The prediction error in CLS and PLS: the importance of feature selection prior to multivariate calibration

By Boaz Nadler, Ronald R. Coifman. 2005

113 citations recorded by the source corpus.

Subfields: Analytical Chemistry, Control and Systems Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/973bbf97fa55f86b08e995f361d6277c4ce455f2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Analytical Chemistry

In Control and Systems Engineering

In Statistics and Probability

Citations in the corpus

Numerical construction of Green's functions in high dimensional elliptic problems with variable coefficients and analysis of renewable energy data via sparse and separable approximations (2012, methodology): “Some authors have employed a probabilistic model of the input data, where the measured concentrations are samples from a potentially noisy underlying distribution [105, 106].”
Finite sample approximation results for principal component analysis: a matrix perturbation approach (2009, methodology): “A similar phenomenon also occurs in linear discriminant analysis [6], and for various multivariate regression algorithms such as partial least squares and classical least squares [26].”
On Consistency and Sparsity for Principal Components Analysis in High Dimensions (2009, background): “In a large p , n setting of partial least squares regression, Nadler and Coifman (2005) noted the importance of prior dimension reduction and suggested the use of wavelets to exploit sparsity.”
Determining the number of components in a factor model from limited noisy data (2008, methodology): “We remark that a similar analysis, highlighting the importance of feature selection, also applies to the performance of multivariate calibration methods such as partial least squares, see [33,27].”
Sorting variables by using informative vectors as a strategy for feature selection in multivariate regression (2009, methodology): “Although the multivariate calibration methods as PLS and PCR are able to deal with a large number of highly correlated response variables (predictors or descriptors) and with small sets of samples, there are several situations in which better predictions are obtained when a subset from a larger numb”
Variable indicators for optimum wavelength selection in diffuse reflectance spectroscopy of soils (2016, background): “The selection of appropriate and optimum number of spectral variables is expected to reducemodel complexity and improve robustness (Xiaobo et al., 2010) and prediction accuracy of calibration models (Jouan-Rimbaud et al., 1995; Nadler and Coifman, 2005).”
Penalized Partial Least Squares with Applications to B-Spline Transformations and Functional Data (2006, background): “It is also common to represent the spectra in terms of basis functions as B-Splines or wavelets [22, 4, 26] before applying regression techniques [32, 36].”
A comparison of random forest and its Gini importance with standard chemometric methods for the feature selection and classification of spectral data (2009, background): “It is observed, however, that although both PCR and PLS are capable learning methods on spectral data – used for example for in [4] – they still have a need to eliminate useless predictors [5,6].”
Sparse partial least squares regression for simultaneous dimension reduction and variable selection (2010, result): “A referee pointed out that a qualitatively equivalent result has been obtained by Nadler and Coifman (2005), where the root-mean-squared error of the PLS estimator has an additional error term that depends on p2=n2.”