linear_regression {mlpack}

Simple Linear Regression and Prediction

Description

An implementation of simple linear regression and ridge regression using ordinary least squares. Given a dataset and responses, a model can be trained and saved for later use, or a pre-trained model can be used to output regression predictions for a test set.

Usage

linear_regression(
  input_model = NA,
  lambda = NA,
  test = NA,
  training = NA,
  training_responses = NA,
  verbose = FALSE
)

Arguments

input_model

Existing LinearRegression model to use (LinearRegression).

lambda

Tikhonov regularization for ridge regression. If 0, the method reduces to linear regression. Default value "0" (numeric).

test

Matrix containing X' (test regressors) (numeric matrix).

training

Matrix containing training set X (regressors) (numeric matrix).

training_responses

Optional vector containing y (responses). If not given, the responses are assumed to be the last row of the input file (numeric row).

verbose

Display informational messages and the full list of parameters and timers at the end of execution. Default value "FALSE" (logical).

Details

An implementation of simple linear regression and simple ridge regression using ordinary least squares. This solves the problem

y = X * b + e

where X (specified by "training") and y (specified either as the last column of the input matrix "training" or via the "training_responses" parameter) are known and b is the desired variable. If the covariance matrix (X'X) is not invertible, or if the solution is overdetermined, then specify a Tikhonov regularization constant (with "lambda") greater than 0, which will regularize the covariance matrix to make it invertible. The calculated b may be saved with the "output_predictions" output parameter.

Optionally, the calculated value of b is used to predict the responses for another matrix X' (specified by the "test" parameter):

y' = X' * b

and the predicted responses y' may be saved with the "output_predictions" output parameter. This type of regression is related to least-angle regression, which mlpack implements as the 'lars' program.

Value

A list with several components:

output_model

Output LinearRegression model (LinearRegression).

output_predictions

If –test_file is specified, this matrix is where the predicted responses will be saved (numeric row).

Author(s)

mlpack developers

Examples

# For example, to run a linear regression on the dataset "X" with responses
# "y", saving the trained model to "lr_model", the following command could be
# used:

## Not run: 
output <- linear_regression(training=X, training_responses=y)
lr_model <- output$output_model

## End(Not run)

# Then, to use "lr_model" to predict responses for a test set "X_test",
# saving the predictions to "X_test_responses", the following command could
# be used:

## Not run: 
output <- linear_regression(input_model=lr_model, test=X_test)
X_test_responses <- output$output_predictions

## End(Not run)