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2,258
The Dantzig selector: statistical estimation when p is much larger than n
, 2005
"... In many important statistical applications, the number of variables or parameters p is much larger than the number of observations n. Suppose then that we have observations y = Ax + z, where x ∈ R p is a parameter vector of interest, A is a data matrix with possibly far fewer rows than columns, n ≪ ..."
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Cited by 879 (14 self)
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, where r is the residual vector y − A˜x and t is a positive scalar. We show that if A obeys a uniform uncertainty principle (with unitnormed columns) and if the true parameter vector x is sufficiently sparse (which here roughly guarantees that the model is identifiable), then with very large probability
Stable signal recovery from incomplete and inaccurate measurements,”
 Comm. Pure Appl. Math.,
, 2006
"... Abstract Suppose we wish to recover a vector x 0 ∈ R m (e.g., a digital signal or image) from incomplete and contaminated observations y = Ax 0 + e; A is an n × m matrix with far fewer rows than columns (n m) and e is an error term. Is it possible to recover x 0 accurately based on the data y? To r ..."
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Cited by 1397 (38 self)
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? To recover x 0 , we consider the solution x to the 1 regularization problem where is the size of the error term e. We show that if A obeys a uniform uncertainty principle (with unitnormed columns) and if the vector x 0 is sufficiently sparse, then the solution is within the noise level As a first example
Buffer stock saving and the lifecycle/permanent income hypothesis
 Quarterly Journal of Economics
, 1997
"... This paper argues that the typical household’s saving is better described by a “bufferstock” version than by the traditional version of the Life Cycle/Permanent Income Hypothesis (LC/PIH) model. Bufferstock behavior emerges if consumers with important income uncertainty are sufficiently impatient. ..."
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Cited by 467 (19 self)
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This paper argues that the typical household’s saving is better described by a “bufferstock” version than by the traditional version of the Life Cycle/Permanent Income Hypothesis (LC/PIH) model. Bufferstock behavior emerges if consumers with important income uncertainty are sufficiently impatient
Hierarchical Modelling and Analysis for Spatial Data. Chapman and Hall/CRC,
, 2004
"... Abstract Often, there are two streams in statistical research one developed by practitioners and other by main stream statisticians. Development of geostatistics is a very good example where pioneering work under realistic assumptions came from mining engineers whereas it is only now that statisti ..."
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Cited by 442 (45 self)
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be estimated by ML. Furthermore, ML provides an uncertainty of the estimated parameters what may be used to decide if point estimates are sufficiently accurate or if interval estimation (giving a region of suitable parameters) is more adequate. We discuss various practical and theoretical problems with MLE
On Modeling and Interpreting the Economics of Catastrophic Climate
, 2007
"... Abstract—With climate change as prototype example, this paper analyzes the implications of structural uncertainty for the economics of lowprobability, highimpact catastrophes. Even when updated by Bayesian learning, uncertain structural parameters induce a critical “tail fattening” of posteriorpre ..."
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Cited by 250 (7 self)
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predictive distributions. Such fattened tails have strong implications for situations, like climate change, where a catastrophe is theoretically possible because prior knowledge cannot place sufficiently narrow bounds on overall damages. This paper shows that the economic consequences of fattailed structural uncertainty
Blocksparse signals: Uncertainty relations and efficient recovery
 IEEE TRANS. SIGNAL PROCESS
, 2010
"... We consider efficient methods for the recovery of blocksparse signals — i.e., sparse signals that have nonzero entries occurring in clusters—from an underdetermined system of linear equations. An uncertainty relation for blocksparse signals is derived, based on a blockcoherence measure, which we ..."
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Cited by 161 (17 self)
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We consider efficient methods for the recovery of blocksparse signals — i.e., sparse signals that have nonzero entries occurring in clusters—from an underdetermined system of linear equations. An uncertainty relation for blocksparse signals is derived, based on a blockcoherence measure, which
Ranksparsity incoherence for matrix decomposition
, 2010
"... Suppose we are given a matrix that is formed by adding an unknown sparse matrix to an unknown lowrank matrix. Our goal is to decompose the given matrix into its sparse and lowrank components. Such a problem arises in a number of applications in model and system identification, and is intractable ..."
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Cited by 230 (21 self)
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to solve in general. In this paper we consider a convex optimization formulation to splitting the specified matrix into its components, by minimizing a linear combination of the ℓ1 norm and the nuclear norm of the components. We develop a notion of ranksparsity incoherence, expressed as an uncertainty
Global and regional climate changes due to black carbon,
 Nat. Geosci.,
, 2008
"... Figure 1: Global distribution of BC sources and radiative forcing. a, BC emission strength in tons per year from a study by Bond et al. Full size image (42 KB) Review Nature Geoscience 1, 221 227 (2008 Black carbon in soot is the dominant absorber of visible solar radiation in the atmosphere. Ant ..."
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Cited by 228 (5 self)
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. The uncertainty in the published estimates for BC emissions is a factor of two to five on regional scales and at least 50% on global scales. High BC emissions ( Regional hotspots Until about the 1950s, North America and Western Europe were the major sources of soot emissions, but now developing nations
A Sufficient and Necessary Condition of Uncertainty Distribution
"... Uncertainty theory is a branch of mathematics based on normality, monotonicity, selfduality, countable subadditivity, and product measure axioms. A key concept to describe uncertain quantity is uncertain variable. Uncertainty distribution is an important tool to specify an uncertain variable. In th ..."
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Cited by 10 (0 self)
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. In this paper, a sufficient and necessary condition of uncertainty distribution is proved to show what function is an uncertainty distribution. and an example is given on how to construct an uncertain measure with respect to a given function.
Perseus: Randomized pointbased value iteration for POMDPs
 Journal of Artificial Intelligence Research
, 2005
"... Partially observable Markov decision processes (POMDPs) form an attractive and principled framework for agent planning under uncertainty. Pointbased approximate techniques for POMDPs compute a policy based on a finite set of points collected in advance from the agent’s belief space. We present a ra ..."
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Cited by 204 (17 self)
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Partially observable Markov decision processes (POMDPs) form an attractive and principled framework for agent planning under uncertainty. Pointbased approximate techniques for POMDPs compute a policy based on a finite set of points collected in advance from the agent’s belief space. We present a
Results 1  10
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