace operator in the fluid in order to represent the rotational rigid motion with irrotational vector fields. Then we have a good framework to consider the coupled problem between the fluid and the rigid motion. The coupling between the free surface and the ad hoc component of the velocity potential introduces a "Neumann to Dirichlet" operator that allows to write the coupled system in a very compact form. The final expresion of a Lagrangian for the coupled system is derived and the Euler-Lagrange equations of the coupled motion are presented.; Comment: 28 pages

Sensitivity Analysis for Multiple Comparisons in Matched Observational Studies through Quadratically Constrained Linear Programming

Fogarty, Colin B.; Small, Dylan S.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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A sensitivity analysis in an observational study assesses the robustness of significant findings to unmeasured confounding. While sensitivity analyses in matched observational studies have been well addressed when there is a single outcome variable, accounting for multiple comparisons through the existing methods yields overly conservative results when there are multiple outcome variables of interest. This stems from the fact that unmeasured confounding cannot affect the probability of assignment to treatment differently depending on the outcome being analyzed. Existing methods allow this to occur by combining the results of individual sensitivity analyses to assess whether at least one hypothesis is significant, which in turn results in an overly pessimistic assessment of a study's sensitivity to unobserved biases. By solving a quadratically constrained linear program, we are able to perform a sensitivity analysis while enforcing that unmeasured confounding must have the same impact on the treatment assignment probabilities across outcomes for each individual in the study. We show that this allows for uniform improvements in the power of a sensitivity analysis not only for testing the overall null of no effect, but also for null hypotheses on \textit{specific} outcome variables while strongly controlling the familywise error rate. We illustrate our method through an observational study on the effect of smoking on naphthalene exposure.

Transition from isotropic to anisotropic beam profiles in a linear focusing channel

Simeoni Jr, Wilson
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 20/04/2009 Português
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This paper examines the transition from isotropic to anisotropic beam profiles in a linear focusing channel. Considering a high-intensity ion beam in space-charge dominated regime and large mismatched {\it RMS} beam size initially, observe a fast anisotropy situation of the beam, characterized for a transition of the transversal section round to elliptical with a coupling of transversal emittance driven for instabilities of nonlinear space-charge forces. Space-charge interactions in high-intensity linear accelerator can lead to equipartitioning of energy between the degrees of freedom. The anisotropization phenomena suggest a kind of route to equipartition. In order to understand the initial dynamical behavior of an anisotropic beam, in particular, to study possible mechanisms of equipartition connected with phase space we have to know how we can compute the variables (volume, area of surface, and area projected) that characterize the anisotropic beam in phase space. The purpose of this paper is to propose one definiton of the anisotropic equipartition \cite{Yankov1}. Anisotropic equipartition corresponds to a phase space density uniform on the surface invariant of the $\xi$, a version of the ergodic hypothesis where the $\xi$ invariant play the role of the conserved energy \cite{Kandrup3}. In the state of anisotropic equipartition...

Covariant Uniform Acceleration

Friedman, Yaakov; Scarr, Tzvi
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
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We show that standard Relativistic Dynamics Equation F=dp/d\tau is only partially covariant. To achieve full Lorentz covariance, we replace the four-force F by a rank 2 antisymmetric tensor acting on the four-velocity. By taking this tensor to be constant, we obtain a covariant definition of uniformly accelerated motion. We compute explicit solutions for uniformly accelerated motion which are divided into four types: null, linear, rotational, and general. For null acceleration, the worldline is cubic in the time. Linear acceleration covariantly extends 1D hyperbolic motion, while rotational acceleration covariantly extends pure rotational motion. We use Generalized Fermi-Walker transport to construct a uniformly accelerated family of inertial frames which are instantaneously comoving to a uniformly accelerated observer. We explain the connection between our approach and that of Mashhoon. We show that our solutions of uniformly accelerated motion have constant acceleration in the comoving frame. Assuming the Weak Hypothesis of Locality, we obtain local spacetime transformations from a uniformly accelerated frame K' to an inertial frame K. The spacetime transformations between two uniformly accelerated frames with the same acceleration are Lorentz. We compute the metric at an arbitrary point of a uniformly accelerated frame. We obtain velocity and acceleration transformations from a uniformly accelerated system K' to an inertial frame K. We derive the general formula for the time dilation between accelerated clocks. We obtain a formula for the angular velocity of a uniformly accelerated object. Every rest point of K' is uniformly accelerated...

