Apply (smoothed) rectified linear transformation

step_relu() creates a specification of a recipe step that will add the rectified linear or softplus transformations of a variable to the data set.

Usage

step_relu(
  recipe,
  ...,
  role = "predictor",
  trained = FALSE,
  shift = 0,
  reverse = FALSE,
  smooth = FALSE,
  prefix = "right_relu_",
  columns = NULL,
  skip = FALSE,
  id = rand_id("relu")
)

Arguments

recipe: A recipe object. The step will be added to the sequence of operations for this recipe.
...: One or more selector functions to choose variables for this step. See selections() for more details.
role: For model terms created by this step, what analysis role should they be assigned? By default, the new columns created by this step from the original variables will be used as predictors in a model.
trained: A logical to indicate if the quantities for preprocessing have been estimated.
shift: A numeric value dictating a translation to apply to the data.
reverse: A logical to indicate if the left hinge should be used as opposed to the right hinge.
smooth: A logical indicating if the softplus function, a smooth approximation to the rectified linear transformation, should be used.
prefix: A prefix for generated column names, defaults to "right_relu_" for right hinge transformation and "left_relu_" for reversed/left hinge transformations.
columns: A character string of the selected variable names. This field is a placeholder and will be populated once prep() is used.
skip: A logical. Should the step be skipped when the recipe is baked by bake()? While all operations are baked when prep() is run, some operations may not be able to be conducted on new data (e.g. processing the outcome variable(s)). Care should be taken when using skip = TRUE as it may affect the computations for subsequent operations.
id: A character string that is unique to this step to identify it.

Value

An updated version of recipe with the new step added to the sequence of any existing operations.

Details

The rectified linear transformation is calculated as $$max(0, x - c)$$ and is also known as the ReLu or right hinge function. If reverse is true, then the transformation is reflected about the y-axis, like so: $$max(0, c - x)$$ Setting the smooth option to true will instead calculate a smooth approximation to ReLu according to $$ln(1 + e^(x - c)$$ The reverse argument may also be applied to this transformation.

Connection to MARS:

The rectified linear transformation is used in Multivariate Adaptive Regression Splines as a basis function to fit piecewise linear functions to data in a strategy similar to that employed in tree based models. The transformation is a popular choice as an activation function in many neural networks, which could then be seen as a stacked generalization of MARS when making use of ReLu activations. The hinge function also appears in the loss function of Support Vector Machines, where it penalizes residuals only if they are within a certain margin of the decision boundary.

Tidying

When you tidy() this step, a tibble is returned with columns terms, shift, reverse , and id:

terms: character, the selectors or variables selected
shift: numeric, location of hinge
reverse: logical, whether left hinge is used
id: character, id of this step

Case weights

The underlying operation does not allow for case weights.

Examples

data(biomass, package = "modeldata")

biomass_tr <- biomass[biomass$dataset == "Training", ]
biomass_te <- biomass[biomass$dataset == "Testing", ]

rec <- recipe(
  HHV ~ carbon + hydrogen + oxygen + nitrogen + sulfur,
  data = biomass_tr
)

transformed_te <- rec %>%
  step_relu(carbon, shift = 40) %>%
  prep(biomass_tr) %>%
  bake(biomass_te)

transformed_te
#> # A tibble: 80 × 7
#>    carbon hydrogen oxygen nitrogen sulfur   HHV right_relu_carbon
#>     <dbl>    <dbl>  <dbl>    <dbl>  <dbl> <dbl>             <dbl>
#>  1   46.4     5.67   47.2     0.3    0.22  18.3              6.35
#>  2   43.2     5.5    48.1     2.85   0.34  17.6              3.25
#>  3   42.7     5.5    49.1     2.4    0.3   17.2              2.70
#>  4   46.4     6.1    37.3     1.8    0.5   18.9              6.4 
#>  5   48.8     6.32   42.8     0.2    0     20.5              8.76
#>  6   44.3     5.5    41.7     0.7    0.2   18.5              4.30
#>  7   38.9     5.23   54.1     1.19   0.51  15.1              0   
#>  8   42.1     4.66   33.8     0.95   0.2   16.2              2.10
#>  9   29.2     4.4    31.1     0.14   4.9   11.1              0   
#> 10   27.8     3.77   23.7     4.63   1.05  10.8              0   
#> # ℹ 70 more rows