Package 'msgps'

msgps (Degrees of Freedom of Elastic Net, Adaptive Lasso and Generalized Elastic Net)

Description

This package computes the degrees of freedom of the lasso, elastic net, generalized elastic net and adaptive lasso based on the generalized path seeking algorithm. The optimal model can be selected by model selection criteria including Mallows' Cp, bias-corrected AIC (AICc), generalized cross validation (GCV) and BIC.

Usage

msgps(X,y,penalty="enet", alpha=0, gamma=1, lambda=0.001, tau2, STEP=20000, 
STEP.max=200000,  DFtype="MODIFIED",  p.max=300, intercept=TRUE, stand.coef=FALSE)

Arguments

X	predictor matrix
y	response vector
penalty	The penalty term. The "enet" indicates the elastic net: $\alpha/2||\beta||_2^2+(1-\alpha)||\beta||_1.$ Note that alpha=0 is the lasso penalty. The "genet" is the generalized elastic net: $log(\alpha+(1-\alpha)||\beta||_1).$ The "alasso" is the adaptive lasso, which is a weighted version of the lasso given by $w_i||\beta||_1,$ where $w_i$ is $1/(\hat{\beta}_i)^{\gamma}$. Here $\gamma>0$ is a tuning parameter, and $\hat{\beta}_i$ is the ridge estimate with regularization parameter being $\lambda \ge 0$.
alpha	The value of $\alpha$ on "enet" and "genet" penalty.
gamma	The value of $\gamma$ on "alasso".
lambda	The value of regularization parameter $\lambda \ge 0$ for ridge regression, which is used to calculate the weight vector of "alasso" penalty. Note that the ridge estimates can be ordinary least squared estimates when lambda=0.
tau2	Estimator of error variance for Mallows' Cp. The default is the unbiased estimator of error vairance of the most complex model. When the unbiased estimator of error vairance of the most complex model is not available (e.g., the number of variables exceeds the number of samples), tau2 is the variance of response vector.
STEP	The approximate number of steps.
STEP.max	The number of steps in this algorithm can often exceed STEP. When the number of steps exceeds STEP.max, this algorithm stops.
DFtype	"MODIFIED" or "NAIVE". The "MODIFIED" update is much more efficient thatn "NAIVE" update.
p.max	If the number of selected variables exceeds p.max, the algorithm stops.
intercept	When intercept is TRUE, the result of intercept is included.
stand.coef	When stand.coef is TRUE, the standardized coefficient is displayed.

Author(s)

Kei Hirose
[email protected]

References

Friedman, J. (2008). Fast sparse regression and classification. $Technical report$, Standford University.
Hirose, K., Tateishi, S. and Konishi, S.. (2011). Efficient algorithm to select tuning parameters in sparse regression modeling with regularization. arXiv:1109.2411 (arXiv).

See Also

coef.msgps, plot.msgps, predict.msgps and summary.msgos objects.

Examples

#data
X <- matrix(rnorm(100*8),100,8)
beta0 <- c(3,1.5,0,0,2,0,0,0)
epsilon <- rnorm(100,sd=3)
y <- X %*% beta0 + epsilon
y <- c(y)

#lasso
fit <- msgps(X,y)
summary(fit) 
coef(fit) #extract coefficients at t selected by model selection criteria
coef(fit,c(0, 0.5, 2.5)) #extract coefficients at some values of t
predict(fit,X[1:10,]) #predict values at t selected by model selection criteria
predict(fit,X[1:10,],c(0, 0.5, 2.5)) #predict values at some values of t
plot(fit,criterion="cp") #plot the solution path with a model selected by Cp criterion

#elastic net
fit2 <- msgps(X,y,penalty="enet",alpha=0.5)
summary(fit2) 

#generalized elastic net
fit3 <- msgps(X,y,penalty="genet",alpha=0.5)
summary(fit3)

#adaptive lasso
fit4 <- msgps(X,y,penalty="alasso",gamma=1,lambda=0)
summary(fit4)

---

plot the solution path from a "msgps" object.

Description

This functions predicts fitted values from a "msgps" object.

