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638
Fast and robust fixedpoint algorithms for independent component analysis
 IEEE TRANS. NEURAL NETW
, 1999
"... Independent component analysis (ICA) is a statistical method for transforming an observed multidimensional random vector into components that are statistically as independent from each other as possible. In this paper, we use a combination of two different approaches for linear ICA: Comon’s informat ..."
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Cited by 511 (34 self)
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Independent component analysis (ICA) is a statistical method for transforming an observed multidimensional random vector into components that are statistically as independent from each other as possible. In this paper, we use a combination of two different approaches for linear ICA: Comon’s informationtheoretic approach and the projection pursuit approach. Using maximum entropy approximations of differential entropy, we introduce a family of new contrast (objective) functions for ICA. These contrast functions enable both the estimation of the whole decomposition by minimizing mutual information, and estimation of individual independent components as projection pursuit directions. The statistical properties of the estimators based on such contrast functions are analyzed under the assumption of the linear mixture model, and it is shown how to choose contrast functions that are robust and/or of minimum variance. Finally, we introduce simple fixedpoint algorithms for practical optimization of the contrast functions. These algorithms optimize the contrast functions very fast and reliably.
Multiuser OFDM with Adaptive Subcarrier, Bit, and Power Allocation
 IEEE Journal on Selected Areas of Communications
, 1999
"... Multiuser orthogonal frequency division multiplexing (OFDM) with adaptive multiuser subcarrier allocation and adaptive modulation is considered. Assuming knowledge of the instantaneous channel gains for all users, we propose a multiuser OFDM subcarrier, bit, and power allocation algorithm to minimiz ..."
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Cited by 187 (1 self)
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Multiuser orthogonal frequency division multiplexing (OFDM) with adaptive multiuser subcarrier allocation and adaptive modulation is considered. Assuming knowledge of the instantaneous channel gains for all users, we propose a multiuser OFDM subcarrier, bit, and power allocation algorithm to minimize the total transmit power. This is done by assigning each user a set of subcarriers and by determining the number of bits and the transmit power level for each subcarrier. We obtain the performance of our proposed algorithm in a multiuser frequency selective fading environment for various time delay spread values and various numbers of users. The results show that our proposed algorithm outperforms multiuser OFDM systems with static timedivision multiple access (TDMA) or frequencydivision multiple access (FDMA) techniques which employ fixed and predetermined timeslot or subcarrier allocation schemes. We have also quantified the improvement in terms of the overall required transmit power, the biterror rate (BER), or the area of coverage for a given outage probability.
Determinant maximization with linear matrix inequality constraints
 SIAM Journal on Matrix Analysis and Applications
, 1998
"... constraints ..."
Treebased batch mode reinforcement learning
 Journal of Machine Learning Research
, 2005
"... Reinforcement learning aims to determine an optimal control policy from interaction with a system or from observations gathered from a system. In batch mode, it can be achieved by approximating the socalled Qfunction based on a set of fourtuples (xt,ut,rt,xt+1) where xt denotes the system state a ..."
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Cited by 134 (28 self)
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Reinforcement learning aims to determine an optimal control policy from interaction with a system or from observations gathered from a system. In batch mode, it can be achieved by approximating the socalled Qfunction based on a set of fourtuples (xt,ut,rt,xt+1) where xt denotes the system state at time t, ut the control action taken, rt the instantaneous reward obtained and xt+1 the successor state of the system, and by determining the control policy from this Qfunction. The Qfunction approximation may be obtained from the limit of a sequence of (batch mode) supervised learning problems. Within this framework we describe the use of several classical treebased supervised learning methods (CART, Kdtree, tree bagging) and two newly proposed ensemble algorithms, namely extremely and totally randomized trees. We study their performances on several examples and find that the ensemble methods based on regression trees perform well in extracting relevant information about the optimal control policy from sets of fourtuples. In particular, the totally randomized trees give good results while ensuring the convergence of the sequence, whereas by relaxing the convergence constraint even better accuracy results are provided by the extremely randomized trees.
Optimal motion and structure estimation
 IEEE Trans. Pattern Anal. Mach. Intell
, 1993
"... This paper studies optimal estimation for motion and structure from point correspondences. (1) A study of the characteristics of thc problem provides insight into the need for optimal estimation. (2) Methods have been developed for optimal estimation with known or unknown noise distribution. The sim ..."
