Package 'sprintr'

Title: Sparse Reluctant Interaction Modeling
Description: An implementation of a computationally efficient method to fit large-scale interaction models based on the reluctant interaction selection principle. The method and its properties are described in greater depth in Yu, G., Bien, J., and Tibshirani, R.J. (2019) "Reluctant interaction modeling", which is available at <arXiv:1907.08414>.
Authors: Guo Yu [aut, cre]
Maintainer: Guo Yu <[email protected]>
License: GPL-3
Version: 0.9.1
Built: 2025-02-01 03:27:10 UTC
Source: https://github.com/hugogogo/sprintr

Help Index

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,
  square = FALSE,
  num_keep = NULL,
  lambda1 = NULL,
  lambda3 = NULL,
  cv_step1 = FALSE,
  nlam1 = 10,
  nlam3 = 100,
  lam_min_ratio = ifelse(nrow(x) < ncol(x), 0.01, 1e-04),
  nfold = 5,
  foldid = NULL,
  verbose = FALSE,
  ...
)

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.
square

Indicator of whether squared effects should be fitted in Step 1. Default to be FALSE.
num_keep

A user specified number of candidate interactions to keep in Step 2. If num_keep is not specified (as default), it will be set to round[n / log n].
lambda1

Tuning parameter values for Step 1. lambda1 is a vector. Default to be NULL, and the program will compute its own lambda1 based on nlam1 and lam_min_ratio.
lambda3

Tuning parameter values for Step 3. lambda3 is a matrix, where the k-th column is the list of tuning parameter in Step 3 corresponding to Step 1 using lambda1[k]. Default to be NULL, and the program will compute its own lambda3 based on nlam3 and lam_min_ratio.
cv_step1

Indicator of whether cross-validation of lambda1 should be carried out in Step 1 before subsequent steps. Default is FALSE.
nlam1

the number of values in lambda1. If not specified, they will be all set to 10.
nlam3

the number of values in each column of lambda3. If not specified, they will be all set to 100.
lam_min_ratio

The ratio of the smallest and the largest values in lambda1 and each column of lambda2. The largest value 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.
verbose

If TRUE, a progress bar shows the progress of the fitting.
...

other arguments to be passed to the glmnet calls, such as alpha or penalty.factor

Value

An object of S3 class "sprinter".

n

The sample size.

p

The number of main effects.

square

The square parameter passed into sprinter.

a0_step3

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.

fitted

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

num_keep

The value of num_keep.

cvm

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

cvse

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

foldid

Fold assignment. A vector of length n.

i_lambda1_best

The index in lambda1 that is chosen by CV by minimizing cvm.

i_lambda3_best

The index in lambda3 that is chosen by CV by minimizing cvm.

lambda1_best

The value of lambda1 that is chosen by CV by minimizing cvm.

lambda3_best

The value of lambda3 that is chosen by CV by minimizing cvm.

call

Function call.

See Also

predict.cv.sprinter

Examples

n <- 100
p <- 100
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)

Two-stage hierarchical lasso

Description

An implementation of the two-stage lasso studied in Hao et, al (2018).

Usage

hier_lasso(
  x,
  y,
  lambda = NULL,
  nlam = 100,
  lam_choice = "min",
  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.
...

other arguments to be passed to the glmnet calls, such as alpha or penalty.factor

Value

An object of S3 class "cv.hier".

n

The sample size.

p

The number of main effects.

fit

The whole cv.glmnet fit object.

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.

Examples

set.seed(123)
n <- 100
p <- 200
# dense input
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 <- hier_lasso(x = x, y = y)

Plot function of cv.sprinter fit

Description

This function produces plots of cross-validation for cv.sprinter.

Usage

## S3 method for class 'cv.sprinter'
plot(fit)

Arguments

fit

A "cv.sprinter" object.

Details

The orange pairs on the top of the plot shows the number of non-zero (main effects, interactions) selected by each value of lambda. Adopted from the function plot.cv.rgam from package relgam by Kenneth Tay and Robert Tibshirani.

See Also

cv.sprinter.

Examples

set.seed(123)
n <- 100
p <- 200
# dense input
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)

plot(mod)

Plot function of sprinter fit

Description

Produces a two-panel plot of the sprinter object showing coefficient paths for both main effects and interactions.

Usage

## S3 method for class 'sprinter'
plot(fit, which = 1, label = TRUE, index = NULL)

Arguments

fit

Fitted sprinter object.
which

The tuning parameter considered in Step 2.
label

If TRUE (default), annotate the plot with variable labels.
index

Lambda indices to plot

Details

A two panel plot is produced, that summarizes the main effects (left) and interaction (right) coefficients, as a function of lambda. Adopted from the function summary.rgam from package relgam by Kenneth Tay and Robert Tibshirani.

Examples

set.seed(123)
n <- 100
p <- 100
# dense input
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)
fit <- sprinter(x = x, y = y)

plot(fit)

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)

Calculate prediction from a other object.

Description

Calculate prediction from a other object.

Usage

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

Arguments

object

a fitted other 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)

Calculate prediction from a sprinter object.

Description

Calculate prediction from a sprinter object.

