cvrsolver {CVR}

Canonical Variate Regression.

Description

Perform canonical variate regression with a set of fixed tuning parameters.

Usage

cvrsolver(Y, Xlist, rank, eta, Lam, family, Wini, penalty, opts)

Arguments

Y

A response matrix. The response can be continuous, binary or Poisson.

Xlist

A list of covariate matrices. Cannot contain missing values.

rank

Number of pairs of canonical variates.

eta

Weight parameter between 0 and 1.

Lam

A vector of penalty parameters \lambda for regularizing the loading matrices corresponding to the covariate matrices in Xlist.

family

Type of response. "gaussian" if Y is continuous, "binomial" if Y is binary, and "poisson" if Y is Poisson.

Wini

A list of initial loading matrices W's. It must be provided. See cvr and scca for using sCCA solution as the default.

penalty

Type of penalty on W's. "GL1" for rowwise sparsity and "L1" for entrywise sparsity.

opts

A list of options for controlling the algorithm. Some of the options are:

standardization: need to standardize the data? Default is TRUE.

maxIters: maximum number of iterations allowed in the algorithm. The default is 300.

tol: convergence criterion. Stop iteration if the relative change in the objective is less than tol.

Details

CVR is used for extracting canonical variates and also predicting the response for multiple sets of covariates (Xlist = list(X1, X2)) and response (Y). The covariates can be, for instance, gene expression, SNPs or DNA methylation data. The response can be, for instance, quantitative measurement or binary phenotype. The criterion minimizes the objective function

(\eta/2)\sum_{k < j} ||X_kW_k - X_jW_j||_F^2 + (1-\eta)\sum_{k} l_k(\alpha, \beta, Y,X_kW_k) + \sum_k \rho_k(\lambda_k, W_k),

s.t. W_k'X_k'X_kW_k = I_r, for k = 1, 2, \ldots, K. l_k() are general loss functions with intercept \alpha and coefficients \beta. \eta is the weight parameter and \lambda_k are the regularization parameters. r is the rank, i.e. the number of canonical pairs. By adjusting \eta, one can change the weight of the first correlation term and the second prediction term. \eta=0 is reduced rank regression and \eta=1 is sparse CCA (with orthogonal constrained W's). By choosing appropriate \lambda_k one can induce sparsity of W_k's to select useful variables for predicting Y. W_k's with B_k's and (\alpha, \beta) are iterated using an ADMM algorithm. See the reference for details.

Value

An object containing the following components

iter

The number of iterations the algorithm takes.

W

A list of fitted loading matrices.

B

A list of fitted B_k's.

Z

A list of fitted B_kW_k's.

alpha

Fitted intercept term in the general loss term.

beta

Fitted regression coefficients in the general loss term.

objvals

A sequence of the objective values.

Author(s)

Chongliang Luo, Kun Chen.

References

Chongliang Luo, Jin Liu, Dipak D. Dey and Kun Chen (2016) Canonical variate regression. Biostatistics, doi: 10.1093/biostatistics/kxw001.

See Also

SimulateCVR, CVR.

Examples

## see  SimulateCVR for simulation examples, see CVR for parameter tuning.