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257,285
Guaranteed minimumrank solutions of linear matrix equations via nuclear norm minimization
, 2007
"... The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system identification and control, Euclidean embedding, and collaborative ..."
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Cited by 568 (23 self)
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with overwhelming probability, provided the codimension of the subspace is sufficiently large. The techniques used in our analysis have strong parallels in the compressed sensing framework. We discuss how affine rank minimization generalizes this preexisting concept and outline a dictionary relating concepts from
Inflation and Growth
, 1996
"... In recent years, many central banks have placed increased emphasis on price stability. Monetary policyâwhether expressed in terms of interest rates or growth of monetary aggregatesâhas been increasingly geared toward the achievement of low and stable inflation. Central bankers and most other obs ..."
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Cited by 3466 (23 self)
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. Although some empirical results (also surveyed by Briault) suggest that inflation is harmful, the evidence is not overwhelming. It is therefore important to carry out additional empirical research on the relation between inflation and economic performance. This article explores this relation in a large
Cumulated Gainbased Evaluation of IR Techniques
 ACM Transactions on Information Systems
, 2002
"... Modem large retrieval environments tend to overwhelm their users by their large output. Since all documents are not of equal relevance to their users, highly relevant documents should be identified and ranked first for presentation to the users. In order to develop IR techniques to this direction, i ..."
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Cited by 656 (3 self)
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Modem large retrieval environments tend to overwhelm their users by their large output. Since all documents are not of equal relevance to their users, highly relevant documents should be identified and ranked first for presentation to the users. In order to develop IR techniques to this direction
MEGA5: Molecular evolutionary genetics analysis using maximum . . .
, 2011
"... Comparative analysis of molecular sequence data is essential for reconstructing the evolutionary histories of species and inferring the nature and extent of selective forces shaping the evolution of genes and species. Here, we announce the release of Molecular Evolutionary Genetics Analysis version ..."
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Cited by 6858 (19 self)
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) analyses for inferring evolutionary trees, selecting bestfit substitution models (nucleotide or amino acid), inferring ancestral states and sequences (along with probabilities), and estimating evolutionary rates sitebysite. In computer simulation analyses, ML tree inference algorithms in MEGA5 compared
For Most Large Underdetermined Systems of Linear Equations the Minimal ℓ1norm Solution is also the Sparsest Solution
 Comm. Pure Appl. Math
, 2004
"... We consider linear equations y = Φα where y is a given vector in R n, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R m. We suppose that the columns of Φ are normalized to unit ℓ 2 norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so that ..."
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Cited by 560 (10 self)
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We consider linear equations y = Φα where y is a given vector in R n, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R m. We suppose that the columns of Φ are normalized to unit ℓ 2 norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so that for large n, and for all Φ’s except a negligible fraction, the following property holds: For every y having a representation y = Φα0 by a coefficient vector α0 ∈ R m with fewer than ρ · n nonzeros, the solution α1 of the ℓ 1 minimization problem min �x�1 subject to Φα = y is unique and equal to α0. In contrast, heuristic attempts to sparsely solve such systems – greedy algorithms and thresholding – perform poorly in this challenging setting. The techniques include the use of random proportional embeddings and almostspherical sections in Banach space theory, and deviation bounds for the eigenvalues of random Wishart matrices.
Estimating Wealth Effects without Expenditure Data— or Tears
 Policy Research Working Paper 1980, The World
, 1998
"... Abstract: We use the National Family Health Survey (NFHS) data collected in Indian states in 1992 and 1993 to estimate the relationship between household wealth and the probability a child (aged 6 to 14) is enrolled in school. A methodological difficulty to overcome is that the NFHS, modeled closely ..."
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Cited by 832 (16 self)
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Abstract: We use the National Family Health Survey (NFHS) data collected in Indian states in 1992 and 1993 to estimate the relationship between household wealth and the probability a child (aged 6 to 14) is enrolled in school. A methodological difficulty to overcome is that the NFHS, modeled
Near Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
, 2004
"... Suppose we are given a vector f in RN. How many linear measurements do we need to make about f to be able to recover f to within precision ɛ in the Euclidean (ℓ2) metric? Or more exactly, suppose we are interested in a class F of such objects— discrete digital signals, images, etc; how many linear m ..."
