Type: Package
Title: Generalized Linear Models with Truncated Lasso Penalty
Version: 2.0.2
Date: 2024-10-01
URL: https://yuyangyy.com/glmtlp/
Depends: R (≥ 3.5.0)
Imports: foreach, doParallel, ggplot2
Suggests: rmarkdown, knitr, testthat (≥ 3.0.0)
Description: Extremely efficient procedures for fitting regularization path with l0, l1, and truncated lasso penalty for linear regression and logistic regression models. This version is a completely new version compared with our previous version, which was mainly based on R. New core algorithms are developed and are now written in C++ and highly optimized.
Encoding: UTF-8
License: GPL-3
LazyData: true
Author: Chunlin Li ORCID iD [aut, cph], Yu Yang ORCID iD [aut, cre, cph], Chong Wu ORCID iD [aut, cph], Xiaotong Shen [ths, cph], Wei Pan [ths, cph]
Maintainer: Yu Yang <yuyang.stat@gmail.com>
RoxygenNote: 7.3.2
VignetteBuilder: knitr
Config/testthat/edition: 3
NeedsCompilation: yes
Packaged: 2024-10-02 14:56:35 UTC; yuyang
Repository: CRAN
Date/Publication: 2024-10-02 20:20:14 UTC

glmtlp: A package for fitting a GLM with l0, l1, and tlp regularization.

Description

The package provides 3 penalties: l0, l1, and tlp and 3 distribution families: gaussian, binomial, and poisson.

Fit generalized linear models via penalized maximum likelihood. The regularization path is computed for the l0, lasso, or truncated lasso penalty at a grid of values for the regularization parameter lambda or kappa. Fits linear and logistic regression models.

Usage

glmtlp(
  X,
  y,
  family = c("gaussian", "binomial"),
  penalty = c("l0", "l1", "tlp"),
  nlambda = ifelse(penalty == "l0", 50, 100),
  lambda.min.ratio = ifelse(nobs < nvars, 0.05, 0.001),
  lambda = NULL,
  kappa = NULL,
  tau = 0.3 * sqrt(log(nvars)/nobs),
  delta = 2,
  tol = 1e-04,
  weights = NULL,
  penalty.factor = rep(1, nvars),
  standardize = FALSE,
  dc.maxit = 20,
  cd.maxit = 10000,
  nr.maxit = 20,
  ...
)

Arguments

X

Input matrix, of dimension nobs x nvars; each row is an observation vector.

y

Response variable, of length nobs. For family="gaussian", it should be quantitative; for family="binomial", it should be either a factor with two levels or a binary vector.

family

A character string representing one of the built-in families. See Details section below.

penalty

A character string representing one of the built-in penalties. "l0" represents the L_0 penalty, "l1" represents the lasso-type penalty (L_1 penalty), and "tlp" represents the truncated lasso penalty.

nlambda

The number of lambda values. Default is 100.

lambda.min.ratio

The smallest value for lambda, as a fraction of lambda.max, the smallest value for which all coefficients are zero. The default depends on the sample size nobs relative to the number of variables nvars. If nobs > nvars, the default is 0.0001, and if nobs < nvars, the default is 0.01.

lambda

A user-supplied lambda sequence. Typically, users should let the program compute its own lambda sequence based on nlambda and lambda.min.ratio. Supplying a value of lambda will override this. WARNING: please use this option with care. glmtlp relies on warms starts for speed, and it's often faster to fit a whole path than a single fit. Therefore, provide a decreasing sequence of lambda values if you want to use this option. Also, when penalty = 'l0', it is not recommended for the users to supply this parameter.

kappa

A user-supplied kappa sequence. Typically, users should let the program compute its own kappa sequence based on nvars and nobs. This sequence is used when penalty = 'l0'.

tau

A tuning parameter used in the TLP-penalized regression models. Default is 0.3 * sqrt(log(nvars)/nobs).

delta

A tuning parameter used in the coordinate majorization descent algorithm. See Yang, Y., & Zou, H. (2014) in the reference for more detail.

