brulee_linear_reg() fits a linear regression model.

## Usage

brulee_linear_reg(x, ...)

# S3 method for default
brulee_linear_reg(x, ...)

# S3 method for data.frame
brulee_linear_reg(
x,
y,
epochs = 20L,
penalty = 0.001,
mixture = 0,
validation = 0.1,
optimizer = "LBFGS",
learn_rate = 1,
momentum = 0,
batch_size = NULL,
stop_iter = 5,
verbose = FALSE,
...
)

# S3 method for matrix
brulee_linear_reg(
x,
y,
epochs = 20L,
penalty = 0.001,
mixture = 0,
validation = 0.1,
optimizer = "LBFGS",
learn_rate = 1,
momentum = 0,
batch_size = NULL,
stop_iter = 5,
verbose = FALSE,
...
)

# S3 method for formula
brulee_linear_reg(
formula,
data,
epochs = 20L,
penalty = 0.001,
mixture = 0,
validation = 0.1,
optimizer = "LBFGS",
learn_rate = 1,
momentum = 0,
batch_size = NULL,
stop_iter = 5,
verbose = FALSE,
...
)

# S3 method for recipe
brulee_linear_reg(
x,
data,
epochs = 20L,
penalty = 0.001,
mixture = 0,
validation = 0.1,
optimizer = "LBFGS",
learn_rate = 1,
momentum = 0,
batch_size = NULL,
stop_iter = 5,
verbose = FALSE,
...
)

## Arguments

x

Depending on the context:

• A data frame of predictors.

• A matrix of predictors.

• A recipe specifying a set of preprocessing steps created from recipes::recipe().

The predictor data should be standardized (e.g. centered or scaled).

...

Options to pass to the learning rate schedulers via set_learn_rate(). For example, the reduction or steps arguments to schedule_step() could be passed here.

y

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

• A data frame with 1 numeric column.

• A matrix with 1 numeric column.

• A numeric vector.

epochs

An integer for the number of epochs of training.

penalty

The amount of weight decay (i.e., L2 regularization).

mixture

Proportion of Lasso Penalty (type: double, default: 0.0). A value of mixture = 1 corresponds to a pure lasso model, while mixture = 0 indicates ridge regression (a.k.a weight decay).

validation

The proportion of the data randomly assigned to a validation set.

optimizer

The method used in the optimization procedure. Possible choices are 'LBFGS' and 'SGD'. Default is 'LBFGS'.

learn_rate

A positive number that controls the initial rapidity that the model moves along the descent path. Values around 0.1 or less are typical.

momentum

A positive number usually on [0.50, 0.99] for the momentum parameter in gradient descent. (optimizer = "SGD" only)

batch_size

An integer for the number of training set points in each batch. (optimizer = "SGD" only)

stop_iter

A non-negative integer for how many iterations with no improvement before stopping.

verbose

A logical that prints out the iteration history.

formula

A formula specifying the outcome term(s) on the left-hand side, and the predictor term(s) on the right-hand side.

data

When a recipe or formula is used, data is specified as:

• A data frame containing both the predictors and the outcome.

## Value

A brulee_linear_reg object with elements:

• models_obj: a serialized raw vector for the torch module.

• estimates: a list of matrices with the model parameter estimates per epoch.

• best_epoch: an integer for the epoch with the smallest loss.

• loss: A vector of loss values (MSE) at each epoch.

• dim: A list of data dimensions.

• y_stats: A list of summary statistics for numeric outcomes.

• parameters: A list of some tuning parameter values.

• blueprint: The hardhat blueprint data.

## Details

This function fits a linear combination of coefficients and predictors to model the numeric outcome. The training process optimizes the mean squared error loss function.

The function internally standardizes the outcome data to have mean zero and a standard deviation of one. The prediction function creates predictions on the original scale.

By default, training halts when the validation loss increases for at least step_iter iterations. If validation = 0 the training set loss is used.

The predictors data should all be numeric and encoded in the same units (e.g. standardized to the same range or distribution). If there are factor predictors, use a recipe or formula to create indicator variables (or some other method) to make them numeric. Predictors should be in the same units before training.

The model objects are saved for each epoch so that the number of epochs can be efficiently tuned. Both the coef() and predict() methods for this model have an epoch argument (which defaults to the epoch with the best loss value).

The use of the L1 penalty (a.k.a. the lasso penalty) does not force parameters to be strictly zero (as it does in packages such as glmnet). The zeroing out of parameters is a specific feature the optimization method used in those packages.

predict.brulee_linear_reg(), coef.brulee_linear_reg(), autoplot.brulee_linear_reg()

## Examples

# \donttest{
if (torch::torch_is_installed()) {

## -----------------------------------------------------------------------------

data(ames, package = "modeldata")

ames$Sale_Price <- log10(ames$Sale_Price)

set.seed(122)
in_train <- sample(1:nrow(ames), 2000)
ames_train <- ames[ in_train,]
ames_test  <- ames[-in_train,]

# Using matrices
set.seed(1)
brulee_linear_reg(x = as.matrix(ames_train[, c("Longitude", "Latitude")]),
y = ames_train\$Sale_Price,
penalty = 0.10, epochs = 1, batch_size = 64)

# Using recipe
library(recipes)

ames_rec <-
recipe(Sale_Price ~ Bldg_Type + Neighborhood + Year_Built + Gr_Liv_Area +
Full_Bath + Year_Sold + Lot_Area + Central_Air + Longitude + Latitude,
data = ames_train) %>%
# Transform some highly skewed predictors
step_BoxCox(Lot_Area, Gr_Liv_Area) %>%
# Lump some rarely occurring categories into "other"
step_other(Neighborhood, threshold = 0.05)  %>%
# Encode categorical predictors as binary.
step_dummy(all_nominal_predictors(), one_hot = TRUE) %>%
step_interact(~ starts_with("Central_Air"):Year_Built) %>%
step_zv(all_predictors()) %>%
step_normalize(all_numeric_predictors())

set.seed(2)
fit <- brulee_linear_reg(ames_rec, data = ames_train,
epochs = 5, batch_size = 32)
fit

autoplot(fit)

library(ggplot2)

predict(fit, ames_test) %>%
bind_cols(ames_test) %>%
ggplot(aes(x = .pred, y = Sale_Price)) +
geom_abline(col = "green") +
geom_point(alpha = .3) +
lims(x = c(4, 6), y = c(4, 6)) +
coord_fixed(ratio = 1)

library(yardstick)
predict(fit, ames_test) %>%
bind_cols(ames_test) %>%
rmse(Sale_Price, .pred)

}
#> For binary classification, the first factor level is assumed to be the event.
#> Use the argument event_level = "second" to alter this as needed.
#> # A tibble: 1 × 3
#>   .metric .estimator .estimate
#>   <chr>   <chr>          <dbl>
#> 1 rmse    standard      0.0999

# }