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Cited by 1513 (20 self)
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Suppose we are given a vector f in RN. How many linear measurements do we need to make about f to be able to recover f to within precision ɛ in the Euclidean (ℓ2) metric? Or more exactly, suppose we are interested in a class F of such objects— discrete digital signals, images, etc; how many linear measurements do we need to recover objects from this class to within accuracy ɛ? This paper shows that if the objects of interest are sparse or compressible in the sense that the reordered entries of a signal f ∈ F decay like a powerlaw (or if the coefficient sequence of f in a fixed basis decays like a powerlaw), then it is possible to reconstruct f to within very high accuracy from a small number of random measurements. typical result is as follows: we rearrange the entries of f (or its coefficients in a fixed basis) in decreasing order of magnitude f  (1) ≥ f  (2) ≥... ≥ f  (N), and define the weakℓp ball as the class F of those elements whose entries obey the power decay law f  (n) ≤ C · n −1/p. We take measurements 〈f, Xk〉, k = 1,..., K, where the Xk are Ndimensional Gaussian
Compressive sampling
, 2006
"... Conventional wisdom and common practice in acquisition and reconstruction of images from frequency data follow the basic principle of the Nyquist density sampling theory. This principle states that to reconstruct an image, the number of Fourier samples we need to acquire must match the desired res ..."
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Cited by 1427 (15 self)
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Conventional wisdom and common practice in acquisition and reconstruction of images from frequency data follow the basic principle of the Nyquist density sampling theory. This principle states that to reconstruct an image, the number of Fourier samples we need to acquire must match the desired resolution of the image, i.e. the number of pixels in the image. This paper surveys an emerging theory which goes by the name of “compressive sampling” or “compressed sensing,” and which says that this conventional wisdom is inaccurate. Perhaps surprisingly, it is possible to reconstruct images or signals of scientific interest accurately and sometimes even exactly from a number of samples which is far smaller than the desired resolution of the image/signal, e.g. the number of pixels in the image. It is believed that compressive sampling has far reaching implications. For example, it suggests the possibility of new data acquisition protocols that translate analog information into digital form with fewer sensors than what was considered necessary. This new sampling theory may come to underlie procedures for sampling and compressing data simultaneously. In this short survey, we provide some of the key mathematical insights underlying this new theory, and explain some of the interactions between compressive sampling and other fields such as statistics, information theory, coding theory, and theoretical computer science.
Differential privacy . . .
, 2009
"... We show by means of several examples that robust statistical estimators present an excellent starting point for differentially private estimators. Our algorithms use a new paradigm for differentially private mechanisms, which we call ProposeTestRelease (PTR), and for which we give a formal definit ..."
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Cited by 629 (10 self)
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We show by means of several examples that robust statistical estimators present an excellent starting point for differentially private estimators. Our algorithms use a new paradigm for differentially private mechanisms, which we call ProposeTestRelease (PTR), and for which we give a formal definition and general composition theorems.
Reversible jump Markov chain Monte Carlo computation and Bayesian model determination
 Biometrika
, 1995
"... Markov chain Monte Carlo methods for Bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some xed standard underlying measure. They have therefore not been available for application to Bayesian model determi ..."
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Cited by 1330 (24 self)
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Markov chain Monte Carlo methods for Bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some xed standard underlying measure. They have therefore not been available for application to Bayesian model determination, where the dimensionality of the parameter vector is typically not xed. This article proposes a new framework for the construction of reversible Markov chain samplers that jump between parameter subspaces of di ering dimensionality, which is exible and entirely constructive. It should therefore have wide applicability in model determination problems. The methodology is illustrated with applications to multiple changepoint analysis in one and two dimensions, and toaBayesian comparison of binomial experiments.
Results 1  10
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257,285