camel (version 0.2.0)

camel.cmr: Calibrated Multivariate Regression

Description

The function "camel.cmr" implements calibrated multivariate regression using jointly sparse regularization.

Usage

camel.cmr(X, Y, lambda = NULL, nlambda = NULL, prec = 1e-3, max.ite = 1e3, mu = 0.01, verbose = TRUE)

Arguments

Y

The $n$ by $m$ dimensional response matrix.

X

The $n$ by $d$ design matrix.

lambda

A sequence of decresing positive value to control the regularization. Typical usage is to leave the input lambda = NULL and have the program compute its own lambda sequence based on nlambda, $d$ and $m$. Users can also specify a sequence to override this.

nlambda

The number of values used in lambda. Default value is 10.

prec

Stopping criterion. The default value is 1e-3.

max.ite

The iteration limit. The default value is 1e3.

mu

The smoothing parameter. The default value is 0.01.

verbose

Tracing information is disabled if verbose = FALSE. The default value is TRUE.

Value

An object with S3 class "camel.cmr" is returned:

beta

A list of matrice of regression estimates where each entry corresponds to a regularization parameter.

intercept

The value of intercepts corresponding to regularization parameters.

Y

The value of Y used in the program.

X

The value of X used in the program.

lambda

The sequence of regularization parameters lambda used in the program.

nlambda

The number of values used in lambda.

sparsity

The sparsity levels of the solution path.

ite

A list of vectors where ite[[1]] is the number of external iteration and ite[[2]] is the number of internal iteration with the i-th entry corresponding to the i-th regularization parameter.

verbose

The verbose from the input.

Details

Calibrated multivariate regression adjusts the regularization with respect to the noise level of each task. Thus it achieves improved statistical performance and the tuning insensitiveness.

References

1. L. Han, L. Wang, and T. Zhao. Multivariate Regression with Calibration. http://arxiv.org/abs/1305.2238, 2013.

See Also

camel-package.

Examples

## Generate the design matrix and regression coefficient vector
n = 200
d = 400
m = 13
Sigma = matrix(0.5,d,d)
diag(Sigma) = 1
X = mvrnorm(n,rep(0,d),Sigma)
B = matrix(0,d,m)
B[1,] = 3
B[2,] = 2
B[4,] = 1.5
W = matrix(rnorm(n*m,0,1),n,m)
sig = sqrt(2)
D = sig*diag(2^(c(0:-12)/4))
Z = W%*%D
Y = X%*%B + Z
out = camel.cmr(X, Y)