camel.cmr: Calibrated Multivariate Regression

In camel: Calibrated Machine Learning

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.

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.

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.

Author(s)

Xingguo Li, Tuo Zhao, and Han Liu
Maintainer: Xingguo Li <[e-mail]>

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)

camel documentation built on May 29, 2017, 10:32 p.m.