Regression Shrinkage and Selection Via the Lasso

Tibshirani, Robert

doi:10.1111/j.2517-6161.1996.tb02080.x

Cited by 39,348 publications

(28,793 citation statements)

References 16 publications

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“…Eigenfiltering is another popular method employed for regularization (Bertero and Boccacci, 1998;Engl et al, 1996). 1 regularizer, so-called lasso, is widely used as an approximation (convex relaxation) of 0 regularizer (Tibshirani, 1996;Trendafilov et al, 2003). Another 1 -based method was proposed in (Brodie et al, 2009) for sparse portfolios.…”

Section: Overview Of Sparsity Methodsmentioning

confidence: 99%

Explicit Kernel and Sparsity of Eigen Subspace for the AR(1) Process

Torun

Yılmaz

Akansu

2016

Financial Signal Processing and Machine Learning

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Section: Overview Of Sparsity Methodsmentioning

confidence: 99%

Explicit Kernel and Sparsity of Eigen Subspace for the AR(1) Process

Torun

Yılmaz

Akansu

2016

Financial Signal Processing and Machine Learning

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“…The ROLS-LASSO algorithm [32] also exploits the ROLS approach, combining it with the least absolute shrinkage and selection operator (LASSO) statistical regularization method [40]. Although slightly less accurate than the RFRP, the ROLS-LASSO is a much lighter method, suitable for timeor computation-critical applications, and thus provides a viable low-cost alternative to the RFRP.…”

Section: Online Model Selection Techniques For Narx Modelsmentioning

confidence: 99%

A dual filtering scheme for nonlinear active noise control

Delvecchio

Piroddi

2013

Adaptive Control & Signal

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Active noise control problems are often affected by nonlinear effects such as distortion and saturation of measurement and actuation devices, which call for suitable nonlinear models and algorithms. The active noise control problem can be interpreted as an indirect model identification problem, due to the secondary path dynamics that follow the control filter block. This complicates the weight update mechanism in the nonlinear case, in that the error gradient depends on the secondary path gradient through nonlinear recursions. A simpler and computationally less demanding approach is here proposed that employs the updating scheme of the standard filtered-x least mean squares (LMS) or filtered-u LMS algorithm. As in those schemes, the calculation of the error gradient requires a signal filtering through an auxiliary system, here obtained through a secondary adaptation loop. The resulting dual filtering LMS algorithm performs the adaptation of the controller parameters in a direct identification mode and can therefore be easily coupled with adaptive model structure selection schemes to provide online tuning of the model structure, for improved model robustness.

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“…In general, 0 minimization is NP-hard, since it is combinatorial in nature and its computational complexity grows exponentially with the size of the image [4]. A common alternative is to relax this norm to the 1 norm [2,5,6], and instead solve…”

Section: Compressive Sensingmentioning

confidence: 99%

“…Other methods solve different formulations of the CS minimization problem. A formulation of the CS minimization problem is least absolute shrinkage and selection operator (LASSO) formulation [5] given by…”

Section: Current Algorithms For Solving the Cs Minimization Problemmentioning

confidence: 99%

Compressive Optical Imaging: Architectures and Algorithms

Marcia

Willett

Harmany

2011

Optical and Digital Image Processing

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Many traditional optical sensors are designed to collect directly interpretable and intuitive measurements. For instance, a standard digital camera directly measures the intensity of a scene at different spatial locations to form a pixel array. Recent advances in the fields of image reconstruction, inverse problems, and compressive sensing (CS) [1,2] indicate, however, that substantial performance gains may be possible in many contexts via less direct measurements combined with computational methods. In particular, CS allows for the extraction of high-resolution images from relatively small focal plane arrays (FPAs). CS is described in detail in Chapter 23. The basic idea of CS theory is that when the image of interest is very sparse or highly compressible in some basis (i.e., most basis coefficients are small or zero valued), relatively few well-chosen observations suffice to reconstruct the most significant nonzero components. In particular, judicious selection of the type of image transformation introduced by measurement systems may significantly improve our ability to extract high-quality images from a limited number of measurements. By designing optical sensors to collect measurements of a scene according to CS theory, we can use sophisticated computational methods to infer critical scene structure and content.These ideas are particularly relevant to imaging applications in which it is useful or even crucial to keep the FPA of an optical system relatively small. For example, in low-light settings where sensitive detectors are costly, smaller FPAs translate directly to less expensive systems. Smaller FPAs also make systems lighter and, thus, more portable. In addition, imaging systems with fewer photodetectors consume less power and, therefore, require fewer battery charges. Finally, smaller cameras can fit into tighter spaces for unobtrusive surveillance. An important goal in the design of many imaging systems, then, is to extract as much information as possible from a small number of detector array measurements.While recent progress in the exploitation of CS theory is highly encouraging, there are several key issues in the context of optical systems that must be addressed:Optical and Digital Image Processing: Fundamentals and Applications, First Edition. Edited

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Regression Shrinkage and Selection Via the Lasso

Cited by 39,348 publications

References 16 publications

Explicit Kernel and Sparsity of Eigen Subspace for the AR(1) Process

Explicit Kernel and Sparsity of Eigen Subspace for the AR(1) Process

A dual filtering scheme for nonlinear active noise control

Compressive Optical Imaging: Architectures and Algorithms

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