Two-Dimensional Pattern-Coupled Sparse Bayesian Learning via Generalized Approximate Message Passing

Fang, Jun; Zhang, Lizao; Li, Hongbin

doi:10.1109/tip.2016.2556582

Cited by 75 publications

(48 citation statements)

References 30 publications

(65 reference statements)

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“…To efficiently solve the reformulated optimization problem, we apply a nature-inspired metaheuristic algorithm; called Beetle Antennae Search (BAS) algorithm. We leverage the properties of metaheuristic algorithms in general, i.e., their well-known ability to efficiently solve complex nonlinear non-convex optimization problems [41]- [45]. Metaheuristic algorithms have found application is several practical situations [46]- [52].…”

Section: B Aim and Organization Of Our Workmentioning

confidence: 99%

Optimal Portfolio Management for Engineering Problems Using Nonconvex Cardinality Constraint: A Computing Perspective

Khan¹,

Cao²,

Katsikis³

et al. 2020

IEEE Access

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The problem of portfolio management relates to the selection of optimal stocks, which results in a maximum return to the investor while minimizing the loss. Traditional approaches usually model the portfolio selection as a convex optimization problem and require the calculation of gradient. Note that gradient-based methods can stuck at local optimum for complex problems and the simplification of portfolio optimization to convex, and further solved using gradient-based methods, is at a high cost of solution accuracy. In this paper, we formulate a nonconvex model for the portfolio selection problem, which considers the transaction cost and cardinality constraint, thus better reflecting the decisive factor affecting the selection of portfolio in the real-world. Additionally, constraints are put into the objective function as penalty terms to enforce the restriction. Note that this reformulated problem cannot be readily solved by traditional methods based on gradient search due to its nonconvexity. Then, we apply the Beetle Antennae Search (BAS), a nature-inspired metaheuristic optimization algorithm capable of efficient global optimization, to solve the problem. We used a large real-world dataset containing historical stock prices to demonstrate the efficiency of the proposed algorithm in practical scenarios. Extensive experimental results are presented to further demonstrate the efficacy and scalability of the BAS algorithm. The comparative results are also performed using Particle Swarm Optimizer (PSO), Genetic Algorithm (GA), Pattern Search (PS), and gradient-based fmincon (interior-point search) as benchmarks. The comparison results show that the BAS algorithm is six times faster in the worst case (25 times in the best case) as compared to the rival algorithms while achieving the same level of performance. INDEX TERMS Portfolio management, constrained optimization, nature-inspired algorithms, beetle search optimization.

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Section: B Aim and Organization Of Our Workmentioning

confidence: 99%

Optimal Portfolio Management for Engineering Problems Using Nonconvex Cardinality Constraint: A Computing Perspective

Khan¹,

Cao²,

Katsikis³

et al. 2020

IEEE Access

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“…The ELBO can be re-expressed as Lðq; ΘÞ ¼ Z qðθÞln pðyjx; βÞpðxjα 1 ; α 2 ; κ; vÞpðα 1 Þpðα 2 ÞpðβÞpðκÞ qðθÞ dθ (24) Because the variables {x i } in p(y|x, β) are non-factorizable, updating the approximate posterior distribution q(x) becomes intractable. The high computational cost involved in obtaining q(x) owing to the computation of the inverse of a K × K matrix at each iteration inhibits the application of the conventional SBL method.…”

Section: Overview Of Variational Inferencementioning

confidence: 99%

Computationally efficient variational Bayesian method for PAPR reduction in multiuser MIMO ‐ OFDM systems

Singh

Sarin

2019

ETRI Journal

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This paper investigates the use of the inverse‐free sparse Bayesian learning (SBL) approach for peak‐to‐average power ratio (PAPR) reduction in orthogonal frequency‐division multiplexing (OFDM)‐based multiuser massive multiple‐input multiple‐output (MIMO) systems. The Bayesian inference method employs a truncated Gaussian mixture prior for the sought‐after low‐PAPR signal. To learn the prior signal, associated hyperparameters and underlying statistical parameters, we use the variational expectation‐maximization (EM) iterative algorithm. The matrix inversion involved in the expectation step (E‐step) is averted by invoking a relaxed evidence lower bound (relaxed‐ELBO). The resulting inverse‐free SBL algorithm has a much lower complexity than the standard SBL algorithm. Numerical experiments confirm the substantial improvement over existing methods in terms of PAPR reduction for different MIMO configurations.

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“…First, our model can be readily applied to either SMV or MMV problems, while the original PC-SBL algorithm proposed in [ 28 ] solves for the clustered pattern SMVs. Although it has been recently extended via generalized approximate message passing (GAMP) to solve for 2D problems [ 44 ], it needs some extra modifications to be used for the MMVs. Secondly, our model uses the Bernoulli-Gaussian prior, and it promotes the clustering pattern by adding hyperpriors on the supports of the solution, while in [ 28 ], this task is performed on the variances of the solution components.…”

Section: Background and Introductionmentioning

confidence: 99%

Bayesian Compressive Sensing of Sparse Signals with Unknown Clustering Patterns

Shekaramiz

Moon

Gunther

2019

Entropy

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We consider the sparse recovery problem of signals with an unknown clustering pattern in the context of multiple measurement vectors (MMVs) using the compressive sensing (CS) technique. For many MMVs in practice, the solution matrix exhibits some sort of clustered sparsity pattern, or clumpy behavior, along each column, as well as joint sparsity across the columns. In this paper, we propose a new sparse Bayesian learning (SBL) method that incorporates a total variation-like prior as a measure of the overall clustering pattern in the solution. We further incorporate a parameter in this prior to account for the emphasis on the amount of clumpiness in the supports of the solution to improve the recovery performance of sparse signals with an unknown clustering pattern. This parameter does not exist in the other existing algorithms and is learned via our hierarchical SBL algorithm. While the proposed algorithm is constructed for the MMVs, it can also be applied to the single measurement vector (SMV) problems. Simulation results show the effectiveness of our algorithm compared to other algorithms for both SMV and MMVs.

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Two-Dimensional Pattern-Coupled Sparse Bayesian Learning via Generalized Approximate Message Passing

Cited by 75 publications

References 30 publications

Optimal Portfolio Management for Engineering Problems Using Nonconvex Cardinality Constraint: A Computing Perspective

Optimal Portfolio Management for Engineering Problems Using Nonconvex Cardinality Constraint: A Computing Perspective

Computationally efficient variational Bayesian method for PAPR reduction in multiuser MIMO ‐ OFDM systems

Bayesian Compressive Sensing of Sparse Signals with Unknown Clustering Patterns

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