cuda_ml_elastic_net {cuda.ml}

Train a linear model using elastic regression.

Description

Train a linear model with combined L1 and L2 priors as the regularizer.

Usage

cuda_ml_elastic_net(x, ...)

## Default S3 method:
cuda_ml_elastic_net(x, ...)

## S3 method for class 'data.frame'
cuda_ml_elastic_net(
  x,
  y,
  alpha = 1,
  l1_ratio = 0.5,
  max_iter = 1000L,
  tol = 0.001,
  fit_intercept = TRUE,
  normalize_input = FALSE,
  selection = c("cyclic", "random"),
  ...
)

## S3 method for class 'matrix'
cuda_ml_elastic_net(
  x,
  y,
  alpha = 1,
  l1_ratio = 0.5,
  max_iter = 1000L,
  tol = 0.001,
  fit_intercept = TRUE,
  normalize_input = FALSE,
  selection = c("cyclic", "random"),
  ...
)

## S3 method for class 'formula'
cuda_ml_elastic_net(
  formula,
  data,
  alpha = 1,
  l1_ratio = 0.5,
  max_iter = 1000L,
  tol = 0.001,
  fit_intercept = TRUE,
  normalize_input = FALSE,
  selection = c("cyclic", "random"),
  ...
)

## S3 method for class 'recipe'
cuda_ml_elastic_net(
  x,
  data,
  alpha = 1,
  l1_ratio = 0.5,
  max_iter = 1000L,
  tol = 0.001,
  fit_intercept = TRUE,
  normalize_input = FALSE,
  selection = c("cyclic", "random"),
  ...
)

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()]. * A __formula__ specifying the predictors and the outcome.

...

Optional arguments; currently unused.

y

A numeric vector (for regression) or factor (for classification) of desired responses.

alpha

Multiplier of the penalty term (i.e., the result would become and Ordinary Least Square model if alpha were set to 0). Default: 1. For numerical reasons, running elastic regression with alpha set to 0 is not advised. For the alpha-equals-to-0 scenario, one should use cuda_ml_ols to train an OLS model instead. Default: 1.

l1_ratio

The ElasticNet mixing parameter, with 0 <= l1_ratio <= 1. For l1_ratio = 0 the penalty is an L2 penalty. For l1_ratio = 1 it is an L1 penalty. For 0 < l1_ratio < 1, the penalty is a combination of L1 and L2. The penalty term is computed using the following formula: penalty = alpha * l1_ratio * ||w||_1 + 0.5 * alpha * (1 - l1_ratio) * ||w||^2_2 where ||w||_1 is the L1 norm of the coefficients, and ||w||_2 is the L2 norm of the coefficients.

max_iter

The maximum number of coordinate descent iterations. Default: 1000L.

tol

Stop the coordinate descent when the duality gap is below this threshold. Default: 1e-3.

fit_intercept

If TRUE, then the model tries to correct for the global mean of the response variable. If FALSE, then the model expects data to be centered. Default: TRUE.

normalize_input

Ignored when fit_intercept is FALSE. If TRUE, then the predictors will be normalized to have a L2 norm of 1. Default: FALSE.

selection

If "random", then instead of updating coefficients in cyclic order, a random coefficient is updated in each iteration. Default: "cyclic".

formula

A formula specifying the outcome terms on the left-hand side, and the predictor terms on the right-hand side.

data

When a __recipe__ or __formula__ is used, data is specified as a __data frame__ containing the predictors and (if applicable) the outcome.

Value

An elastic net regressor that can be used with the 'predict' S3 generic to make predictions on new data points.

Examples

library(cuda.ml)

model <- cuda_ml_elastic_net(
  formula = mpg ~ ., data = mtcars, alpha = 1e-3, l1_ratio = 0.6
)
cuda_ml_predictions <- predict(model, mtcars)

# predictions will be comparable to those from a `glmnet` model with `lambda`
# set to 1e-3 and `alpha` set to 0.6
# (in `glmnet`, `lambda` is the weight of the penalty term, and `alpha` is
#  the elastic mixing parameter between L1 and L2 penalties.

library(glmnet)

glmnet_model <- glmnet(
  x = as.matrix(mtcars[names(mtcars) != "mpg"]), y = mtcars$mpg,
  alpha = 0.6, lambda = 1e-3, nlambda = 1, standardize = FALSE
)

glm_predictions <- predict(
  glmnet_model, as.matrix(mtcars[names(mtcars) != "mpg"]),
  s = 0
)

print(
  all.equal(
    as.numeric(glm_predictions),
    cuda_ml_predictions$.pred,
    tolerance = 1e-2
  )
)