Nonnegative-lasso and application in index tracking

Wu, Lan; Yang, Yuehan; Liu, Hanzhong

doi:10.1016/j.csda.2013.08.012

Cited by 76 publications

(49 citation statements)

References 22 publications

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“…The condition (14) is a sufficient but not necessary condition for the event supp( x) ⊆ Λ. However, (14) is quite close to a necessary condition, as shown in the following theorem. is contained in Λ, then the following condition holds for all solutions v Λ ∈ R J of the restricted NLasso (13) over the column subset Λ:…”

Section: A Fundamental Results For Nlassomentioning

confidence: 79%

“…This theorem indicates that the condition (15) is a necessary condition for supp( x) ⊆ Λ. Hence, a necessary and sufficient condition for the event supp( x) ⊆ Λ lies somewhere between (14) and (15). More specifically, equalities need to be added to (14) only for some indices j to obtain a necessary and sufficient condition.…”

Section: A Fundamental Results For Nlassomentioning

confidence: 94%

“…The weight γ could be adaptively tuned for each element, e.g., as done in adaptive lasso [39]. NLasso has been used as a regression method in hyperspectral unmixing [11], [40], as a variable selection method in economics [14], and as a sparse recovery algorithm for face recognition [7], [8], [41] and hyperspectral classification [42]. Many methods have been proposed for solving (2) such as non-negativity constrained least angle regression and selection [43], full regularization path [44], alternating direction algorithms [40], iterative reweighted shrinkage [11], split Bregman [10], interior point [45], and multiplicative updates [14].…”

Section: A Problem Descriptionmentioning

confidence: 99%

“…Recently, NNLS has been combined with sparsity with improvements in the unmixing performance [10], [11]. Other examples of combining non-negativity and sparse modeling can be found in astronomical imaging [12], proteomics [13], and economics [14]. It has been noted that sparse solutions can be obtained by NNLS with subsequent thresholding [15]- [17].…”

Section: Introductionmentioning

confidence: 99%

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Perfect Recovery Conditions for Non-negative Sparse Modeling

Itoh

Duarte

Parente

2017

IEEE Trans. Signal Process.

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Sparse modeling has been widely and successfully used in many applications such as computer vision, machine learning, and pattern recognition. Accompanied with those applications, significant research has studied the theoretical limits and algorithm design for convex relaxations in sparse modeling. However, theoretical analyses on non-negative versions of sparse modeling are limited in the literature either to a noiseless setting or a scenario with a specific statistical noise model such as Gaussian noise. This paper studies the performance of nonnegative sparse modeling in a more general scenario where the observed signals have an unknown arbitrary distortion, especially focusing on non-negativity constrained and L1-penalized least squares, and gives an exact bound for which this problem can recover the correct signal elements. We pose two conditions to guarantee the correct signal recovery: minimum coefficient condition (MCC) and nonlinearity vs. subset coherence condition (NSCC). The former defines the minimum weight for each of the correct atoms present in the signal and the latter defines the tolerable deviation from the linear model relative to the positive subset coherence (PSC), a novel type of "coherence" metric. We provide rigorous performance guarantees based on these conditions and experimentally verify their precise predictive power in a hyperspectral data unmixing application.Index Terms-sparse modeling, sparse regression, sparse recovery, non-negative constraint, lasso, recovery conditions, hyperspectral unmixing.

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Section: A Fundamental Results For Nlassomentioning

confidence: 79%

Section: A Fundamental Results For Nlassomentioning

confidence: 94%

Section: A Problem Descriptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Perfect Recovery Conditions for Non-negative Sparse Modeling

Itoh

Duarte

Parente

2017

IEEE Trans. Signal Process.

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“…Answers use 5 point Likert Scale method: "1" means "strongly disagree", "5" represents "strongly agree". Because when the answers more than 5, most of the respondents will be lack of sufficient discern ability [20], so we didn't adopt the 7 point Likert Scale.…”

Section: Sn5mentioning

confidence: 99%

The Study of Influencing Factors of Mobile E-commerce Software Use Intention-based on TAM and TRA

Zhao¹,

Xue²,

Jin³

et al. 2016

IJGDC

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An index tracking model with stratified sampling and optimal allocation

Wang

Dai

2017

Appl Stoch Models Bus & Ind

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This paper investigates the portfolio strategy problem for passive fund management. We propose a novel portfolio strategy that combines the existing stratified strategy and optimized sampling strategy. The proposed method enables one to include adequate practical information in portfolio decision making, and promotes better out-of-sample performance. A mixed-integer program model is built that captures the stratification information, the cardinality requirement, and other practical constraints. The corresponding model is able to forecast and generate optimal tracking portfolios with high performance, especially in out-of-sample time period. As mixed-integer program is a well-known NP-hard problem, to tackle the computational challenge, we propose a stratified hybrid genetic algorithm, in which a novel crossover operator is introduced. To evaluate the proposed strategy and algorithm, we conduct numerical tests on real data sets collected from China Stock Exchange Markets. The experimental resultsshow that the algorithm runs efficiently and the portfolio strategy performs significantly better than other existing strategies.KEYWORDS index tracking, out-of-sample performance, stratified sampling, stratified hybrid genetic algorithm, s-rar crossover

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Nonnegative-lasso and application in index tracking

Cited by 76 publications

References 22 publications

Perfect Recovery Conditions for Non-negative Sparse Modeling

Perfect Recovery Conditions for Non-negative Sparse Modeling

The Study of Influencing Factors of Mobile E-commerce Software Use Intention-based on TAM and TRA

An index tracking model with stratified sampling and optimal allocation

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