Usage

## S3 method for class 'msgps'
plot(x, criterion="cp", xvar="norm", yvar="coef", yvar.dflasso=TRUE, 
stand.coef=TRUE, plot.step = 1000, col=TRUE,...)

Arguments

x	Fitted "msgps" model object.
criterion	The code criterion plots the value of tuning parameter of each criterion ("cp", "aicc", "gcv", "bic"). The code "none" does not depict the tuning parameter.
xvar	The type of x variable. "xvar=norm" is max|beta|/|beta|, "xvar=sum" is max|beta|, "xvar=step" is the number of steps, and "xvar=t" is tuning parameter.
yvar	The type of y variable. "yvar=coef" is the standardized coefficients, and "tvar=df" is the degrees of freedom.
yvar.dflasso	For lasso penalty, the degrees of freedom of the lasso (the number of non-zero parameters) is given when "yvar=df" and "yvar.dflasso=TRUE".
stand.coef	The standardized coefficients and tuning parameters are dipicted if "stand.coef=TRUE".
plot.step	The number of steps to plot the solution of df. As plot.step increases, the picture will be well-looking whereas the file size of the picture will increase.
col	The color option.
...	Other graphical parameters to plot

Value

The object returned depends on type.

Author(s)

Kei Hirose
[email protected]

See Also

coef.msgps, predict.msgps and summary.msgps objects.

Examples

#data
X <- matrix(rnorm(100*8),100,8)
beta0 <- c(3,1.5,0,0,2,0,0,0)
epsilon <- rnorm(100,sd=3)
y <- X %*% beta0 + epsilon
y <- c(y)

#fit
fit <- msgps(X,y)
plot(fit,criterion="cp") #plot the solution path with a model selected by Cp criterion

---

make predictions from a "msgps" object.

Description

This functions predicts fitted values via msgps function.

Usage

## S3 method for class 'msgps'
predict(object, X, tuning,...)
## S3 method for class 'msgps'
coef(object, tuning,...)

Arguments

object	Fitted "msgps" model object.
X	Matrix of vector of new input x.
tuning	Tuning parameter vector t where predictions are required. If tuning is missing, solutions selected by Cp, bias-corrected AIC (AICC), generalized cross validation (GCV) and BIC are displayed.
...	Other parameters

Value

The object returned depends on type.

Author(s)

Kei Hirose
[email protected]

Examples

#data
X <- matrix(rnorm(100*8),100,8)
beta0 <- c(3,1.5,0,0,2,0,0,0)
epsilon <- rnorm(100,sd=3)
y <- X %*% beta0 + epsilon
y <- c(y)

#fit
fit <- msgps(X,y)
coef(fit) #extract coefficients at t selected by model selection criteria
coef(fit,c(0, 0.5, 2.5)) #extract coefficients at some values of t
predict(fit,X[1:10,]) #predict values at t selected by model selection criteria
predict(fit,X[1:10,],c(0, 0.5, 2.5)) #predict values at some values of t

---

A summary of "msgps" object..

Description

This functions summarizes the "msgps" object.

Usage

## S3 method for class 'msgps'
summary(object, digits=max(3, getOption("digits") - 3), num.result = 20, 
coef.result=100,...)

Arguments

object	Fitted "msgps" model object.
digits	The digits of the output.
num.result	The number of tuning parameter and the corresponding degrees of freedom displayed in this code.
coef.result	If the coef.result exceeds the number of variables, the result of coefficient is not described in this code.
...	Other parameters on summary

Value

df	The degrees of freedom for each tuning parameter.
tuning.max	Maximum value of tuning parameter.
ms.coef	The coefficient selected by each model selection criterion.
ms.tuning	The values of tuning parameter of models selected by each model selection criterion.
ms.df	The degerees of freedom selected of models each model selection criterion.

Author(s)

Kei Hirose
[email protected]

Examples

#data
X <- matrix(rnorm(100*8),100,8)
beta0 <- c(3,1.5,0,0,2,0,0,0)
epsilon <- rnorm(100,sd=3)
y <- X %*% beta0 + epsilon
y <- c(y)

#fit
fit <- msgps(X,y)
summary(fit)

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