Type: Package
Title: Sparse Generalized Linear Model with L0 Approximation for Feature Selection
Version: 0.1.6
Date: 2020-02-03
Author: Wenchuan Guo, Shujie Ma, Zhenqiu Liu
Maintainer: Wenchuan Guo <wguo007@ucr.edu>
Description: An efficient procedure for feature selection for generalized linear models with L0 penalty, including linear, logistic, Poisson, gamma, inverse Gaussian regression. Adaptive ridge algorithms are used to fit the models.
License: GPL-2
Imports: Rcpp (≥ 0.12.6)
LinkingTo: Rcpp, RcppArmadillo
LazyData: TRUE
RoxygenNote: 6.1.1
NeedsCompilation: yes
Packaged: 2020-02-06 01:44:57 UTC; wguo
Repository: CRAN
Date/Publication: 2020-02-06 05:40:02 UTC

print coefficients from a "cv.l0ara" object.

Description

Print the coefficients from the model with the optimal lambda.

Usage

## S3 method for class 'cv.l0ara'
coef(object, ...)

Arguments

object

Fitted "cv.l0ara" object.

...

Not used argument.

Details

This function fit the model with the optimal lambda first and then print the coefficients. This function makes it easier to use the results to make a prediction or to see the fitted model.

Value

The object returns the coefficients.

Author(s)

Wenchuan Guo <wguo007@ucr.edu>, Shujie Ma <shujie.ma@ucr.edu>, Zhenqiu Liu <Zhenqiu.Liu@cshs.org>

See Also

predict method and l0ara function.

print coefficients from a "l0ara" object.

Description

Print the coefficients from the model.

Usage

## S3 method for class 'l0ara'
coef(object, ...)

Arguments

object

Fitted "l0ara" object.

...

Not used argument.

Details

This function makes it easier to use the results to make a prediction or to see the fitted model.

Value

The object returns the coefficients.

Author(s)

Wenchuan Guo <wguo007@ucr.edu>, Shujie Ma <shujie.ma@ucr.edu>, Zhenqiu Liu <Zhenqiu.Liu@cshs.org>

See Also

predict method and l0ara function.

cross-validation for l0ara

Description

Does k-fold cross-validation for l0ara, produces a plot, and returns the optimal lambda

Usage

cv.l0ara(x, y, family, lam, measure, nfolds, maxit, eps, seed)

Arguments

x

Input matrix as in l0ara.

y

Response variable as in l0ara.

family

Response type as in l0ara.

lam

A user supplied lambda sequence in descending or asecending order. This function does not fit models. To fit a model with given lam value, use l0ara.

measure

Loss function used for corss validation. measurer="mse" or "mae" for all models. "measure"="class" or "measure"="auc" only for logsitic regression.

nfolds

Number of folds. Default value is 10. Smallest value is 3.

maxit

Maximum number of passes over the data for lambda. Default value is 1e3.

eps

Convergence threshold. Default value is 1e-4.

seed

Seed of random number generator.

Details

This function calls l0ara nfolds times, each time leaving out 1/nfolds of the data. The cross-validation error is based on etiher mean square error (mse) or mean absolute error (mae).

Value

An object with S3 class "cv.l0ara" containing:

cv.error

The mean cross validated error for given lambda sequence

cv.std

The estimates of standard error of cv.error

lam.min

The lambda gives min cv.error

lambda

The lambda used

measure

Type of measure

family

Model used

x

Design matrix

y

Response variable

name

Full name of the measure

Author(s)

Wenchuan Guo <wguo007@ucr.edu>, Shujie Ma <shujie.ma@ucr.edu>, Zhenqiu Liu <Zhenqiu.Liu@cshs.org>

See Also

l0ara, coef.cv.l0ara, plot.cv.l0ara methods.

Examples

#' # Linear regression
# Generate design matrix and response variable
n <- 100
p <- 40
x <- matrix(rnorm(n*p), n, p)
beta <- c(1,0,2,3,rep(0,p-4))
noise <- rnorm(n)
y <- x%*%beta+noise
lam <- c(0.1, 0.3, 0.5)
fit <- cv.l0ara(x, y, family="gaussian", lam, measure = "mse")

fit a generalized linear model with l0 penalty

Description

An adaptive ridge algorithm for feature selection with L0 penalty.

Usage

l0ara(x, y, family, lam, standardize, maxit, eps)

Arguments

x

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

y

Response variable. Quantitative for family="gaussian"; positive quantitative for family="gamma" or family="inv.gaussian" ; a factor with two levels for family="logit"; non-negative counts for family="poisson".

family

Response type(see above).

lam

A user supplied lambda value. If you have a lam sequence, use cv.l0ara first to select optimal tunning and then refit with lam.min . To use AIC, set lam=2; to use BIC, set lam=log(n).

standardize

Logical flag for data normalization. If standardize=TRUE(default), independent variables in the design matrix x will be standardized with mean 0 and standard deviation 1.

maxit

Maximum number of passes over the data for lambda. Default value is 1e3.

eps

Convergence threshold. Default value is 1e-4.

Details

The sequence of models indexed by the parameter lambda is fit using adptive ridge algorithm. The objective function for generalized linear models (including family above) is defined to be

-(log likelihood)+(\lambda/2)*|\beta|_0

|\beta|_0 is the number of non-zero elements in \beta. To select the "best" model with AIC or BIC criterion, let lambda to be 2 or log(n). This adaptive ridge algorithm is developed to approximate L0 penalized generalized linear models with sequential optimization and is efficient for high-dimensional data.