tol

Tolerance level for all iterative optimization algorithms.

weights

Observation weights. Default is 1 for each observation.

penalty.factor

Separate penalty factors applied to each coefficient, which allows for differential shrinkage. Default is 1 for all variables.

standardize

Logical. Whether or not standardize the input matrix X; default is TRUE.

dc.maxit

Maximum number of iterations for the DC (Difference of Convex Functions) programming; default is 20.

cd.maxit

Maximum number of iterations for the coordinate descent algorithm; default is 10^4.

nr.maxit

Maximum number of iterations for the Newton-Raphson method; default is 500.

...

Additional arguments.

Details

The sequence of models indexed by lambda (when penalty = c('l1', 'tlp')) or kappa (when penalty = 'l0') is fit by the coordinate descent algorithm.

The objective function for the "gaussian" family is:

1/2 RSS/nobs + \lambda*penalty,

and for the other models it is:

-loglik/nobs + \lambda*penalty.

Also note that, for "gaussian", glmtlp standardizes y to have unit variance (using 1/(n-1) formula).

## Details on family option

glmtlp currently only supports built-in families, which are specified by a character string. For all families, the returned object is a regularization path for fitting the generalized linear regression models, by maximizing the corresponding penalized log-likelihood. glmtlp(..., family="binomial") fits a traditional logistic regression model for the log-odds.

## Details on penalty option

The built-in penalties are specified by a character string. For l0 penalty, kappa sequence is used for generating the regularization path, while for l1 and tlp penalty, lambda sequence is used for generating the regularization path.

Value

An object with S3 class "glmtlp".

beta

a nvars x length(kappa) matrix of coefficients when penalty = 'l0'; or a nvars x length(lambda) matrix of coefficients when penalty = c('l1', 'tlp').

call

the call that produces this object.

family

the distribution family used in the model fitting.

intercept

the intercept vector, of length(kappa) when penalty = 'l0' or length(lambda) when penalty = c('l1', 'tlp').

lambda

the actual sequence of lambda values used. Note that the length may be smaller than the provided nlambda due to removal of saturated values.

penalty

the penalty type in the model fitting.

penalty.factor

the penalty factor for each coefficient used in the model fitting.

tau

the tuning parameter used in the model fitting, available when penalty = 'tlp'.

glmtlp functions

'glmtlp()', 'cv.glmtlp()'

Author(s)

Maintainer: Yu Yang yuyang.stat@gmail.com (ORCID) [copyright holder]

Authors:

Other contributors:

Chunlin Li, Yu Yang, Chong Wu
Maintainer: Yu Yang yang6367@umn.edu

References

Shen, X., Pan, W., & Zhu, Y. (2012). Likelihood-based selection and sharp parameter estimation. Journal of the American Statistical Association, 107(497), 223-232.
Shen, X., Pan, W., Zhu, Y., & Zhou, H. (2013). On constrained and regularized high-dimensional regression. Annals of the Institute of Statistical Mathematics, 65(5), 807-832.
Li, C., Shen, X., & Pan, W. (2021). Inference for a Large Directed Graphical Model with Interventions. arXiv preprint arXiv:2110.03805.
Yang, Y., & Zou, H. (2014). A coordinate majorization descent algorithm for l1 penalized learning. Journal of Statistical Computation and Simulation, 84(1), 84-95.
Two R package Github: ncvreg and glmnet.

See Also

Useful links:

print, predict, coef and plot methods, and the cv.glmtlp function.

Examples


# Gaussian
X <- matrix(rnorm(100 * 20), 100, 20)
y <- rnorm(100)
fit1 <- glmtlp(X, y, family = "gaussian", penalty = "l0")
fit2 <- glmtlp(X, y, family = "gaussian", penalty = "l1")
fit3 <- glmtlp(X, y, family = "gaussian", penalty = "tlp")

# Binomial

X <- matrix(rnorm(100 * 20), 100, 20)
y <- sample(c(0, 1), 100, replace = TRUE)
fit <- glmtlp(X, y, family = "binomial", penalty = "l1")

A simulated binomial data set.

