Package 'sprintr'

Running sprinter with cross-validation

Description

The main cross-validation function to select the best sprinter fit for a path of tuning parameters.

Usage

cv.sprinter(x, y, num_keep = NULL, square = FALSE, lambda = NULL,
  nlam = 100, lam_min_ratio = ifelse(nrow(x) < ncol(x), 0.01, 1e-04),
  nfold = 5, foldid = NULL)

Arguments

x	An n by p design matrix of main effects. Each row is an observation of p main effects.
y	A response vector of size n.
num_keep	Number of candidate interactions to keep in Step 2. If num_keep is not specified (as default), it will be set to [n / log n].
square	Indicator of whether squared effects should be fitted in Step 1. Default to be FALSE.
lambda	A user specified list of tuning parameter. Default to be NULL, and the program will compute its own lambda path based on nlam and lam_min_ratio.
nlam	The number of lambda values. Default value is 100.
lam_min_ratio	The ratio of the smallest and the largest values in lambda. The largest value in lambda is usually the smallest value for which all coefficients are set to zero. Default to be 1e-2 in the n < p setting.
nfold	Number of folds in cross-validation. Default value is 5. If each fold gets too view observation, a warning is thrown and the minimal nfold = 3 is used.
foldid	A vector of length n representing which fold each observation belongs to. Default to be NULL, and the program will generate its own randomly.

Value

An object of S3 class "sprinter".

n

The sample size.

p

The number of main effects.

a0

estimate of intercept corresponding to the CV-selected model.

compact

A compact representation of the selected variables. compact has three columns, with the first two columns representing the indices of a selected variable (main effects with first index = 0), and the last column representing the estimate of coefficients.

fit

The whole glmnet fit object in Step 3.

fitted

fitted value of response corresponding to the CV-selected model.

lambda

The sequence of lambda values used.

cvm

The averaged estimated prediction error on the test sets over K folds.

cvsd

The standard error of the estimated prediction error on the test sets over K folds.

foldid

Fold assignment. A vector of length n.

ibest

The index in lambda that is chosen by CV.

call

Function call.

See Also

predict.cv.sprinter

Examples

n <- 100
p <- 200
x <- matrix(rnorm(n * p), n, p)
y <- x[, 1] - 2 * x[, 2] + 3 * x[, 1] * x[, 3] - 4 * x[, 4] * x[, 5] + rnorm(n)
mod <- cv.sprinter(x = x, y = y)

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Calculate prediction from a cv.sprinter object.

Description

Calculate prediction from a cv.sprinter object.

Usage

## S3 method for class 'cv.sprinter'
predict(object, newdata, ...)

Arguments

object	a fitted cv.sprinter object.
newdata	a design matrix of all the p main effects of some new observations of which predictions are to be made.
...	additional argument (not used here, only for S3 generic/method consistency)

Value

The prediction of newdata by the cv.sprinter fit object.

Examples

n <- 100
p <- 200
x <- matrix(rnorm(n * p), n, p)
y <- x[, 1] + 2 * x[, 2] - 3 * x[, 1] * x[, 2] + rnorm(n)
mod <- cv.sprinter(x = x, y = y)
fitted <- predict(mod, newdata = x)

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Sure Independence Screening in Step 2

Description

Sure Independence Screening in Step 2

Usage

screen_cpp(x, y, num_keep, square = FALSE, main_effect = FALSE)

Arguments

x	a n-by-p matrix of main effects, with i.i.d rows, and each row represents a vector of observations of p main-effects
y	a vector of length n. In sprinter, y is the residual from step 1
num_keep	the number of candidate interactions in Step 2. Default to be n / [log n]
square	An indicator of whether squared effects should be considered in Step 1 (NOT Step 2!). square == TRUE if squared effects have been considered in Step 1, i.e., squared effects will NOT be considered in Step 2.
main_effect	An indicator of whether main effects should also be screened. Default to be false. The functionality of main_effect = true is not used in sprinter, but for SIS_lasso.

Value

an matrix of 2 columns, representing the index pair of the selected interactions.

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Sparse Reluctant Interaction Modeling

Description

This is the main function that fits interaction models with a path of tuning parameters (for Step 3).

Usage

sprinter(x, y, num_keep = NULL, square = FALSE, lambda = NULL,
  nlam = 100, lam_min_ratio = ifelse(nrow(x) < ncol(x), 0.01, 1e-04))

Arguments

x	An n by p design matrix of main effects. Each row is an observation of p main effects.
y	A response vector of size n.
num_keep	Number of candidate interactions to keep in Step 2. If num_keep is not specified (as default), it will be set to [n / log n].
square	Indicator of whether squared effects should be fitted in Step 1. Default to be FALSE.
lambda	A user specified list of tuning parameter. Default to be NULL, and the program will compute its own lambda path based on nlam and lam_min_ratio.
nlam	The number of lambda values. Default value is 100.
lam_min_ratio	The ratio of the smallest and the largest values in lambda. The largest value in lambda is usually the smallest value for which all coefficients are set to zero. Default to be 1e-2 in the n < p setting.

Value

An object of S3 class "sprinter".

n

The sample size.

p

The number of main effects.

a0

Estimate of intercept.

coef

Estimate of regression coefficients.

idx

Indices of all main effects and interactions in Step 3.

fitted

Fitted response value. It is a n-by-nlam matrix, with each column representing a fitted response vector for a value of lambda.

lambda

The sequence of lambda values used.

call

Function call.

See Also

cv.sprinter

Examples

set.seed(123)
n <- 100
p <- 200
x <- matrix(rnorm(n * p), n, p)
y <- x[, 1] - 2 * x[, 2] + 3 * x[, 1] * x[, 3] - 4 * x[, 4] * x[, 5] + rnorm(n)
mod <- sprinter(x = x, y = y)

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