Value

An object with S3 class "l0ara" containing:

beta

A vector of coefficients

df

Number of nonzero coefficients

iter

Number of iterations

lambda

The lambda used

x

Design matrix

y

Response variable

Author(s)

Wenchuan Guo <wguo007@ucr.edu>, Shujie Ma <shujie.ma@ucr.edu>, Zhenqiu Liu <Zhenqiu.Liu@cshs.org>

See Also

cv.l0ara, predict.l0ara, coef.l0ara, plot.l0ara methods.

Examples

# Linear regression
# Generate design matrix and response variable
n <- 100
p <- 40
x <- matrix(rnorm(n*p), n, p)
beta <- c(1,0,2,3,rep(0,p-4))
noise <- rnorm(n)
y <- x%*%beta+noise
# fit sparse linear regression using BIC 
res.gaussian <- l0ara(x, y, family="gaussian", log(n))

# predict for new observations
print(res.gaussian)
predict(res.gaussian, newx=matrix(rnorm(3,p),3,p))
coef(res.gaussian)

# Logistic regression
# Generate design matrix and response variable
n <- 100
p <- 40
x <- matrix(rnorm(n*p), n, p)
beta <- c(1,0,2,3,rep(0,p-4))
prob <- exp(x%*%beta)/(1+exp(x%*%beta))
y <- rbinom(n, rep(1,n), prob)
# fit sparse logistic regression
res.logit <- l0ara(x, y, family="logit", 0.7)

# predict for new observations
print(res.logit)
predict(res.logit, newx=matrix(rnorm(3,p),3,p))
coef(res.logit)

# Poisson regression
# Generate design matrix and response variable
n <- 100
p <- 40
x <- matrix(rnorm(n*p), n, p)
beta <- c(1,0,0.5,0.3,rep(0,p-4))
mu <- exp(x%*%beta)
y <- rpois(n, mu)
# fit sparse Poisson regression using AIC
res.pois <- l0ara(x, y, family="poisson", 2)

# predict for new observations
print(res.pois)
predict(res.pois, newx=matrix(rnorm(3,p),3,p))
coef(res.pois)

plot for an "cv.l0ara" object

Description

Produces curves from a fitted "cv.l0ara" object.

Usage

## S3 method for class 'cv.l0ara'
plot(x, col = 3, ...)

Arguments

x

Fitted "cv.l0ara" object.

col

color of the dots.

...

Not used argument.

Author(s)

Wenchuan Guo <wguo007@ucr.edu>, Shujie Ma <shujie.ma@ucr.edu>, Zhenqiu Liu <Zhenqiu.Liu@cshs.org>

See Also

predict, coef methods, cv.l0ara and l0ara function.

plot for an "l0ara" object

Description

Two plots are availiable: a plot of fitted value against linear predictor; roc(auc) curve for family="logit".

Usage

## S3 method for class 'l0ara'
plot(x, auc = FALSE, split = FALSE, col = 4, ...)

Arguments

x

Fitted "l0ara" object.

auc

logical; if TRUE, produces auc curve for family=logit.

split

logical; if if TRUE, produces seperate plots.

col

color of the dots.

...

Not used argument.

Author(s)

Wenchuan Guo <wguo007@ucr.edu>, Shujie Ma <shujie.ma@ucr.edu>, Zhenqiu Liu <Zhenqiu.Liu@cshs.org>

See Also

predict, coef methods and l0ara function.

make predictions from a "l0ara" object.

Description

Make predictions from the model.

Usage

## S3 method for class 'l0ara'
predict(object, newx, type = c("link", "response",
  "coefficients", "class"), ...)

Arguments

object

Fitted "l0ara" object.

newx

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

type

Type of prediction required. "link" gives the linear predictors(for "gaussian" models it gives the fitted values). "response" gives the fitted probabilities for "logit" and fitted mean for "poisson". "coefficients" gives the coefficients which is same as "coef" function. "class" (applies only to "logit") produces the class label corresponding to the maximum probability.

...

Not used argument.

Details

This function makes it easier to use the results to make a prediction or to see the fitted model.

Value

The object returned depends the functions.

Author(s)

Wenchuan Guo <wguo007@ucr.edu>, Shujie Ma <shujie.ma@ucr.edu>, Zhenqiu Liu <Zhenqiu.Liu@cshs.org>

See Also

coef method and l0ara function.

summarizing the fits from a "cv.l0ara" object.

Description

Print the general information of the cross validated fit.

Usage

## S3 method for class 'cv.l0ara'
print(x, ...)

Arguments

x

Fitted "cv.l0ara" object.

...

Not used argument.

Details

This function makes it easier to see the cross-validation results.

Author(s)

Wenchuan Guo <wguo007@ucr.edu>, Shujie Ma <shujie.ma@ucr.edu>, Zhenqiu Liu <Zhenqiu.Liu@cshs.org>

See Also

predict, coef methods and l0ara function.

summarizing the fits from a "l0ara" object.

Description

Print the general information of the fit.

Usage

## S3 method for class 'l0ara'
print(x, ...)

Arguments

x

Fitted "l0ara" object.

...

Not used argument.

Details

This function makes it easier to see the fitted model.

Author(s)

Wenchuan Guo <wguo007@ucr.edu>, Shujie Ma <shujie.ma@ucr.edu>, Zhenqiu Liu <Zhenqiu.Liu@cshs.org>

See Also

predict, coef methods and l0ara function.