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Cited by 131 (5 self)
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This paper studies optimal estimation for motion and structure from point correspondences. (1) A study of the characteristics of thc problem provides insight into the need for optimal estimation. (2) Methods have been developed for optimal estimation with known or unknown noise distribution. The simulations showed that the optimal estimations achieve remarkable improvement over the preliminary estimates given by the linear algorithm. (3) An approach to estimating errors in the optimized solution is presented. (4) The performance of the algorithm is compared with a theoretical lower bound CramCrRao bound. Simulations show that the actual errors have essentially reached the bound. (5) A batch leastsquares technique (LevenbergMarquardt) and a sequential leastsquares technique (iterated extended Kalman filtering) are analyzed and compared. The analysis and experiments show that, in general, a batch technique will perform better than a sequential technique for any nonlinear problems. Recursive batch processing technique is proposed for nonlinear problems that require recursive estimation. 1.
Demand Reduction and Inefficiency in MultiUnit Auctions
, 1998
"... Auctions typically involve the sale of many related goods. The FCC spectrum auctions and the Treasury debt auctions are examples. With conventional auction designs, large bidders have an incentive to reduce demand in order to pay less for their winnings. This incentive creates an inefficiency in mul ..."
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Cited by 128 (13 self)
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Auctions typically involve the sale of many related goods. The FCC spectrum auctions and the Treasury debt auctions are examples. With conventional auction designs, large bidders have an incentive to reduce demand in order to pay less for their winnings. This incentive creates an inefficiency in multiunit auctions. Large bidders reduce demand for additional units and so sometimes lose to smaller bidders with lower values. We demonstrate this inefficiency in several auction settings: flat demand and downwardsloping demand, independent private values and correlated values, and uniform pricing and payyourbid pricing. We also establish that the ranking of the uniformprice and payyourbid auctions is ambiguous. We show how a Vickrey auction avoids this inefficiency and how the Vickrey auction can be implemented with a simultaneous, ascendingbid design (Ausubel 1997). Bidding behavior in the FCC spectrum auctions illustrates the incentives for demand reduction and the associated inefficiency.
Joint TxRx beamforming design for multicarrier MIMO channels: a unified framework for convex optimization
 IEEE TRANS. SIGNAL PROCESSING
, 2003
"... This paper addresses the joint design of transmit and receive beamforming or linear processing (commonly termed linear precoding at the transmitter and equalization at the receiver) for multicarrier multipleinput multipleoutput (MIMO) channels under a variety of design criteria. Instead of consid ..."
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Cited by 127 (12 self)
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This paper addresses the joint design of transmit and receive beamforming or linear processing (commonly termed linear precoding at the transmitter and equalization at the receiver) for multicarrier multipleinput multipleoutput (MIMO) channels under a variety of design criteria. Instead of considering each design criterion in a separate way, we generalize the existing results by developing a unified framework based on considering two families of objective functions that embrace most reasonable criteria to design a communication system: Schurconcave and Schurconvex functions. Once the optimal structure of the transmitreceive processing is known, the design problem simplifies and can be formulated within the powerful framework of convex optimization theory, in which a great number of interesting design criteria can be easily accommodated and efficiently solved, even though closedform expressions may not exist. From this perspective, we analyze a variety of design criteria, and in particular, we derive optimal beamvectors in the sense of having minimum average bit error rate (BER). Additional constraints on the peaktoaverage ratio (PAR) or on the signal dynamic range are easily included in the design. We propose two multilevel waterfilling practical solutions that perform very close to the optimal in terms of average BER with a low implementation complexity. If cooperation among the processing operating at different carriers is allowed, the performance improves significantly. Interestingly, with carrier cooperation, it turns out that the exact optimal solution in terms of average BER can be obtained in closed form.
The Complex Structures Singular Value
, 1993
"... A tutorial introduction to the complex structured singular value (µ) is presented, with an emphasis on the mathematical aspects of µ. The µbased methods discussed here have been useful for analyzing the performance and robustness properties of linear feedback systems. Several tests ..."
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Cited by 119 (10 self)
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A tutorial introduction to the complex structured singular value (µ) is presented, with an emphasis on the mathematical aspects of µ. The µbased methods discussed here have been useful for analyzing the performance and robustness properties of linear feedback systems. Several tests
2002): “Envelope Theorems for Arbitrary Choice Sets
 Econometrica
"... The standard envelope theorems apply to choice sets with convex and topological structure, providing sufficient conditions for the value function to be differentiable in a parameter and characterizing its derivative. This paper studies optimization with arbitrary choice sets and shows that the tradi ..."
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Cited by 107 (9 self)
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The standard envelope theorems apply to choice sets with convex and topological structure, providing sufficient conditions for the value function to be differentiable in a parameter and characterizing its derivative. This paper studies optimization with arbitrary choice sets and shows that the traditional envelope formula holds at any differentiability point of the value function. We also provide conditions for the value function to be, variously, absolutely continuous, left and rightdifferentiable, or fully differentiable. These results are applied to mechanism design, convex programming, continuous optimization problems, saddlepoint problems, problems with parameterized constraints, and optimal stopping problems.