Description Usage Arguments Details Value Author(s) References See Also Examples
Perform canonical variate regression with a set of fixed tuning parameters.
1 |
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 λ for regularizing the loading matrices
corresponding to the covariate matrices in |
family |
Type of response. |
Wini |
A list of initial loading matrices W's. It must be provided. See |
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:
|
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
(η/2) Σ_{k<j}||X_kW_k - X_jW_j||_F^2 + (1 - η) Σ_k l_k(α, β, Y, X_kW_k) + Σ_k ρ_k(λ_k, W_k),
s.t. W_k'X_k'X_kW_k = I_r, for k = 1, 2, …, K. l_k() are general loss functions with intercept α and coefficients β. η is the weight parameter and λ_k are the regularization parameters. r is the rank, i.e. the number of canonical pairs. By adjusting η, one can change the weight of the first correlation term and the second prediction term. η=0 is reduced rank regression and η=1 is sparse CCA (with orthogonal constrained W's). By choosing appropriate λ_k one can induce sparsity of W_k's to select useful variables for predicting Y. W_k's with B_k's and (α, β) are iterated using an ADMM algorithm. See the reference for details.
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. |
Chongliang Luo, Kun Chen.
Chongliang Luo, Jin Liu, Dipak D. Dey and Kun Chen (2016) Canonical variate regression. Biostatistics, doi: 10.1093/biostatistics/kxw001.
1 | ## see SimulateCVR for simulation examples, see CVR for parameter tuning.
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