prediction_ElasticNet: Find the optimum pair (alpha, lambda) for an Elastic Net...

In MokyoZhou/lassoenet: An Interactive Implementation of Penalised Regressions

Description

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

Usage

prediction_ElasticNet(data = data, x.indices = x.indices,
  response = response, err.curves = 0, splits = 0, step.size = 0.2,
  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, the result can vary qutie a bit (if without a seed). In order to stabilise the CV process, the function fits a collection of Elastic Net models, each with a different α value, multiple times. Therefore, for EACH α, we will create multiple error curves over a range of λs and the optimum pair (α, λ) is the pair that has the lowest averaged error curves value (local optimum). We have an optimum pair (α, λ) for each α and the global optimum pair is the pair that has the overall lowest averaged error curved value. Note, with this setting, the process tends to be slow. Thus, we highly suggest multiple-cores parallelisation. 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 postive integer indicates the stabilisation process is desired. For more information about how this works, please see section details below.
splits	A element specifying the training proportion and test proportion will be set as 1- traing.proportion. Note if you set splits = 0, the function will use the whole dataset for modelling. The default is splits = 0.
step.size	The step size of the α grid. An adjustable value within [0,1]. Default is step.size = 0.2. Considering the time consumption, this should be chosen very carefully if err.curves >0 is also desired.
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 α and λ.
number of err.curves	if err.curves >0, this shows how many error curves there are (for each α).
best alpha	if err.curves = 0 (no stabilization), this is a part of the optimum pair (α, λ) that has the lowest cross validation error (out of a single 2D grid search) with seed (1234567). This is the usual way of finding out (α, λ). if err.curves > 0 (with stabilization), this is a part of the global optimum pair (α, λ) that has the overall lowest averaged error curves value among all the local optimum pairs.
best lambda	A part of the global optimum pair (α, λ). For more information on how the α and λ get selected, please see the detail section.
prediction error	if err.curves = 0 and splits = 0, (no error curves and no splitting), this is the cross validation score associated with the best (α,λ) pair from the a 2D grid search with seed (1234567). if err.curves > 0 and splits = 0, (error curves but no splitting), this is the overall lowest averaged cross-validation scores associated with the global optimum (α, λ) pair 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 the optimum pair (α,λ) selected with a 2D grid search 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 the global optimum pair (α,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. The function allows users the option to split the dataset into a traning set and a test set, which usually gives more realistic assessment of perdictive performance than using the whole dataset.

The function also offers an alternative to compute the global optimum (α, λ) pair by averaging across the error curves instead of using a fixed seed. More specifically, this stabilisation takes a double looping structure where the outer layer contains the α grid and the inner loop builds multiple Elastic Net models for each α in the outer layer. In this way, for each α, we create say, B, Elastic Net models and thus, this results in B error curves over a range of λs. For each α then, the function finds the local optimum pair (α, λ) by averaging across these error curves and find the pair that has the lowest averaged cross validation errors. After the function finds all the local optimum pairs, the golbal optimum pair is the pair that has the overall lowest averaged cross validation error. From experneice, for medium size datasets, with err.curves larger than 1500, the global optimum (α, λ) will usually converge to stable values that consistently achieves the overall lowest averaged across error curves value.

When splits = 0 (no spliting), the 95 percent confidence interval for such a prediction error (overall lowest averaged error curves value) is generated as follows: from the corresponding error curves for that optimum α, the cross-validation scores corresponding to the global optimum (α, λ) are extracted and the command quantile() is then used to compute the 95 percent confidence interval. 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 pair values 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 (α, λ) pair 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, step.size =0.2, using lambda.min
result <- prediction_ElasticNet(data = data.frame(y,x), x.indices = seq(2,21),
response = 1, err.curves = 0 ,splits = 0, step.size =0.2,
type.lambda="lambda.min")

#0.8 /0.2 split, no error curves, step.size=0.1, using lambda.1se
result <- prediction_ElasticNet(data = data.frame(y,x), x.indices = seq(2,21),
response = 1, err.curves = 0, splits = 0.8, step.size = 0.1,
type.lambda = "lambda.1se")

#non-split, but with 100 error curves, step.size=0.3, with parallel (2 cores)
#cl <- parallel::makeCluster(2)
#doParallel::registerDoParallel(cl)
result <- prediction_ElasticNet(data = data.frame(y,x), x.indices = seq(2,21),
response = 1, err.curves = 100, splits = 0, step.size = 0.3, parallel = TRUE)

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

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