Usage

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

Arguments

object

a fitted 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 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 <- sprinter(x = x, y = y)
fitted <- predict(mod, newdata = x)

Print the cross validation information of cv.sprinter

Description

Print a summary of the cross-validation information for running cv.sprinter.

Usage

## S3 method for class 'cv.sprinter'
print(fit, digits = max(3, getOption("digits") - 3), ...)

Arguments

fit

A fitted cv.sprinter object.
digits

Significant digits in printout.

Details

This function takes in a cv.sprinter object and produces summary of the cross-validation informationabout the tuning parameters (in Step 3) selected by lambda.min and lambda.1se. Adopted from the function print.cv.rgam from package relgam by Kenneth Tay and Robert Tibshirani.

See Also

cv.sprinter, print.printer.

Examples

set.seed(123)
n <- 100
p <- 100
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)

fit.cv <- cv.sprinter(x = x, y = y)
print(fit.cv)

Print a summary of the sprinter fit

Description

Print a summary of the sprinter fit at each step along the path of tuning parameters used in Step 3, for any given tuning parameter in Step 1.

Usage

## S3 method for class 'sprinter'
print(fit, which = 1, digits = max(3, getOption("digits") - 3), ...)

Arguments

fit

A sprinter object.
which

Which tuning parameter of Step 1 to print. Default is 1.
digits

Significant digits in printout.
...

Additional print arguments.

Details

The function produces a three-column matrix with tuning parameter values (in Step 3), number of nonzero main effects, and the number of nonzero interactions. Adopted from the function print.rgam from package relgam by Kenneth Tay and Robert Tibshirani.

See Also

sprinter.

Examples

set.seed(123)
n <- 100
p <- 100
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)
fit <- sprinter(x = x, y = y)

print(fit, which = 3)

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 3 columns, representing the index pair of the selected interactions, and the corresponding absolute correlation with the residual.

Sure Independence Screening in Step 2 for sparse design matrix

Description

Sure Independence Screening in Step 2 for sparse design matrix

Usage

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

Arguments

x

a n-by-p sparse matrix of 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 3 columns, representing the index pair of the selected interactions, and the corresponding absolute correlation with the residual.

Sure independence screening followed by lasso

Description

Sure independence screening followed by lasso

Usage

sis_lasso(
  x,
  y,
  num_keep = NULL,
  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 variables to keep in the screening phase
...

other arguments to be passed to the glmnet calls, such as alpha or penalty.factor

Value

An object of S3 class "cv.hier".

n

The sample size.

p

The number of main effects.

fit

The whole cv.glmnet fit object.

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.

Examples

set.seed(123)
n <- 100
p <- 200
# dense input
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 <- hier_lasso(x = x, y = y)

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,
  square = FALSE,
  num_keep = NULL,
  lambda1 = NULL,
  lambda3 = NULL,
  cv_step1 = FALSE,
  nlam1 = 10,
  nlam3 = 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.
square

Indicator of whether squared effects should be fitted in Step 1. Default to be FALSE.
num_keep

A user specified number of candidate interactions to keep in Step 2. If num_keep is not specified (as default), it will be set to round[n / log n].
lambda1

Tuning parameter values for Step 1. lambda1 is a vector. Default to be NULL, and the program will compute its own lambda1 based on nlam1 and lam_min_ratio.
lambda3

Tuning parameter values for Step 3. lambda3 is a matrix, where the k-th column is the list of tuning parameter in Step 3 corresponding to Step 1 using lambda1[k]. Default to be NULL, and the program will compute its own lambda3 based on nlam3 and lam_min_ratio.
cv_step1

Indicator of whether cross-validation of lambda1 should be carried out in Step 1 before subsequent steps. Default is FALSE.
nlam1

the number of values in lambda1. If not specified, they will be all set to 10.
nlam3

the number of values in each column of lambda3. If not specified, they will be all set to 100.
lam_min_ratio

The ratio of the smallest and the largest values in lambda1 and each column of lambda2. The largest value is usually the smallest value for which all coefficients are set to zero. Default to be 1e-2 in the n < p setting.
...

other arguments to be passed to the glmnet calls, such as alpha or penalty.factor

Value

An object of S3 class "sprinter".

square

The square parameter passed into sprinter

n

The number of observations in the dataset

p

The number of main effects

step1

The output from fitting Step 1

lambda1

The path of tuning parameters passed into / computed for fitting Step 1

step2

The output from the screening Step 2

num_keep

The path of tuning parameters for Step 2

step3

The output from fitting Step 3

lambda3

The path of tuning parameters passed into / computed for fitting Step 3

main_center

Column centers of the input main effects

main_scale

Column scales of the input main effects

call

Function call.

See Also

cv.sprinter

Examples

set.seed(123)
n <- 100
p <- 100
# dense input
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)

# sparse input
library(Matrix)
x <- Matrix::Matrix(0, n, p)
idx <- cbind(sample(seq(n), size = 10, replace = TRUE), sample(seq(p), size = 10, replace = TRUE))
x[idx] <- 1
y <- x[, 1] - 2 * x[, 2] + 3 * x[, 1] * x[, 3] - 4 * x[, 4] * x[, 5] + rnorm(n)
mod <- sprinter(x = x, y = y)