Partial least squares cross-validation

L Stable and S. Wold, Partial least square analysis with cross-validation for the two-class problem a Monte Carlo study. J. Chemometrics, 1 (1987) 185-196. 

M. Stone and R.J. Brooks, Continuum regression cross-validated sequentially constructed prediction embracing ordinary least sqaures, partial least squares, and principal component regression. J. Roy. Stat. Soc. B52 (1990) 237-269. 

Figure 18 Regression equation obtained from partial-least-squares data cross-validated in Figure 17.

For partial least-squares (PLS) or principal component regression (PCR), the infrared spectra were transferred to a DEC VAX 11/750 computer via the NIC-COM software package from Nicolet. This package also provided utility routines used to put the spectra into files compatible with the PLS and PCR software. The PLS and PCR program with cross-validation was provided by David Haaland of Sandia National Laboratory. A detailed description of the program and the procedures used in it has been given (5). 

Ekins et al. (163) used the rat ortholog 2B6 to generate a pharmacophore model and compared these findings with a partial least squares (PLS) model using MS-WHIM descriptors. The model was constructed using 16 B-lymphoblastoids and yielded a good cross-validated r2 of 0.607. The analysis included molecular surface properties (size) together with positive elec-... 

A more complex method is described by WOLD [1978], who used cross-validation to estimate the number of factors in FA and PCA. WOLD applied the NIPALS (non linear iterative partial least squares) algorithm and also mentioned its usefulness in cases of incomplete data. 

Cramer, R.D., Bunce, J.D., Patterson, D.E. and Frank, I.E., Cross-validation, bootstrapping, and partial least squares compared with multiple regression in conventional QSAR studies, Quant. Struct.-Act. Relat., 7, 18-25, 1988. 

Quantitative structure-activity/pharmacokinetic relationships (QSAR/ QSPKR) for a series of synthesized DHPs and pyridines as Pgp (type I (100) II (101)) inhibitors was generated by 3D molecular modelling using SYBYL and KowWin programs. A multivariate statistical technique, partial least square (PLS) regression, was applied to derive a QSAR model for Pgp inhibition and QSPKR models. Cross-validation using the leave-one-out method was performed to evaluate the predictive performance of models. For Pgp reversal, the model obtained by PLS could account for most of the variation in Pgp inhibition (R2 = 0.76) with fair predictive performance (Q2 = 0.62). Nine structurally related 1,4-DHPs drugs were used for QSPKR analysis. The models could explain the majority of the variation in clearance (R2 = 0.90), and cross-validation confirmed the prediction ability (Q2 = 0.69) [ 129]. 

PCM modeling aims to find an empirical relation (a PCM equation or model) that describes the interaction activities of the biopolymer-molecule pairs as accurate as possible. To this end, various linear and nonlinear correlation methods can be used. Nonlinear methods have hitherto been used to only a limited extent. The method of prime choice has been partial least-squares projection to latent structures (PLS), which has been found to work very satisfactorily in PCM. PCA is also an important data-preprocessing tool in PCM modeling. Modeling includes statistical model-validation techniques such as cross validation, external prediction, and variable-selection and signal-correction methods to obtain statistically valid models. (For general overviews of modeling methods see [10]). 

There is an approach in QSRR in which principal components extracted from analysis of large tables of structural descriptors of analytes are regressed against the retention data in a multiple regression, i.e., principal component regression (PCR). Also, the partial least square (PLS) approach with cross-validation 29 finds application in QSRR. Recommendations for reporting the results of PC A have been published 130). 

Intermediate Least Squares regression (ILS) is an extension of the Partial Least Squares (PLS) algorithm where the optimal variable subset model is calculated as intermediate to PLS and stepwise regression, by two parameters whose values are estimated by cross-validation [Frank, 1987]. The first parameter is the number of optimal latent variables and the second is the number of elements in the weight vector w set to zero. This last parameter (ALIM) controls the number of selected variables by acting on the weight vector of each mth latent variable as the following ... 

Partial least squares (PLS) is similar to MLR in that it also assumes a linear relationship between a vector x and a target property y. However, it avoids the problems of collinear descriptors by calculating the principal components for the molecular descriptors and target property separately. The scores for the molecular descriptors are used as the feature vector x and are also used to predict the scores for the target property, which can in turn be used to predict y. An important consideration in PLS is the appropriate number of principal components to be used for the QSAR model. This is usually determined by using cross-validation methods like fivefold cross validation and leave-one-out. PLS has been applied to the prediction of carcinogenicity [19], fathead minnow toxicity [20], Tetrahymena pyriformis toxicity [21], mammalian toxicity [22], and Daphnia magna toxicity [23],... 

Partial least squares Partial least squares (PLS) is a statistical technique often applied to relate physicochemical properties to one or several measurements of biological activity. The PLS results consist of two sets of computed factors which are, on the one hand, linear combinations of the chemical descriptors and, on the other hand, linear combinations of the biological activities. Partial least squares finds many applications in chemometrics and, e.g., in the Tripos CoMFA approach. Normally used in conjunction with cross-validation. 

SE Standard error, R coefficient of determination, SEC standard error of calibration, SEV(C) standard error of cross-validation, PLS terms number of terms used for modified partial least squares regression. 

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