Description

A data set simulated for illustrating logistic regression models. Generated by gen.binomial.data(n = 200, p = 20, seed = 2021).

Usage

data(bin_data)

Format

A list with three elements: design matrix X, response y, and the true coefficient vector beta.

X

design matrix

y

response

beta

the true coefficient vector

Examples

data("bin_data")
cv.fit <- cv.glmtlp(bin_data$X, bin_data$y, family = "binomial", penalty = "l1")
plot(cv.fit)

Cross-validation for glmtlp

Description

Performs k-fold cross-validation for l0, l1, or TLP-penalized regression models over a grid of values for the regularization parameter lambda (if penalty="l0") or kappa (if penalty="l0").

Usage

cv.glmtlp(X, y, ..., seed = NULL, nfolds = 10, obs.fold = NULL, ncores = 1)

Arguments

X

input matrix, of dimension nobs x nvars, as in glmtlp.

y

response, of length nobs, as in glmtlp.

...

Other arguments that can be passed to glmtlp.

seed

the seed for reproduction purposes

nfolds

number of folds; default is 10. The smallest value allowable is nfolds=3

obs.fold

an optional vector of values between 1 and nfolds identifying what fold each observation is in. If supplied, nfolds can be missing.

ncores

number of cores utilized; default is 1. If greater than 1, then doParallel::foreach will be used to fit each fold; if equal to 1, then for loop will be used to fit each fold. Users don't have to register parallel clusters outside.

Details

The function calls glmtlp nfolds+1 times; the first call to get the lambda or kappa sequence, and then the rest to compute the fit with each of the folds omitted. The cross-validation error is based on deviance (check here for more details). The error is accumulated over the folds, and the average error and standard deviation is computed.

When family = "binomial", the fold assignment (if not provided by the user) is generated in a stratified manner, where the ratio of 0/1 outcomes are the same for each fold.

Value

an object of class "cv.glmtlp" is returned, which is a list with the ingredients of the cross-validation fit.

call

the function call

cv.mean

The mean cross-validated error - a vector of length length(kappa) if penalty = "l0" and length{lambda} otherwise.

cv.se

estimate of standard error of cv.mean.

fit

a fitted glmtlp object for the full data.

idx.min

the index of the lambda or kappa sequence that corresponding to the smallest cv mean error.

kappa

the values of kappa used in the fits, available when penalty = 'l0'.

kappa.min

the value of kappa that gives the minimum cv.mean, available when penalty = 'l0'.

lambda

the values of lambda used in the fits.

lambda.min

value of lambda that gives minimum cv.mean, available when penalty is 'l1' or 'tlp'.

null.dev

null deviance of the model.

obs.fold

the fold id for each observation used in the CV.

Author(s)

Chunlin Li, Yu Yang, Chong Wu
Maintainer: Yu Yang yang6367@umn.edu

References

Shen, X., Pan, W., & Zhu, Y. (2012). Likelihood-based selection and sharp parameter estimation. Journal of the American Statistical Association, 107(497), 223-232.
Shen, X., Pan, W., Zhu, Y., & Zhou, H. (2013). On constrained and regularized high-dimensional regression. Annals of the Institute of Statistical Mathematics, 65(5), 807-832.
Li, C., Shen, X., & Pan, W. (2021). Inference for a Large Directed Graphical Model with Interventions. arXiv preprint arXiv:2110.03805.
Yang, Y., & Zou, H. (2014). A coordinate majorization descent algorithm for l1 penalized learning. Journal of Statistical Computation and Simulation, 84(1), 84-95.
Two R package Github: ncvreg and glmnet.

See Also

glmtlp and plot, predict, and coef methods for "cv.glmtlp" objects.

