A note on the computation of the generalized cross-validation function for ill-conditioned least squares problems

1984 ◽  
Vol 24 (4) ◽  
pp. 467-472 ◽  
Author(s):  
Lars Eldén
Keyword(s):  
Least Squares ◽  
Cross Validation ◽  
Least Squares Problems ◽  
Generalized Cross Validation

Automatic blind deconvolution with Toeplitz-structured sparse total least squares

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. V345-V357 ◽  
Author(s):  
Nasser Kazemi
Keyword(s):  
Least Squares ◽  
Cross Validation ◽  
Blind Deconvolution ◽  
Real Data ◽  
Total Least Squares ◽  
Data Matrix ◽  
Seismic Survey ◽  
Structural Constraints ◽  
Generalized Cross Validation ◽  
Free Data

Given the noise-corrupted seismic recordings, blind deconvolution simultaneously solves for the reflectivity series and the wavelet. Blind deconvolution can be formulated as a fully perturbed linear regression model and solved by the total least-squares (TLS) algorithm. However, this algorithm performs poorly when the data matrix is a structured matrix and ill-conditioned. In blind deconvolution, the data matrix has a Toeplitz structure and is ill-conditioned. Accordingly, we develop a fully automatic single-channel blind-deconvolution algorithm to improve the performance of the TLS method. The proposed algorithm, called Toeplitz-structured sparse TLS, has no assumptions about the phase of the wavelet. However, it assumes that the reflectivity series is sparse. In addition, to reduce the model space and the number of unknowns, the algorithm benefits from the structural constraints on the data matrix. Our algorithm is an alternating minimization method and uses a generalized cross validation function to define the optimum regularization parameter automatically. Because the generalized cross validation function does not require any prior information about the noise level of the data, our approach is suitable for real-world applications. We validate the proposed technique using synthetic examples. In noise-free data, we achieve a near-optimal recovery of the wavelet and the reflectivity series. For noise-corrupted data with a moderate signal-to-noise ratio (S/N), we found that the algorithm successfully accounts for the noise in its model, resulting in a satisfactory performance. However, the results deteriorate as the S/N and the sparsity level of the data are decreased. We also successfully apply the algorithm to real data. The real-data examples come from 2D and 3D data sets of the Teapot Dome seismic survey.

scholarly journals Pemodelan Persentase Penduduk Miskin Kabupaten/Kota di Provinsi Jawa Barat dengan Pendekatan Regresi Nonparametrik Spline Truncated

2021 ◽  
Vol 14 (1) ◽  
pp. 24-29
Author(s):  
Andrea Tri Rian Dani ◽  
Ludia Ni'matuzzahroh
Keyword(s):  
Least Squares ◽  
Cross Validation ◽  
Ordinary Least Squares ◽  
Generalized Cross Validation

Estimator Spline Truncated adalah salah satu pendekatan dalam regresi nonparametrik yang dapat digunakan ketika pola hubungan antara variabel respon dan variabel prediktor tidak diketahui dengan pasti polanya. Estimator Spline Truncated memiliki fleksibilitas yang tinggi dalam proses pemodelan. Pada penelitian ini  bertujuan untuk memodelkan persentase penduduk miskin Kabupaten/Kota di Provinsi Jawa Barat dengan menggunakan model regresi nonparametrik estimator Spline Truncated. Metode estimasi yang digunakan adalah Ordinary Least Squares (OLS). Kriteria kebaikan model regresi nonparametrik yang digunakan adalah Generalized Cross-Validation (GCV). Berdasarkan hasil analisis, diperoleh model terbaik dari regresi nonparametrik Spline Truncated, yaitu model dengan 3 titik knot, dimana diperoleh nilai GCV minimum sebesar 2.14. Berdasarkan hasil pengujian hipotesis, baik secara simultan maupun parsial, diketahui bahwa variabel prediktor yang digunakan pada penelitian ini, berpengaruh signifikan terhadap persentase penduduk miskin, dengan nilai koefisien determinasi sebesar 95.33%.

Least Squares Model Averaging Based on Generalized Cross Validation

2021 ◽  
Vol 37 (3) ◽  
pp. 495-509
Author(s):  
Xin-min Li ◽  
Guo-hua Zou ◽  
Xin-yu Zhang ◽  
Shang-wei Zhao
Keyword(s):  
Least Squares ◽  
Cross Validation ◽  
Model Averaging ◽  
Generalized Cross Validation

Are orthogonal transformations worthwhile for least squares problems?

1987 ◽  
Vol 22 (1) ◽  
pp. 14-19 ◽  
Author(s):  
Richard L Branham
Keyword(s):  
Least Squares ◽  
Least Squares Problems

scholarly journals Alternative structured spectral gradient algorithms for solving nonlinear least-squares problems

Heliyon ◽  
2021 ◽  
pp. e07499
Author(s):  
Mahmoud Muhammad Yahaya ◽  
Poom Kumam ◽  
Aliyu Muhammed Awwal ◽  
Sani Aji
Keyword(s):  
Least Squares ◽  
Nonlinear Least Squares ◽  
Least Squares Problems ◽  
Gradient Algorithms

scholarly journals Rapid and Cost-Effective Assessment of the Neutral and Acid Detergent Fiber Fractions of Chickpea (Cicer arietinum L.) by Combining Modified PLS and Visible with Near-Infrared Spectroscopy

Agronomy ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 666
Author(s):  
Rafael Font ◽  
Mercedes del Río-Celestino ◽  
Diego Luna ◽  
Juan Gil ◽  
Antonio de Haro-Bailón
Keyword(s):  
Infrared Spectroscopy ◽  
Least Squares ◽  
Partial Least Squares ◽  
Cicer Arietinum ◽  
Near Infrared Spectroscopy ◽  
Near Infrared ◽  
Cross Validation ◽  
Neutral Detergent Fiber ◽  
Acid Detergent Fiber ◽  
Cicer Arietinum L

The near-infrared spectroscopy (NIRS) combined with modified partial least squares (modified PLS) regression was used for determining the neutral detergent fiber (NDF) and the acid detergent fiber (ADF) fractions of the chickpea (Cicer arietinum L.) seed. Fifty chickpea accessions (24 desi and 26 kabuli types) and fifty recombinant inbred lines F5:6 derived from a kabuli × desi cross were evaluated for NDF and ADF, and scanned by NIRS. NDF and ADF values were regressed against different spectral transformations by modified partial least squares regression. The coefficients of determination in the cross-validation and the standard deviation from the standard error of cross-validation ratio were, for NDF, 0.91 and 3.37, and for ADF, 0.98 and 6.73, respectively, showing the high potential of NIRS to assess these components in chickpea for screening (NDF) or quality control (ADF) purposes. The spectral information provided by different chromophores existing in the chickpea seed highly correlated with the NDF and ADF composition of the seed, and, thus, those electronic transitions are highly influenced on model fitting for fiber.

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