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610
High dimensional graphs and variable selection with the Lasso
 ANNALS OF STATISTICS
, 2006
"... The pattern of zero entries in the inverse covariance matrix of a multivariate normal distribution corresponds to conditional independence restrictions between variables. Covariance selection aims at estimating those structural zeros from data. We show that neighborhood selection with the Lasso is a ..."
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Cited by 736 (22 self)
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show that the proposed neighborhood selection scheme is consistent for sparse highdimensional graphs. Consistency hinges on the choice of the penalty parameter. The oracle value for optimal prediction does not lead to a consistent neighborhood estimate. Controlling instead the probability of falsely
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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‖ˆx − x ‖ 2 ℓ2 ≤ C2 ( · 2 log p · σ 2 + ∑ min(x 2 i, σ 2) Our results are nonasymptotic and we give values for the constant C. In short, our estimator achieves a loss within a logarithmic factor of the ideal mean squared error one would achieve with an oracle which would supply perfect information
NonDeterministic Exponential Time has TwoProver Interactive Protocols
"... We determine the exact power of twoprover interactive proof systems introduced by BenOr, Goldwasser, Kilian, and Wigderson (1988). In this system, two allpowerful noncommunicating provers convince a randomizing polynomial time verifier in polynomial time that the input z belongs to the language ..."
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Cited by 416 (37 self)
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, linking more standard concepts of structural complexity, states that if EX P has polynomial size circuits then EXP = Cg = MA. The first part of the proof of the main result extends recent techniques of polynomial extrapolation of truth values used in the single prover case. The second part is a
On Hiding Information from an Oracle
, 1989
"... We consider the problem of computing with encrypted data. Player A wishes to know the value f(x) for some x but lacks the power to compute it. Player B has the power to compute f and is willing to send f(y) to A if she sends him y, for any y. Informally, an encryption scheme for the problem f is a m ..."
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Cited by 146 (15 self)
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We consider the problem of computing with encrypted data. Player A wishes to know the value f(x) for some x but lacks the power to compute it. Player B has the power to compute f and is willing to send f(y) to A if she sends him y, for any y. Informally, an encryption scheme for the problem f is a
Optimal Approximation for the Submodular Welfare Problem in the value oracle model
 STOC'08
, 2008
"... In the Submodular Welfare Problem, m items are to be distributed among n players with utility functions wi: 2 [m] → R+. The utility functions are assumed to be monotone and submodular. Assuming that player i receives a set of items Si, we wish to maximize the total utility Pn i=1 wi(Si). In this pap ..."
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Cited by 123 (13 self)
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(Si). In this paper, we work in the value oracle model where the only access to the utility functions is through a black box returning wi(S) for a given set S. Submodular Welfare is in fact a special case of the more general problem of submodular maximization subject to a matroid constraint: max{f(S) : S ∈ I}, where
Security Proofs for Signature Schemes
, 1996
"... In this paper, we address the question of providing security proofs for signature schemes in the socalled random oracle model [1]. In particular, we establish the generality of this technique against adaptively chosen message attacks. Our main application achieves such a security proof for a slight ..."
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Cited by 263 (25 self)
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In this paper, we address the question of providing security proofs for signature schemes in the socalled random oracle model [1]. In particular, we establish the generality of this technique against adaptively chosen message attacks. Our main application achieves such a security proof for a
On Using Oracles That Compute Values
 In Proc. 10th Annual Symp. on Theoret. Aspects of Computer Science, Lecture Notes in Computer Science
, 1993
"... This paper focuses on complexity classes of partial functions that are computed in polynomial time with oracles in NPMV, the class of all multivalued partial functions that are computable nondeterministically in polynomial time. Concerning deterministic polynomialtime reducibilities, it is shown th ..."
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Cited by 17 (6 self)
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This paper focuses on complexity classes of partial functions that are computed in polynomial time with oracles in NPMV, the class of all multivalued partial functions that are computable nondeterministically in polynomial time. Concerning deterministic polynomialtime reducibilities, it is shown
Oracles That Compute Values
, 1997
"... . This paper focuses on complexity classes of partial functions that are computed in polynomial time with oracles in NPMV, the class of all multivalued partial functions that are computable nondeterministically in polynomial time. Concerning deterministic polynomialtime reducibilities, it is shown ..."
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Cited by 13 (4 self)
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. This paper focuses on complexity classes of partial functions that are computed in polynomial time with oracles in NPMV, the class of all multivalued partial functions that are computable nondeterministically in polynomial time. Concerning deterministic polynomialtime reducibilities, it is shown
Oracle Inequalities for Inverse Problems
, 2000
"... We consider a sequence space model of statistical linear inverse problems where we need to estimate a function f from indirect noisy observations. Let a finite set of linear estimators be given. Our aim is to mimic the estimator in that has the smallest risk on the true f . Under general conditions, ..."
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Cited by 74 (9 self)
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, we show that this can be achieved by simple minimization of unbiased risk estimator, provided the singular values of the operator of the inverse problem decrease as a power law. The main result is a nonasymptotic oracle inequality that is shown to be asymptotically exact. This inequality can be also
Towards realizing random oracles: Hash functions that hide all partial information
, 1997
"... The random oracle model is a very convenient setting for designing cryptographic protocols. In this idealized model all parties have access to a common, public random function, called a random oracle. Protocols in this model are often very simple and efficient; also the analysis is often clearer. ..."
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Cited by 137 (14 self)
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'. A salient property of oracle hashing is that it is probabilistic: different applications to the same input result in different hash values. Still, we maintain the ability to verify whether a given hash value was generated from a given input. We describe constructions of oracle hashing, as well
Results 1  10
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