Examples


# Gaussian
X <- matrix(rnorm(100 * 20), 100, 20)
y <- rnorm(100)
cv.fit <- cv.glmtlp(X, y, family = "gaussian", penalty = "l1", seed=2021)

# Binomial
X <- matrix(rnorm(100 * 20), 100, 20)
y <- sample(c(0,1), 100, replace = TRUE)
cv.fit <- cv.glmtlp(X, y, family = "binomial", penalty = "l1", seed=2021)

A simulated gaussian data set.

Description

A data set simulated for illustrating linear regression models. Generated by gen.gaussian.data(n = 200, p = 20, seed = 2021).

Usage

data(gau_data)

Format

A list with five elements: design matrix X, response y, correlation structure of the covariates Sigma, true beta beta, and the noise level sigma.

X

design matrix

y

response

beta

true beta values

sigma

the noise level

Examples

data("gau_data")
cv.fit <- cv.glmtlp(gau_data$X, gau_data$y, family = "gaussian", penalty = "tlp")
plot(cv.fit)

Simulate a binomial data set

Description

Simulate a data set with binary response following the logistic regression model.

Usage

gen.binomial.data(n, p, rho = 0, kappa = 5, beta.type = 1, seed = 2021)

Arguments

n

Sample size.

p

Number of covariates.

rho

The parameter defining the AR(1) correlation matrix.

kappa

The number of nonzero coefficients.

beta.type

Numeric indicator for choosing the beta type. For beta.type = 1, the true coefficient vector has kappa components being 1, roughly equally distributed between 1 to p. For beta.type = 2, the first kappa values are 1, and the rest are 0. For beta.type = 3, the first kappa values are equally-spaced values from 10 to 0.5, and the rest are 0. For beta.type = 4, the first kappa values are the first kappa values in c(-10, -6, -2, 2, 6, 10), and the rest are 0. For beta.type = 5, the first kappa values are 1, and the rest decay exponentially to 0 with base 0.5.

seed

The seed for reproducibility. Default is 2021.

Value

A list containing the simulated data.

X

the covariate matrix, of dimension n x p.

y

the response, of length n.

beta

the true coefficients, of length p.

Examples

bin_data <- gen.binomial.data(n = 200, p = 20, seed = 2021)
head(bin_data$X)
head(bin_data$y)
head(bin_data$beta)

Simulate a gaussian data set

Description

Simulate a data set with gaussian response following the linear regression model.

Usage

gen.gaussian.data(
  n,
  p,
  rho = 0,
  kappa = 5,
  beta.type = 1,
  snr = 1,
  seed = 2021
)

Arguments

n

Sample size.

p

Number of covariates.

rho

The parameter defining the AR(1) correlation matrix.

kappa

The number of nonzero coefficients.

beta.type

Numeric indicator for choosing the beta type. For beta.type = 1, the true coefficient vector has kappa components being 1, roughly equally distributed between 1 to p. For beta.type = 2, the first kappa values are 1, and the rest are 0. For beta.type = 3, the first kappa values are equally-spaced values from 10 to 0.5, and the rest are 0. For beta.type = 4, the first kappa values are the first kappa values in c(-10, -6, -2, 2, 6, 10), and the rest are 0. For beta.type = 5, the first kappa values are 1, and the rest decay exponentially to 0 with base 0.5.

snr

Signal-to-noise ratio. Default is 1.

seed

The seed for reproducibility. Default is 2021.

Value

A list containing the simulated data.

X

the covariate matrix, of dimension n x p.

y

the response, of length n.

beta

the true coefficients, of length p.

sigma

the standard error of the noise.

Examples

gau_data <- gen.gaussian.data(n = 200, p = 20, seed = 2021)
head(gau_data$X)
head(gau_data$y)
head(gau_data$beta)
gau_data$sigma

Plot Method for a "cv.glmtlp" Object

Description

Plots the cross-validation curve, and the upper and lower standard deviation curves, as a function of the lambda or kappa values.

Usage

## S3 method for class 'cv.glmtlp'
plot(x, vertical.line = TRUE, ...)

Arguments

x

Fitted cv.glmtlp object

vertical.line

Logical. Whether or not include a vertical line indicating the position of the index which gives the smallest CV error.

