| Type: | Package |
| Title: | Robust Variable Selection with Exponential Squared Loss |
| Description: | Computationally efficient tool for performing variable selection and obtaining robust estimates, which implements robust variable selection procedure proposed by Wang, X., Jiang, Y., Wang, S., Zhang, H. (2013) <doi:10.1080/01621459.2013.766613>. Users can enjoy the near optimal, consistent, and oracle properties of the procedures. |
| Version: | 0.1.0 |
| Date: | 2021-03-21 |
| Maintainer: | Jin Zhu <zhuj37@mail2.sysu.edu.cn> |
| Imports: | MASS, matrixStats |
| License: | GPL-3 |
| Encoding: | UTF-8 |
| LazyData: | true |
| RoxygenNote: | 7.1.1 |
| Suggests: | knitr, rmarkdown, |
| VignetteBuilder: | knitr |
| NeedsCompilation: | no |
| Packaged: | 2021-03-21 12:35:58 UTC; JinZhu |
| Author: | Jin Zhu [cre, aut], Borui Tang [aut], Yunlu Jiang [aut], Xueqin Wang [aut] |
| Repository: | CRAN |
| Date/Publication: | 2021-03-22 15:40:02 UTC |
Provides estimated coefficients from a fitted "robustlm" object.
Description
This function provides estimatedcoefficients from a fitted "robustlm" object.
Usage
## S3 method for class 'robustlm'coef(object, ...)Arguments
object | An " |
... | Other arguments. |
Value
A list consisting of the intercept and regression coefficients of the fitted model.
Make predictions from a "robustlm" object.
Description
Returns predictions from a fitted"robustlm" object.
Usage
## S3 method for class 'robustlm'predict(object, newx, ...)Arguments
object | Output from the |
newx | New data used for prediction |
... | Additional arguments affecting the predictions produced. |
Value
The predicted responses.
Print method for a "robustlm" object
Description
Print the primary elements of the "robustlm" object.
Usage
## S3 method for class 'robustlm'print(x, ...)Arguments
x | A " |
... | Additional print arguments. |
Value
print arobustlm object.
Robust variable selection with exponential squared loss
Description
robustlm carries out robust variable selection with exponential squared loss. A block coordinate gradient descent algorithm is used to minimize the loss function.
Usage
robustlm(x, y, gamma = NULL, weight = NULL, intercept = TRUE)Arguments
x | Input matrix, of dimension nobs * nvars; each row is an observation vector. Should be in matrix format. |
y | Response variable. Should be a numerical vector or matrix with a single column. |
gamma | Tuning parameter in the loss function, which controls the degree of robustness and efficiency of the regression estimators.The loss function is defined as
When |
weight | Weight in the penalty. The penalty is given by
|
intercept | Should intercepts be fitted (TRUE) or set to zero (FALSE) |
Details
robustlm solves the following optimization problem to obtain robust estimators of regression coefficients:
argmin_{\beta} \sum_{i=1}^n(1-exp{-(y_i-x_i^T\beta)^2/\gamma_n})+n\sum_{i=1}^d p_{\lambda_{nj}}(|\beta_j|),
wherep_{\lambda_{n j}}(|\beta_{j}|)=\lambda_{n j}|\beta_{j}| is the adaptive LASSO penalty. Block coordinate gradient descent algorithm is used to efficiently solve the optimization problem. The tuning parametergamma and regularization parameterweight are chosen adaptively by default, while they can be supplied by the user.Specifically, the defaultweight meets the following BIC-type criterion:
min_{\tau_n} \sum_{i=1}^{n}[1-exp {-(Y_i-x_i^T} {\beta})^{2} / \gamma_{n}]+n \sum_{j=1}^{d} \tau_{n j}|\beta_j| /|\tilde{\beta}_{n j}|-\sum_{j=1}^{d} \log (0.5 n \tau_{n j}) \log (n).
Value
An object with S3 class "robustlm", which is alist with the following components:
beta | The regression coefficients. |
alpha | The intercept. |
gamma | The tuning parameter used in the loss. |
weight | The regularization parameters. |
loss | Value of the loss function calculated on the training set. |
Author(s)
Borui Tang, Jin Zhu, Xueqin Wang
References
Xueqin Wang, Yunlu Jiang, Mian Huang & Heping Zhang (2013) Robust Variable Selection With Exponential Squared Loss, Journal of the American Statistical Association, 108:502, 632-643, DOI: 10.1080/01621459.2013.766613
Tseng, P., Yun, S. A coordinate gradient descent method for nonsmooth separable minimization. Math. Program. 117, 387-423 (2009). https://doi.org/10.1007/s10107-007-0170-0
Examples
library(MASS)N <- 100p <- 8rho <- 0.2mu <- rep(0, p)Sigma <- rho * outer(rep(1, p), rep(1, p)) + (1 - rho) * diag(p)ind <- 1:pbeta <- (-1)^ind * exp(-2 * (ind - 1) / 20)lambda_seq <- seq(0.05, 5, length.out = 100)X <- mvrnorm(N, mu, Sigma)Z <- rnorm(N, 0, 1)k <- sqrt(var(X %*% beta) / (3 * var(Z)))Y <- X %*% beta + drop(k) * Zrobustlm(X, Y)