Bayesian Hypothesis Test using Nonparametric Belief Propagation for Noisy Sparse Recovery

Kang, Jaewook; Lee, Heung-No; Kim, Kiseon
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 19/01/2015 Português
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This paper proposes a low-computational Bayesian algorithm for noisy sparse recovery (NSR), called BHT-BP. In this framework, we consider an LDPC-like measurement matrices which has a tree-structured property, and additive white Gaussian noise. BHT-BP has a joint detection-and-estimation structure consisting of a sparse support detector and a nonzero estimator. The support detector is designed under the criterion of the minimum detection error probability using a nonparametric belief propagation (nBP) and composite binary hypothesis tests. The nonzeros are estimated in the sense of linear MMSE, where the support detection result is utilized. BHT-BP has its strength in noise robust support detection, effectively removing quantization errors caused by the uniform sampling-based nBP. Therefore, in the NSR problems, BHT-BP has advantages over CS-BP which is an existing nBP algorithm, being comparable to other recent CS solvers, in several aspects. In addition, we examine impact of the minimum nonzero value of sparse signals via BHT-BP, on the basis of the results of the recent literature. Our empirical result shows that variation of x_min is reflected to recovery performance in the form of SNR shift.; Comment: 14 page, 11 figures, Digitally Published in IEEE Transaction on Signal Processing at Dec. 2014; IEEE Trans. Signal Process....

Intentionally biased bootstrap methods

Hall, Peter; Presnell, B
Fonte: Aiden Press Publicador: Aiden Press
Tipo: Artigo de Revista Científica
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A class of weighted bootstrap techniques, called biased bootstrap or b-bootstrap methods, is introduced. It is motivated by the need to adjust empirical methods, such as the "uniform" bootstrap, in a surgical way to alter some of their features while leaving others unchanged. Depending on the nature of the adjustment, the b-bootstrap can be used to reduce bias, or to reduce variance or to render some characteristic equal to a predetermined quantity. Examples of the last application include a b-bootstrap approach to hypothesis testing in nonparametric contexts, where the b-bootstrap enables simulation "under the null hypothesis", even when the hypothesis is false, and a b-bootstrap competitor to Tibshirani's variance stabilization method. An example of the bias reduction application is adjustment of Nadaraya-Watson kernel estimators to make them competitive with local linear smoothing. Other applications include density estimation under constraints, outlier trimming, sensitivity analysis, skewness or kurtosis reduction and shrinkage.

Uniform convergence and learnability.

Anthony, Martin Henry George
Fonte: London School of Economics and Political Science Thesis Publicador: London School of Economics and Political Science Thesis
Tipo: Thesis; NonPeerReviewed Formato: application/pdf
Publicado em //1991 Português
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This thesis analyses some of the more mathematical aspects of the Probably Approximately Correct (PAC) model of computational learning theory. The main concern is with the sample size required for valid learning in the PAC model. A sufficient sample-size involving the Vapnik-Chervonenkis (VC) dimension of the hypothesis space is derived; this improves the best previously known bound of this nature. Learnability results and sufficient sample-sizes can in many cases be derived from results of Vapnik on the uniform convergence (in probability) of relative frequencies of events to their probabilities, when the collection of events has finite VC dimension. Two simple new combinatorial proofs of each of two of Vapnik's results are proved here and the results are then applied to the theory of learning stochastic concepts, where again improved sample-size bounds are obtained. The PAC model of learning is a distribution-free model; the resulting sample sizes are not permitted to depend on the usually fixed but unknown probability distribution on the input space. Results of Ben-David, Benedek and Mansour are described, presenting a theory for distribution-dependent learnability. The conditions under which a feasible upper bound on sample-size can be obtained are investigated...