...

Additional arguments.

Details

The generated plot is a ggplot object, and therefore, the users are able to customize the plots following the ggplot2 syntax.

Author(s)

Chunlin Li, Yu Yang, Chong Wu
Maintainer: Yu Yang yang6367@umn.edu

References

Shen, X., Pan, W., & Zhu, Y. (2012). Likelihood-based selection and sharp parameter estimation. Journal of the American Statistical Association, 107(497), 223-232.
Shen, X., Pan, W., Zhu, Y., & Zhou, H. (2013). On constrained and regularized high-dimensional regression. Annals of the Institute of Statistical Mathematics, 65(5), 807-832.
Li, C., Shen, X., & Pan, W. (2021). Inference for a Large Directed Graphical Model with Interventions. arXiv preprint arXiv:2110.03805.
Yang, Y., & Zou, H. (2014). A coordinate majorization descent algorithm for l1 penalized learning. Journal of Statistical Computation and Simulation, 84(1), 84-95.
Two R package Github: ncvreg and glmnet.

Examples

X <- matrix(rnorm(100 * 20), 100, 20)
y <- rnorm(100)
cv.fit <- cv.glmtlp(X, y, family = "gaussian", penalty = "tlp")
plot(cv.fit)
plot(cv.fit, vertical.line = FALSE)
cv.fit2 <- cv.glmtlp(X, y, family = "gaussian", penalty = "l0")
plot(cv.fit2)
plot(cv.fit2, vertical.line = FALSE)

data("gau_data")
cv.fit <- cv.glmtlp(gau_data$X, gau_data$y, family = "gaussian", penalty = "tlp")
plot(cv.fit)

data("bin_data")
cv.fit <- cv.glmtlp(bin_data$X, bin_data$y, family = "binomial", penalty = "l1")
plot(cv.fit)

Plot Method for a "glmtlp" Object

Description

Generates a solution path plot for a fitted "glmtlp" object.

Usage

## S3 method for class 'glmtlp'
plot(
  x,
  xvar = c("lambda", "kappa", "deviance", "l1_norm", "log_lambda"),
  xlab = iname,
  ylab = "Coefficients",
  title = "Solution Path",
  label = FALSE,
  label.size = 3,
  ...
)

Arguments

x

Fitted glmtlp object.

xvar

The x-axis variable to plot against, including "lambda", "kappa", "deviance", "l1_norm", and "log_lambda".

xlab

The x-axis label of the plot, default is "Lambda", "Kappa", "Fraction of Explained Deviance", "L1 Norm", and "Log Lambda".

ylab

The y-axis label of the plot, default is "Coefficients".

title

The main title of the plot, default is "Solution Path".

label

Logical, whether or not attach the labels for the non-zero coefficients, default is FALSE.

label.size

The text size of the labels, default is 3.

...

Additional arguments.

Details

The generated plot is a ggplot object, and therefore, the users are able to customize the plots following the ggplot2 syntax.

Value

A ggplot object.

Author(s)

Chunlin Li, Yu Yang, Chong Wu
Maintainer: Yu Yang yang6367@umn.edu

References

Shen, X., Pan, W., & Zhu, Y. (2012). Likelihood-based selection and sharp parameter estimation. Journal of the American Statistical Association, 107(497), 223-232.
Shen, X., Pan, W., Zhu, Y., & Zhou, H. (2013). On constrained and regularized high-dimensional regression. Annals of the Institute of Statistical Mathematics, 65(5), 807-832.
Li, C., Shen, X., & Pan, W. (2021). Inference for a Large Directed Graphical Model with Interventions. arXiv preprint arXiv:2110.03805.
Yang, Y., & Zou, H. (2014). A coordinate majorization descent algorithm for l1 penalized learning. Journal of Statistical Computation and Simulation, 84(1), 84-95.
Two R package Github: ncvreg and glmnet.

See Also

print, predict, coef and plot methods, and the cv.glmtlp function.

