Fit a locally-weighted partial least squares model

lwpls_fit() is the computational engine behind lwpls(). It can also be used on its own through the matrix, data frame, formula or recipe interfaces.

LW-PLS is a lazy learner: fitting validates and standardizes the training data and stores it together with the hyperparameters. The local models are built at prediction time (see predict.lwpls_fit()).

Sparse (sparsity > 0) and robust (robust = TRUE) local models are described in lwpls().

Usage

lwpls_fit(x, ...)

# Default S3 method
lwpls_fit(x, ...)

# S3 method for class 'data.frame'
lwpls_fit(
  x,
  y,
  num_comp = 2L,
  localization = 1,
  neighbors = NULL,
  similarity = "euclidean",
  sparsity = 0,
  scale = TRUE,
  robust = FALSE,
  weight_function = "fair",
  robust_constant = NULL,
  max_iter = 30L,
  ...
)

# S3 method for class 'matrix'
lwpls_fit(
  x,
  y,
  num_comp = 2L,
  localization = 1,
  neighbors = NULL,
  similarity = "euclidean",
  sparsity = 0,
  scale = TRUE,
  robust = FALSE,
  weight_function = "fair",
  robust_constant = NULL,
  max_iter = 30L,
  ...
)

# S3 method for class 'formula'
lwpls_fit(
  formula,
  data,
  num_comp = 2L,
  localization = 1,
  neighbors = NULL,
  similarity = "euclidean",
  sparsity = 0,
  scale = TRUE,
  robust = FALSE,
  weight_function = "fair",
  robust_constant = NULL,
  max_iter = 30L,
  ...
)

# S3 method for class 'recipe'
lwpls_fit(
  x,
  data,
  num_comp = 2L,
  localization = 1,
  neighbors = NULL,
  similarity = "euclidean",
  sparsity = 0,
  scale = TRUE,
  robust = FALSE,
  weight_function = "fair",
  robust_constant = NULL,
  max_iter = 30L,
  ...
)

Arguments

x

Depending on the context:

A data frame or matrix of numeric predictors.
A recipe specifying a set of preprocessing steps created from recipes::recipe().

...

Not currently used, but required for extensibility.

y

When x is a data frame or matrix, y is the outcome:

A factor (or a one-column data frame with a factor) for classification.
A numeric vector, or a matrix/data frame with one or more numeric columns, for regression.

num_comp

The number of PLS components in each local model. It is capped at the maximum possible value, min(ncol(x), nrow(x) - 1).

localization

A positive number: the localization parameter of the similarity weights (see lwpls()). Smaller values give more local models.

neighbors

Either NULL (default), to use all training samples, or the number of nearest training samples used to build each local model.

similarity

The similarity index used to weight the training samples: "euclidean" (default) or "covariance" (covariance-based LW-PLS, CbLW-PLS). See lwpls() for details.

sparsity

A number in [0, 1): the sparsity threshold \(\eta\) of the local models (Hoffmann et al., 2015). Zero (default) gives ordinary local PLS models.

scale

A logical: should the predictors (and numeric outcomes) be standardized to unit variance? Predictors are always centered, which does not affect the predictions. For robust models, the center and scale are the median and the median absolute deviation (MAD).

robust

A logical: should the local models be robust to outliers (partial robust M-regression, Serneels et al., 2005)?

weight_function

The weight function of the robust models: "fair" (default) or "hampel".

robust_constant

The tuning constant(s) of the weight function: for "fair", the constant \(c\) of the Fair function (default 4); for "hampel", three increasing probabilities that define the cutoffs (default c(0.95, 0.975, 0.999)). NULL uses the defaults.

max_iter

The maximum number of iterations of the robust models.

formula

A formula specifying the outcome terms on the left-hand side and the predictor terms on the right-hand side. Multiple numeric outcomes can be given as y1 + y2 ~ ..

data

When a recipe or formula is used, data is a data frame containing both the predictors and the outcome(s).

Value

A lwpls_fit object, which stores the standardized training data, the standardization constants and the hyperparameters.

Examples

train <- mtcars[-(1:5), ]
test <- mtcars[1:5, ]

# XY interface
fit <- lwpls_fit(train[, -1], train$mpg, num_comp = 3, localization = 0.5)
fit
#> Locally-weighted PLS (regression)
#> 
#> Training samples: 27 
#> Predictors:       10 (standardized) 
#> Components:       3 
#> Localization:     0.5 
#> Similarity:       Euclidean 
#> Neighbors:        all (27) 
predict(fit, test[, -1])
#> # A tibble: 5 × 1
#>   .pred
#>   <dbl>
#> 1  21.1
#> 2  20.7
#> 3  27.0
#> 4  18.8
#> 5  17.4

# Formula interface, with two outcomes
fit2 <- lwpls_fit(mpg + qsec ~ ., data = train, num_comp = 3)
predict(fit2, test)
#> # A tibble: 5 × 2
#>   .pred_mpg .pred_qsec
#>       <dbl>      <dbl>
#> 1      22.1       16.4
#> 2      21.7       16.4
#> 3      28.6       18.9
#> 4      19.2       20.0
#> 5      16.8       16.9

# Classification
fit3 <- lwpls_fit(Species ~ ., data = iris, num_comp = 2)
predict(fit3, iris[c(1, 51, 101), ], type = "prob")
#> # A tibble: 3 × 3
#>   .pred_setosa .pred_versicolor .pred_virginica
#>          <dbl>            <dbl>           <dbl>
#> 1      0.990            0.00970           0    
#> 2      0.0269           0.502             0.471
#> 3      0.00553          0.0235            0.971

# Robust and sparse local models
fit4 <- lwpls_fit(mpg ~ ., data = train, num_comp = 3, robust = TRUE, sparsity = 0.3)
fit4
#> Locally-weighted PLS (regression)
#> 
#> Training samples: 27 
#> Predictors:       10 (standardized) 
#> Outcomes:         mpg 
#> Components:       3 
#> Localization:     1 
#> Similarity:       Euclidean 
#> Neighbors:        all (27) 
#> Sparsity:         0.3 (SNIPLS)
#> Robust:           PRM, Fair weights (c = 4)
predict(fit4, test)
#> # A tibble: 5 × 1
#>   .pred
#>   <dbl>
#> 1  20.3
#> 2  20.7
#> 3  25.2
#> 4  18.6
#> 5  16.0

Fit a locally-weighted partial least squares model

Usage

Arguments

Value

See also

Examples