Sparse Index Tracking With K-Sparsity or ϵ-Deviation Constraint via ℓ<sub>0</sub>-Norm Minimization

Li, Xiao Peng; Shi, Zhang-Lei; Leung, Chi-Sing; So, Hing Cheung

doi:10.1109/tnnls.2022.3171819

Cited by 14 publications

(11 citation statements)

References 55 publications

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“…Te data are generated from model (19) and model (20), and ρ is, respectively, taken as 0.01, 0.5, 5, 10, 20, and 50.…”

Section: Numerical Simulationsmentioning

confidence: 99%

“…Recently, many researchers adopted ADMM algorithm to high-dimensional statistics and machine learning, see Yin et al [14], Xue et al [15], Zhang and Zou [16], Gu et al [17], and Kapla et al [18], and many other topics, such as matrix completion, tensor completion, and sparse recovery, see Li et al [19,20], Liu et al [21], and Shi et al [22]. Te main advantages of the ADMM algorithm are its fexibility at simplifying a diversity of optimization problems and its good convergence property, see Boyd et al [23].…”

Section: Introductionmentioning

confidence: 99%

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The Alternating Direction Method of Multipliers for Sufficient Dimension Reduction

Ma,

Jiang,

2024

Journal of Mathematics

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The minimum average variance estimation (MAVE) method has proven to be an effective approach to sufficient dimension reduction. In this study, we apply the computationally efficient optimization algorithm named alternating direction method of multipliers (ADMM) to a particular approach (MAVE or minimum average variance estimation) to the problem of sufficient dimension reduction (SDR). Under some assumptions, we prove that the iterative sequence generated by ADMM converges to some point of the associated augmented Lagrangian function. Moreover, that point is stationary. It also presents some numerical simulations on synthetic data to demonstrate the computational efficiency of the algorithm.

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“…Te data are generated from model (19) and model (20), and ρ is, respectively, taken as 0.01, 0.5, 5, 10, 20, and 50.…”

Section: Numerical Simulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Alternating Direction Method of Multipliers for Sufficient Dimension Reduction

Ma,

Jiang,

2024

Journal of Mathematics

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“…To test the performance of the index tracking methods, we adopt the rolling window scheme [5], [8]. The first T train time-frames are used to design the first portfolio, which will be used for out-of-sample testing in the next T test timeframes.…”

Section: Experiments a Dataset And Settingsmentioning

confidence: 99%

“…Another straightforward approach is to evenly distribute capital across all assets composing the index, effectively creating a fully and uniformly weighted portfolio. However, this strategy has notable disadvantages: firstly, it necessitates substantial trading with each rebalance, inflating transaction costs; secondly, it incorporates small and illiquid assets, The objective of sparse index tracking [4]- [8] is to construct a sparse portfolio w ∈ R N , matching the performance of the benchmark market index, with K(<< N ) nonzero weights out of N total assets.…”

Section: Introductionmentioning

confidence: 99%

Sparse Index Tracking: Simultaneous Asset Selection and Capital Allocation via ℓ₀ -Constrained Portfolio

Yamagata,

Ono

2024

IEEE Open J. Signal Process.

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Sparse index tracking is a prominent passive portfolio management strategy that constructs a sparse portfolio to track a financial index. A sparse portfolio is preferable to a full portfolio in terms of reducing transaction costs and avoiding illiquid assets. To achieve portfolio sparsity, conventional studies have utilized ℓ p -norm regularizations as a continuous surrogate of the ℓ 0 -norm regularization. Although these formulations can construct sparse portfolios, their practical application is challenging due to the intricate and time-consuming process of tuning parameters to define the precise upper limit of assets in the portfolio. In this paper, we propose a new problem formulation of sparse index tracking using an ℓ 0 -norm constraint that enables easy control of the upper bound on the number of assets in the portfolio. Moreover, our approach offers a choice between constraints on portfolio and turnover sparsity, further reducing transaction costs by limiting asset updates at each rebalancing interval. Furthermore, we develop an efficient algorithm for solving this problem based on a primal-dual splitting method. Finally, we illustrate the effectiveness of the proposed method through experiments on the S&P500 and Russell3000 index datasets.INDEX TERMS ℓ 0 -norm constraint, Primal-dual splitting, Sparse index tracking.

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“…To address this problem, an alternative method is explored in this paper. It has been proven by some studies [ 30 , 31 , 32 , 33 ] that the nonconvex optimization problem of the L0 norm is relaxed to an L1 norm minimization problem that can also obtain a sparse solution. In other words, the L1 norm constraint makes the problem to be solved behave as a convex optimization problem and can thus obtain the optimal solution by using the linear programming method.…”

Section: Sparse Time-frequency Decomposition Of Proximal Gradient Des...mentioning

confidence: 99%

Rolling Bearing Fault Monitoring for Sparse Time-Frequency Representation and Feature Detection Strategy

Tang

Qing

et al. 2022

Entropy

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Data-driven fault diagnosis methods for rotating machinery have developed rapidly with the help of deep learning methods. However, traditional intelligent fault diagnosis methods still have some limitations in fault feature extraction and the latest object detection theory has not been applied in fault diagnosis. To this end, a fault diagnosis method based on a sparse short-term Fourier transform (SSTFT) and object detection theory is developed in this paper. First, a sparse constraint is introduced in time-frequency analysis to improve the time-frequency resolution of the model without cross-term interference and proximal gradient descent (PGD) is adopted to quickly and effectively optimize the model to obtain a high-quality time-frequency representation (TFR). Second, a fault diagnosis model based on a region-based convolutional neural network (RCNN) is built; the model can extract multiple regions that can characterize fault features from the TFR. This process avoids the interference of irrelevant vibration components and improves the interpretability of the fault diagnosis model. Finally, multicategory rolling bearing fault identification is realized. The effectiveness of the proposed method is validated by simulation signals and bearing experiments. The results indicate that the proposed method is more effective than existing methods.

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Sparse Index Tracking With K-Sparsity or ϵ-Deviation Constraint via ℓ₀-Norm Minimization

Cited by 14 publications

References 55 publications

The Alternating Direction Method of Multipliers for Sufficient Dimension Reduction

The Alternating Direction Method of Multipliers for Sufficient Dimension Reduction

Sparse Index Tracking: Simultaneous Asset Selection and Capital Allocation via ℓ₀ -Constrained Portfolio

Rolling Bearing Fault Monitoring for Sparse Time-Frequency Representation and Feature Detection Strategy

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Sparse Index Tracking With K-Sparsity or ϵ-Deviation Constraint via ℓ0-Norm Minimization

Cited by 14 publications

References 55 publications

The Alternating Direction Method of Multipliers for Sufficient Dimension Reduction

The Alternating Direction Method of Multipliers for Sufficient Dimension Reduction

Sparse Index Tracking: Simultaneous Asset Selection and Capital Allocation via ℓ0 -Constrained Portfolio

Rolling Bearing Fault Monitoring for Sparse Time-Frequency Representation and Feature Detection Strategy

Contact Info

Product

Resources

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Sparse Index Tracking With K-Sparsity or ϵ-Deviation Constraint via ℓ₀-Norm Minimization

Sparse Index Tracking: Simultaneous Asset Selection and Capital Allocation via ℓ₀ -Constrained Portfolio