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384
Vector Greedy Algorithms
"... Our objective is to study nonlinear approximation with regard to redundant systems. Redundancy on the one hand offers much promise for greater efficiency in terms of approximation rate, but on the other hand gives rise to highly nontrivial theoretical and practical problems. Greedy type approximati ..."
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Cited by 67 (11 self)
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approximations proved to be convenient and efficient ways of constructing mterm approximants. We introduce and study vector greedy algorithms that are designed with aim of constructing mth greedy approximants simultaneously for a given finite number of elements. We prove convergence theorems and obtain some
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 568 (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
Policy gradient methods for reinforcement learning with function approximation.
 In NIPS,
, 1999
"... Abstract Function approximation is essential to reinforcement learning, but the standard approach of approximating a value function and determining a policy from it has so far proven theoretically intractable. In this paper we explore an alternative approach in which the policy is explicitly repres ..."
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Cited by 439 (20 self)
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into estimating a value function, with the actionselection policy represented implicitly as the "greedy" policy with respect to the estimated values (e.g., as the policy that selects in each state the action with highest estimated value). The valuefunction approach has worked well in many applications
Sparse Greedy Matrix Approximation for Machine Learning
, 2000
"... In kernel based methods such as Regularization Networks large datasets pose signi cant problems since the number of basis functions required for an optimal solution equals the number of samples. We present a sparse greedy approximation technique to construct a compressed representation of the ..."
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Cited by 222 (10 self)
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In kernel based methods such as Regularization Networks large datasets pose signi cant problems since the number of basis functions required for an optimal solution equals the number of samples. We present a sparse greedy approximation technique to construct a compressed representation
Algorithms for simultaneous sparse approximation. Part II: Convex relaxation
, 2004
"... Abstract. A simultaneous sparse approximation problem requests a good approximation of several input signals at once using different linear combinations of the same elementary signals. At the same time, the problem balances the error in approximation against the total number of elementary signals th ..."
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Cited by 366 (5 self)
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that participate. These elementary signals typically model coherent structures in the input signals, and they are chosen from a large, linearly dependent collection. The first part of this paper proposes a greedy pursuit algorithm, called Simultaneous Orthogonal Matching Pursuit, for simultaneous sparse
Maximizing Queueing Network Utility Subject to Stability: Greedy Primaldual algorithm
 Queueing Systems
, 2005
"... We study a model of controlled queueing network, which operates and makes control decisions in discrete time. An underlying random network mode determines the set of available controls in each time slot. Each control decision \produces " a certain vector of \commodities"; it also has assoc ..."
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Cited by 204 (9 self)
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is the average value of commodity vector, subject to the constraint that network queues remain stable. We introduce a dynamic control algorithm, which we call Greedy PrimalDual (GPD) algorithm, and prove its asymptotic optimality. We show that our network model and GPD algorithm accommodate a wide range
Greedy Distance Vector Routing
, 2010
"... Abstract—Greedy Distance Vector (GDV) is the first geographic routing protocol designed to optimize endtoend path costs using any additive routing metric, such as: hop count, latency, ETX, ETT, etc. GDV requires no node location information. Instead, GDV uses estimated routing costs to destination ..."
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Cited by 14 (9 self)
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Abstract—Greedy Distance Vector (GDV) is the first geographic routing protocol designed to optimize endtoend path costs using any additive routing metric, such as: hop count, latency, ETX, ETT, etc. GDV requires no node location information. Instead, GDV uses estimated routing costs
Greedy vector quantization
"... We investigate the greedy version of the Lpoptimal vector quantization problem for an Rdvalued random vector X ∈ Lp. We show the existence of a sequence (aN)N≥1 such that aN minimizes a 7 → ∥∥min1≤i≤N−1 X−ai  ∧ X−a∥∥Lp (Lpmean quantization error at level N induced by (a1,..., aN−1, a)). We s ..."
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We investigate the greedy version of the Lpoptimal vector quantization problem for an Rdvalued random vector X ∈ Lp. We show the existence of a sequence (aN)N≥1 such that aN minimizes a 7 → ∥∥min1≤i≤N−1 X−ai  ∧ X−a∥∥Lp (Lpmean quantization error at level N induced by (a1,..., aN−1, a)). We
Greedy Aggregation for Vector Quantization
, 2005
"... Abstract. Vector quantization is a classical problem that appears in many fields. Unfortunately, the quantization problem is generally nonconvex, and therefore affords many local minima. The main problem is finding an initial approximation that is close to a “good ” local minimum. Once such an appr ..."
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present a novel greedy algorithm for the vector quantization problem. The algorithm begins by allocating a large number of representation levels throughout the input domain and thereafter iteratively aggregates pairs of representation levels and replaces them by a single one. The pair of representation
Sparse online greedy support vector regression
 13th European Conference on Machine Learning
, 2002
"... Abstract. We present a novel algorithm for sparse online greedy kernelbased nonlinear regression. This algorithm improves current approaches to kernelbased regression in two aspects. First, it operates online at each time step it observes a single new input sample, performs an update and discards ..."
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Cited by 45 (8 self)
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Abstract. We present a novel algorithm for sparse online greedy kernelbased nonlinear regression. This algorithm improves current approaches to kernelbased regression in two aspects. First, it operates online at each time step it observes a single new input sample, performs an update and discards
Results 1  10
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384