Examples

X <- matrix(rnorm(100 * 20), 100, 20)
y <- rnorm(100)
fit <- glmtlp(X, y, family = "gaussian", penalty = "l1")
plot(fit, xvar = "lambda")
plot(fit, xvar = "log_lambda")
plot(fit, xvar = "l1_norm")
plot(fit, xvar = "log_lambda", label = TRUE)
fit2 <- glmtlp(X, y, family = "gaussian", penalty = "l0")
plot(fit2, xvar = "kappa", label = TRUE)

Predict Method for a "cv.glmtlp" Object.

Description

Makes predictions for a cross-validated glmtlp model, using the stored "glmtlp" object, and the optimal value chosen for lambda.

Usage

## S3 method for class 'cv.glmtlp'
predict(
  object,
  X,
  type = c("link", "response", "class", "coefficients", "numnzs", "varnzs"),
  lambda = NULL,
  kappa = NULL,
  which = object$idx.min,
  ...
)

## S3 method for class 'cv.glmtlp'
coef(object, lambda = NULL, kappa = NULL, which = object$idx.min, ...)

Arguments

object

Fitted "cv.glmtlp" object.

X

X Matrix of new values for X at which predictions are to be made. Must be a matrix.

type

Type of prediction to be made. For "gaussian" models, type "link" and "response" are equivalent and both give the fitted values. For "binomial" models, type "link" gives the linear predictors and type "response" gives the fitted probabilities. Type "coefficients" computes the coefficients at the provided values of lambda or kappa. Note that for "binomial" models, results are returned only for the class corresponding to the second level of the factor response. Type "class" applies only to "binomial" models, and gives the class label corresponding to the maximum probability. Type "numnz" gives the total number of non-zero coefficients for each value of lambda or kappa. Type "varnz" gives a list of indices of the nonzero coefficients for each value of lambda or kappa.

lambda

Value of the penalty parameter lambda at which predictions are to be made Default is NULL.

kappa

Value of the penalty parameter kappa at which predictions are to be made. Default is NULL.

which

Index of the penalty parameter lambda or kappa sequence at which predictions are to be made. Default is the idx.min stored in the cv.glmtp object.

...

Additional arguments.

Value

The object returned depends on type.

Author(s)

Chunlin Li, Yu Yang, Chong Wu
Maintainer: Yu Yang yang6367@umn.edu

References

Shen, X., Pan, W., & Zhu, Y. (2012). Likelihood-based selection and sharp parameter estimation. Journal of the American Statistical Association, 107(497), 223-232.
Shen, X., Pan, W., Zhu, Y., & Zhou, H. (2013). On constrained and regularized high-dimensional regression. Annals of the Institute of Statistical Mathematics, 65(5), 807-832.
Li, C., Shen, X., & Pan, W. (2021). Inference for a Large Directed Graphical Model with Interventions. arXiv preprint arXiv:2110.03805.
Yang, Y., & Zou, H. (2014). A coordinate majorization descent algorithm for l1 penalized learning. Journal of Statistical Computation and Simulation, 84(1), 84-95.
Two R package Github: ncvreg and glmnet.

See Also

print, predict, coef and plot methods, and the cv.glmtlp function.

Examples

X <- matrix(rnorm(100 * 20), 100, 20)
y <- rnorm(100)
cv.fit <- cv.glmtlp(X, y, family = "gaussian", penalty = "l1")
predict(cv.fit, X = X[1:5, ])
coef(cv.fit)
predict(cv.fit, X = X[1:5, ], lambda = 0.1)

Predict Method for a "glmtlp" Object

Description

Predicts fitted values, logits, coefficients and more from a fitted glmtlp object.

Usage

## S3 method for class 'glmtlp'
predict(
  object,
  X,
  type = c("link", "response", "class", "coefficients", "numnz", "varnz"),
  lambda = NULL,
  kappa = NULL,
  which = 1:(ifelse(object$penalty == "l0", length(object$kappa), length(object$lambda))),
  ...
)

## S3 method for class 'glmtlp'
coef(
  object,
  lambda = NULL,
  kappa = NULL,
  which = 1:(ifelse(object$penalty == "l0", length(object$kappa), length(object$lambda))),
  drop = TRUE,
  ...
)

Arguments

object

Fitted glmtlp model object.

