prediction_Lasso: Find the optimum lambda for a Lasso model

In MokyoZhou/lassoenet: An Interactive Implementation of Penalised Regressions

Description

This function takes in inputs defined by the user and computes the optimum λ for a Lasso model. The function is very flexible and allows for many different settings such as, data splitting and repeated error curves. This function also fully supports multiple-cores parallelisation. The main fitting process is cv.glmnet() from the package glmnet.

Usage

prediction_Lasso(data = data, x.indices = x.indices, response = response,
  err.curves = 0, splits = 0, type.lambda = "lambda.min",
  interactive = FALSE, parallel = FALSE)

Arguments

data	A well-cleaned data.frame which will be used for modelling. The data.frame is also required to have more rows than columns.
x.indices	The coordinates of the predictors that you would like to model with. Please provide a vecotr of locations e.g. seq(2,6).
response	The location of the response within the data.frame.
err.curves	Due to the fact that the Cross-validation process is random, it is very likely that the result will vary quite a bit (if without a seed). This function offers to fit the model multiple times (thus, creating multiple error curves over a range of λs) and average across these multiple error curves. The optimum λ within the range is the one that has the lowest averaged error. Note you can set this argument to 0 if you do not wish to stabilise the process, in which case the seed (1234567) will be used for the CV process. A positive integer indicates the number of error curves to be fitted. Default is 0.
splits	A element specifying the training proportion and the test proportion will be set as 1 - traning.proportion. Note if you set splits = 0, the function will use the whole dataset for modelling. The default is splits = 0.
type.lambda	Either "lambda.min" or "lambda.1se". Default is "lambda.min. Note when err.curves >0, this argument will not be used.
interactive	If you are running this function, please ALWAYS keep this argument to FALSE, which is the default.
parallel	parallelisation supported,default is FALSE.

Value

a list with elements:

seed	if err.curves = 0, the seed (1234567) will be used to compute the λ.
number of err.curves	if err.curves > 0, this argument shows how many error curves there are.
best lambda	if err.curves = 0, this is the λ that has the lowest cross validation error from a Lasso fit with seed (1234567).This is the usual way to select λ. if err.curves > 0, this is the the λ that has the lowest averaged error curves value.
prediction error	if err.curves = 0 and splits = 0, (no error curves and no splitting), this simply is the cross validation score (associated with the best λ) from the seed (1234567). if err.curves > 0 and splits = 0, (error curves but no splitting), this is the averaged cross-validation scores associated with the optimum λ from using the whole dataset. if err.curves = 0 and splits != 0, (no error curves but with split), this is the out of sample Mean-squared error on the test set with λ selected with seed(1234567) on the training set. if err.curves > 0 and splits != 0, (error curves and splitting), this is the out of sample Mean-squared error on the test set with λ selected by averaging across the error curves on the training set.
prediction_lower	The function will only compute this when splits = 0. For more information see details below.
prediction_upper	The function will only compute this when splits = 0, For more information see details below.
rooted prediction error	The function will only compute this when splits != 0. This is the out of sample root mean-square error on the test set.
absolute prediction error	The function will only compute this when splits != 0. This is the out of sample mean absolute error on the test set.

Details

This function further develops on the cv.glmnet() function from the glmnet package to allow for more flexibility. More specifically, it allows users the option to split the dataset into a traning set and a test set, which usually gives give more realistic assessment of perdictive performance than using the whole dataset.

The function also offers an alternative to compute the optimum λ by averaging across the error curves instead of using a fixed seed. From experneice, for medium size datasets, with err.curves larger than 1000, the optimum λ will usually converge to a stable value that consistently achieves the lowest averaged across error curves value.

The 95 percent confidence interval for this lowest averaged error curves value, when using the whole dataset e.g. splits = 0, is computed by using the quantile() command on the cross-validation scores associated with this optimum λ. Do not worry, we will also provide you with a plot that contains these error curves from the output, so you can see how it is that the optimum λ value got selected and with its 95 percent CI around it. When we are not stabilising the process e.g. err.curve = 0 but still using the whole dataset splits = 0, we compute the λ with the seed (1234567) and the associated CI is computed by using the standard error provided by the glmnet package and assuming normality. When we do split the dataset however, we provide out of sample mean squared error(MSE), RMSE and MAE instead of 95 percent CI.

Author(s)

Mokyo Zhou

Examples

library(glmnet)
data(QuickStartExample)
#please NOTE: you can access "QuickStartExample" by using: data.frame(y,x)


#non-split, no error curves, using lambda.min
result <- prediction_Lasso(data = data.frame(y,x), x.indices = seq(2,21),
response = 1, err.curves = 0,splits = 0)

#0.8 /0.2 split, no error curves, using lambda.1se
result <- prediction_Lasso(data = data.frame(y,x), x.indices = seq(2,21),
response = 1, err.curves = 0, splits = 0.8,type.lambda = "lambda.1se")

#non-split, but with 100 error curves with parallel (2 cores)
#cl <- parallel::makeCluster(2)
#doParallel::registerDoParallel(cl)
result <- prediction_Lasso(data = data.frame(y,x), x.indices = seq(2,21),
response = 1, err.curves = 100, splits = 0,parallel = TRUE)

#0.8 / 0.2 split, with 100 error curves with parallel (2 cores)
#cl <- parallel::makeCluster(2)
#doParallel::registerDoParallel(cl)
result <- prediction_Lasso(data = data.frame(y,x), x.indices = seq(2,21),
response = 1, err.curves = 100, splits = 0.8,parallel = TRUE)

MokyoZhou/lassoenet documentation built on May 20, 2019, 11:38 a.m.