Calculation of PLS prediction intervals using efficient recursive relations for the Jacobian matrix

Serneels, Sven; Lemberge, P.; Espen, Pierre J. Van

doi:10.1002/cem.849

Cited by 29 publications

(23 citation statements)

References 9 publications

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“…A literature survey shows that deriving formulas using the method of error propagation has been a major research topic. When employing first-order multivariate data, most publications are concerned with standard (i.e., linear) PLSR [22,23,[82][83][84][85][86][87][88][89][90][91][92][93][94][95][96][97][98][99][100][101] 8 The limit of detection is the analyte level that with sufficiently high probability (1 -β) will lead to a correct positive detection decision. The detection decision amounts to comparing the prediction ĉ with the critical level (L c ).…”

Section: Previously Proposed Methodology In Multivariate Calibrationmentioning

confidence: 99%

Uncertainty estimation and figures of merit for multivariate calibration (IUPAC Technical Report)

Olivieri

Faber²,

Ferré

et al. 2006

Pure and Applied Chemistry

322

166

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This paper gives an introduction to multivariate calibration from a chemometrics perspective and reviews the various proposals to generalize the well-established univariate methodology to the multivariate domain. Univariate calibration leads to relatively simple models with a sound statistical underpinning. The associated uncertainty estimation and figures of merit are thoroughly covered in several official documents. However, univariate model predictions for unknown samples are only reliable if the signal is sufficiently selective for the analyte of interest. By contrast, multivariate calibration methods may produce valid predictions also from highly unselective data. A case in point is quantification from near-infrared (NIR) spectra. With the ever-increasing sophistication of analytical instruments inevitably comes a suite of multivariate calibration methods, each with its own underlying assumptions and statistical properties. As a result, uncertainty estimation and figures of merit for multivariate calibration methods has become a subject of active research, especially in the field of chemometrics.

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Section: Previously Proposed Methodology In Multivariate Calibrationmentioning

confidence: 99%

Uncertainty estimation and figures of merit for multivariate calibration (IUPAC Technical Report)

Olivieri

Faber²,

Ferré

et al. 2006

Pure and Applied Chemistry

322

166

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“…[6,8]) since it only consists of four equations. However, computationally it is outperformed by Sijmen de Jong's SIMPLS algorithm, which has over the last years steadily become the" standard" PLS algorithm included in commercial packages due to its computational efficiency (less flops and memory are required than in any other PLS algorithm).…”

Section: Pls At the Population Levelmentioning

confidence: 99%

“…Then the functional Yh,~ corresponding to the predicted value based on ~ is defined as (8) for any distribution G. At the sample level this corresponds to predicting a concentration of a (possibly new) sample on the basis of the calibration matrix.…”

Section: Pls At the Population Levelmentioning

confidence: 99%

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Influence properties of partial least squares regression

Serneels

Croux

Espen

2004

Chemometrics and Intelligent Laboratory Systems

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In this paper, we compute the influence function for partial least squares regression.Thereunto, we design two alternative algorithms, according to the PLS algorithm used.One algorithm for the computation of the influence function is based on the Helland PLS algorithm, whilst the other is compatible with SIMPLS. The calculation of the influence function leads to new influence diagnostic plots forPLS. An alternative to the well known Cook distance plot is proposed, as well as a variant which is sample specific. Moreover, a novel estimate of prediction variance is deduced. The validity of the latter is corroborated by dint of a Monte Carlo simulation.

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“…Following the calculation of a PLS model, prediction intervals can be obtained (Denham[7]; Faber and Kowalski [8]; Serneels et al [9]; Lu et al [10]) to quantify the predictive uncertainty within the regression model.…”

Section: Introductionmentioning

confidence: 99%

Prediction from Uncertain Inputs for Partial Least Squares Regression

Chen¹,

Zhang²,

Ren³

et al. 2017

IJCA

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This paper presents two approaches to calculating the predictions for a partial least squares (PLS) regression model in the presence of uncertain inputs (predictors, covariates). Input uncertainty is a common issue associated with the practical application of PLS, such as in the use of multi-way PLS for the modeling of a batch process and the development of multi-step ahead predictions in time series. By assuming a multivariate normal distribution for the input variables, two methods are considered to accommodate the input uncertainty when calculating the mean and prediction intervals for a PLS model:Monte Carlo approximation and an analytical method. The proposed approaches are demonstrated for the prediction of the end-of-batch quality of a simulated batch polymerization process. 

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Calculation of PLS prediction intervals using efficient recursive relations for the Jacobian matrix

Cited by 29 publications

References 9 publications

Uncertainty estimation and figures of merit for multivariate calibration (IUPAC Technical Report)

Uncertainty estimation and figures of merit for multivariate calibration (IUPAC Technical Report)

Influence properties of partial least squares regression

Prediction from Uncertain Inputs for Partial Least Squares Regression

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