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A greedy algorithm for a class of convex optimization problems is presented in this paper. The algorithm is motivated from function approximation using sparse combination of basis functions as well as some of its variants. We derive a bound on the rate of approximate minimization for this algorithm, and present examples of its application. Our analysis generalizes a number of earlier studies. [ABSTRACT FROM AUTHOR]

The aim of this paper is to develop discrete stochastic approximation algorithms that adaptively optimize the spreading codes of users in a code-division multiple-access (CDMA) system employing linear minimum mean-square error (MMSE) receivers. The proposed algorithms are able to adapt to slowly time-varying channel conditions. One of the most important properties of the algorithms is their self-learning capability-they spend most of the computational effort at the global optimizer of the objective function. Tracking analysis of the adaptive algorithms is presented together with mean-square convergence. An adaptive-step-size algorithm is also presented for optimally adjusting the step size based on the observations. Numerical examples, illustrating the performance of the algorithms in multipath fading channels, show substantial improvement over heuristic algorithms. [ABSTRACT FROM AUTHOR]

This paper investigates how recursive partitioning methods can be adapted to the bipartite ranking problem. In ranking, the pursued goal is global: based on past data, define an order on the whole input space X, so that positive instances take up the top ranks with maximum probability. The most natural way to order all instances consists of projecting the input data onto the real line through a real-valued scoring function s and use the natural order on ℝ. The accuracy of the ordering induced by a candidate s is classically measured in terms of the ROC curve or the AUC. Here we discuss the design of tree-structured scoring functions obtained by recursively maximizing the AUC criterion. The connection with recursive piecewise linear approximation of the optimal ROC curve both in the L1-sense and in the L∞-sense is highlighted. A novel tree-based algorithm for ranking, called TREERANK, is proposed. Consistency results and generalization bounds of functional nature are established for this ranking method, when considering either the L1 or L∞ distance. We also describe committee-based learning procedures using TREERANK as a "base ranker," in order to overcome obvious drawbacks of such a top-down partitioning technique. Simulation results on artificial data are also displayed. [ABSTRACT FROM AUTHOR]

We consider a canonical model for coded code-division multiple access (CDMA) with random spreading, where the receiver makes use of iterative belief-propagation (BP) joint decoding. We provide simple density-evolution analysis in the large- system limit (large number of users) of the performance of the BP decoder and of some suboptimal approximations based on interference cancellation (IC). Based on this analysis, we optimize the received user signal-to-noise ratio (SNR) distribution in order to maximize the system spectral efficiency for given user channel codes, channel load (users per chip), and target user bit-error rate (BER). The optimization of the received SNR distribution is obtained by solving a simple linear program and can be easily incorporated into practical power control algorithms. Remarkably, under the optimized SNR assignment, the suboptimal minimum mean-square error (MMSE) IC-based decoder performs almost as well as the more complex BP decoder. Moreover, for a large class of commonly used convolutional codes, we observe that the optimized SNR distribution consists of a finite number of discrete SNR levels. Based on this observation, we provide a low-complexity approximation of the MMSE-IC decoder that suffers from very small performance degradation while attaining considerable savings in complexity. As by-products of this work, we obtain a closed-form expression of the multiuser efficiency (ME) of power-mismatched MMSE filters in the large-system limit, and we extend the analysis of the symbol-by-symbol maximum a posteriori probability (MAP) multiuser detector in the large-system limit to the case of nonconstant user powers and nonuniform symbol prior probabilities. [ABSTRACT FROM AUTHOR]