X

Matrix of new values for X at which predictions are to be made. Must be a matrix. This argument will not used for type=c("coefficients","numnz", "varnz").

type

Type of prediction to be made. For "gaussian" models, type "link" and "response" are equivalent and both give the fitted values. For "binomial" models, type "link" gives the linear predictors and type "response" gives the fitted probabilities. Type "coefficients" computes the coefficients at the provided values of lambda or kappa. Note that for "binomial" models, results are returned only for the class corresponding to the second level of the factor response. Type "class" applies only to "binomial" models, and gives the class label corresponding to the maximum probability. Type "numnz" gives the total number of non-zero coefficients for each value of lambda or kappa. Type "varnz" gives a list of indices of the nonzero coefficients for each value of lambda or kappa.

lambda

Value of the penalty parameter lambda at which predictions are to be made Default is NULL.

kappa

Value of the penalty parameter kappa at which predictions are to be made. Default is NULL.

which

Index of the penalty parameter lambda or kappa sequence at which predictions are to be made. Default are the indices for the entire penalty parameter sequence.

...

Additional arguments.

drop

Whether or not keep the dimension that is of length 1.

Details

coef(...) is equivalent to predict(type="coefficients",...)

Value

The object returned depends on type.

Author(s)

Chunlin Li, Yu Yang, Chong Wu
Maintainer: Yu Yang yang6367@umn.edu

References

Shen, X., Pan, W., & Zhu, Y. (2012). Likelihood-based selection and sharp parameter estimation. Journal of the American Statistical Association, 107(497), 223-232.
Shen, X., Pan, W., Zhu, Y., & Zhou, H. (2013). On constrained and regularized high-dimensional regression. Annals of the Institute of Statistical Mathematics, 65(5), 807-832.
Li, C., Shen, X., & Pan, W. (2021). Inference for a Large Directed Graphical Model with Interventions. arXiv preprint arXiv:2110.03805.
Yang, Y., & Zou, H. (2014). A coordinate majorization descent algorithm for l1 penalized learning. Journal of Statistical Computation and Simulation, 84(1), 84-95.
Two R package Github: ncvreg and glmnet.

See Also

print, predict, coef and plot methods, and the cv.glmtlp function.

Examples


# Gaussian
X <- matrix(rnorm(100 * 20), 100, 20)
y <- rnorm(100)
fit <- glmtlp(X, y, family = "gaussian", penalty = "l1")
predict(fit, X = X[1:5, ])
coef(fit)
predict(fit, X = X[1:5, ], lambda = 0.1)

# Binomial
X <- matrix(rnorm(100 * 20), 100, 20)
y <- sample(c(0,1), 100, replace = TRUE)
fit <- glmtlp(X, y, family = "binomial", penalty = "l1")
coef(fit)
predict(fit, X = X[1:5, ], type = "response")
predict(fit, X = X[1:5, ], type = "response", lambda = 0.01)
predict(fit, X = X[1:5, ], type = "class", lambda = 0.01)
predict(fit, X = X[1:5, ], type = "numnz", lambda = 0.01)

Generate lambda sequence.

Description

Generate lambda sequence.

Usage

setup_lambda(X, y, weights, lambda.min.ratio, nlambda)

Arguments

X

Input matrix, of dimension nobs x nvars; each row is an observation vector.

y

Response variable, of length nobs. For family="gaussian", it should be quantitative; for family="binomial", it should be either a factor with two levels or a binary vector.

weights

Observation weights.

lambda.min.ratio

The smallest value for lambda, as a fraction of lambda.max, the smallest value for which all coefficients are zero. The default depends on the sample size nobs relative to the number of variables nvars.

nlambda

The number of lambda values.