These functions create configuration objects that specify how local
regression models are fitted within the mbl function.
Arguments
- ncomp
an integer indicating the number of PLS components to use in local regressions when
fit_plsis used.- min_ncomp
an integer indicating the minimum number of PLS components to use in local regressions when
fit_waplsis used. See details.- max_ncomp
an integer indicating the maximum number of PLS components to use in local regressions when
fit_waplsis used. See details.- method
a character string indicating the PLS algorithm to use. Options are:
'pls': standard PLS using covariance between X and Y for weight computation (NIPALS algorithm).'mpls': modified PLS using correlation between X and Y for weight computation (NIPALS algorithm). See Shenk and Westerhaus (1991).'simpls': SIMPLS algorithm (de Jong, 1993). Computationally faster as it avoids iterative X deflation. Parametersmax_iterandtolare ignored when this method is used.
Default is
'pls'forfit_plsand'mpls'forfit_wapls.- scale
logical indicating whether predictors must be scaled. Default is
FALSEfor PLS methods andTRUEfor GPR.- max_iter
an integer indicating the maximum number of iterations for convergence in the NIPALS algorithm. Only used when
method = 'pls'ormethod = 'mpls'. Default is 100.- tol
a numeric value indicating the convergence tolerance for calculating scores in the NIPALS algorithm. Only used when
method = 'pls'ormethod = 'mpls'. Default is 1e-6.- noise_variance
a numeric value indicating the variance of the noise for Gaussian process local regressions (
fit_gpr). Default is 0.001.- center
logical indicating whether predictors should be centered before fitting. Only used for
fit_gpr. Default isTRUE.
Value
An object of class c("fit_<method>", "fit_method")
containing the specified parameters. This object is passed to
mbl to configure local model fitting.
Details
These functions create configuration objects that are passed to
mbl to specify how local regression models are fitted.
There are three fitting methods available:
Partial least squares (fit_pls)
Uses orthogonal scores partial least squares regression. Three algorithm variants are available:
Standard PLS (
method = 'pls'): Uses the NIPALS algorithm with covariance-based weights.Modified PLS (
method = 'mpls'): Uses the NIPALS algorithm with correlation-based weights. Proposed by Shenk and Westerhaus (1991), this approach gives equal influence to all predictors regardless of their variance scale.SIMPLS (
method = 'simpls'): Uses the SIMPLS algorithm (de Jong, 1993), which deflates the cross-product matrix rather than X itself. This is computationally faster, especially for wide matrices, and produces identical predictions to standard PLS.
The only parameter to optimise is the number of PLS components
(ncomp).
Weighted average PLS (fit_wapls)
This method was developed by Shenk et al. (1997) and is used as the
regression method in the LOCAL algorithm. It fits multiple PLS models
using different numbers of components (from min_ncomp to
max_ncomp). The final prediction is a weighted average of
predictions from all models, where the weight for component \(j\)
is:
\[w_{j} = \frac{1}{s_{1:j} \times g_{j}}\]
where \(s_{1:j}\) is the root mean square of the spectral reconstruction error of the target observation(s) when \(j\) PLS components are used, and \(g_{j}\) is the root mean square of the squared regression coefficients for the \(j\)th component.
The same algorithm variants ('pls', 'mpls', 'simpls')
are available. The default is 'mpls' following the original LOCAL
implementation.
Gaussian process regression (fit_gpr)
Gaussian process regression is a non-parametric Bayesian method characterised by a mean and covariance function. This implementation uses a dot product covariance.
The prediction vector \(A\) is computed from training data (\(X\), \(Y\)) as:
\[A = (X X^{T} + \sigma^2 I)^{-1} Y\]
where \(\sigma^2\) is the noise variance and \(I\) is the identity matrix. Prediction for a new observation \(x_{u}\) is:
\[\hat{y}_{u} = x_{u} X^{T} A\]
The only parameter is the noise variance (noise_variance).
References
de Jong, S. (1993). SIMPLS: An alternative approach to partial least squares regression. Chemometrics and Intelligent Laboratory Systems, 18(3), 251-263.
Rasmussen, C.E., Williams, C.K. (2006). Gaussian Processes for Machine Learning. MIT Press.
Shenk, J.S., & Westerhaus, M.O. (1991). Populations structuring of near infrared spectra and modified partial least squares regression. Crop Science, 31(6), 1548-1555.
Shenk, J., Westerhaus, M., & Berzaghi, P. (1997). Investigation of a LOCAL calibration procedure for near infrared instruments. Journal of Near Infrared Spectroscopy, 5, 223-232.
Westerhaus, M. (2014). Eastern Analytical Symposium Award for outstanding achievements in near infrared spectroscopy: my contributions to near infrared spectroscopy. NIR news, 25(8), 16-20.
Examples
# PLS with 10 components using standard algorithm
fit_pls(ncomp = 10)
#> Fitting method: pls
#> ncomp : 10
#> method : pls
#> scale : FALSE
#> max_iter : 100
#> tol : 1e-06
# PLS with modified algorithm (correlation-based weights)
fit_pls(ncomp = 10, method = "mpls")
#> Fitting method: pls
#> ncomp : 10
#> method : mpls
#> scale : FALSE
#> max_iter : 100
#> tol : 1e-06
# PLS with SIMPLS (faster, no iteration)
fit_pls(ncomp = 10, method = "simpls")
#> Fitting method: pls
#> ncomp : 10
#> method : simpls
#> scale : FALSE
#> max_iter : 100
#> tol : 1e-06
# Weighted average PLS (LOCAL-style)
fit_wapls(min_ncomp = 3, max_ncomp = 12)
#> Fitting method: wapls
#> min_ncomp : 3
#> max_ncomp : 12
#> method : mpls
#> scale : FALSE
#> max_iter : 100
#> tol : 1e-06
# Weighted average PLS with SIMPLS
fit_wapls(min_ncomp = 3, max_ncomp = 15, method = "simpls")
#> Fitting method: wapls
#> min_ncomp : 3
#> max_ncomp : 15
#> method : simpls
#> scale : FALSE
#> max_iter : 100
#> tol : 1e-06
# Gaussian process regression
fit_gpr()
#> Fitting method: gpr
#> noise_variance : 0.001
#> center : TRUE
#> scale : TRUE
fit_gpr(noise_variance = 0.01)
#> Fitting method: gpr
#> noise_variance : 0.01
#> center : TRUE
#> scale : TRUE