fit_methods: Local fitting method constructors

In resemble: Similarity Retrieval and Local Learning for Spectral Chemometrics

Local fitting method constructors

Description

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These functions create configuration objects that specify how local regression models are fitted within the mbl function.

Usage

fit_pls(ncomp, method = c("pls", "mpls", "simpls"), 
        scale = FALSE, max_iter = 100L, tol = 1e-6)

fit_wapls(min_ncomp, max_ncomp, method = c("mpls", "pls", "simpls"),
          scale = FALSE, max_iter = 100L, tol = 1e-6)

fit_gpr(noise_variance = 0.001, center = TRUE, scale = TRUE)

Arguments

ncomp	an integer indicating the number of PLS components to use in local regressions when fit_pls is used.
min_ncomp	an integer indicating the minimum number of PLS components to use in local regressions when fit_wapls is used. See details.
max_ncomp	an integer indicating the maximum number of PLS components to use in local regressions when fit_wapls is 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. Parameters max_iter and tol are ignored when this method is used. Default is 'pls' for fit_pls and 'mpls' for fit_wapls.
scale	logical indicating whether predictors must be scaled. Default is FALSE for PLS methods and TRUE for GPR.
max_iter	an integer indicating the maximum number of iterations for convergence in the NIPALS algorithm. Only used when method = 'pls' or method = 'mpls'. Default is 100.
tol	a numeric value indicating the convergence tolerance for calculating scores in the NIPALS algorithm. Only used when method = 'pls' or method = '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 is TRUE.

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 \mjeqnjj is:

\mjdeqn

w_j = \frac1s_1:j \times g_jw_j = 1/(s_1:j * g_j)

where \mjeqns_1:js_1:j is the root mean square of the spectral reconstruction error of the target observation(s) when \mjeqnjj PLS components are used, and \mjeqng_jg_j is the root mean square of the squared regression coefficients for the \mjeqnjjth 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 \mjeqnAA is computed from training data (\mjeqnXX, \mjeqnYY) as:

\mjdeqn

A = (X X^T + \sigma^2 I)^-1 YA = (X X^T + sigma^2 I)^-1 Y

where \mjeqn\sigma^2sigma^2 is the noise variance and \mjeqnII is the identity matrix. Prediction for a new observation \mjeqnx_ux_u is:

\mjdeqn\hat

y_u = x_u X^T Ahat y_u = x_u X^T A

The only parameter is the noise variance (noise_variance).

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.

Author(s)

Leonardo Ramirez-Lopez

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.

See Also

mbl

Examples

# PLS with 10 components using standard algorithm
fit_pls(ncomp = 10)

# PLS with modified algorithm (correlation-based weights)
fit_pls(ncomp = 10, method = "mpls")

# PLS with SIMPLS (faster, no iteration)
fit_pls(ncomp = 10, method = "simpls")

# Weighted average PLS (LOCAL-style)
fit_wapls(min_ncomp = 3, max_ncomp = 12)

# Weighted average PLS with SIMPLS
fit_wapls(min_ncomp = 3, max_ncomp = 15, method = "simpls")

# Gaussian process regression
fit_gpr()
fit_gpr(noise_variance = 0.01)

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