| Type: | Package |
| Title: | Correlation-Based Penalized Estimators |
| Version: | 0.1.0 |
| Maintainer: | Mina Norouzirad <mina.norouzirad@gmail.com> |
| Description: | Provides correlation-based penalty estimators for both linear and logistic regression models by implementing a new regularization method that incorporates correlation structures within the data. This method encourages a grouping effect where strongly correlated predictors tend to be in or out of the model together. See Tutz and Ulbricht (2009) <doi:10.1007/s11222-008-9088-5> and Algamal and Lee (2015) <doi:10.1016/j.eswa.2015.08.016>. |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| URL: | https://github.com/mnrzrad/CBPE |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.3.2 |
| Depends: | R (≥ 3.5) |
| Imports: | stats |
| NeedsCompilation: | no |
| Packaged: | 2024-07-02 07:23:55 UTC; minan |
| Author: | Mohammad Arashi 
[ctb],
Mahdi Rahimi [ctb],
Mina Norouzirad
[aut, cre, cph],
FCT, I.P. [fnd] (under the scope of the projects UIDB/00297/2020 and
UIDP/00297/2020 (NovaMath)) |
| Repository: | CRAN |
| Date/Publication: | 2024-07-02 15:30:02 UTC |
Correlation-based Estimator for Linear Regression Models
Description
This function computes the correlation-based estimator for linear regression models.
Usage
CBPLinearE(X, y, lambda)
Arguments
X |
A numeric matrix of predictors where rows represent observations and columns represent variables. |
y |
A numeric vector of response variables. |
lambda |
A regularization parameter. |
Details
The correlation-based penalized linear estimator is calculated as:
\hat{\beta} = \text{argmin} \left\{ \sum_{i=1}^n (y_i - \mathbf{x}_i^\top \boldsymbol{\beta})^2 + \lambda \sum_{i=1}^{p-1} \sum_{j>i} \left( \frac{(\beta_i - \beta_j)^2}{1 - \rho_{ij}} + \frac{(\beta_i + \beta_j)^2}{1 + \rho_{ij}} \right) \right\}
where \rho_{ij} denotes the (empirical) correlation between the ith and the jth predictor.
Value
A numeric vector of the estimated coefficients for the specified model.
References
Tutz, G., Ulbricht, J. (2009). Penalized regression with correlation-based penalty. Stat Comput 19, 239–253.
Examples
set.seed(42)
n <- 100
p <- 4
X <- matrix(rnorm(n * p), n, p)
beta_true <- c(0.5, -1, 2, 5)
y <- X %*% beta_true + rnorm(n)
lambda <- 0.1
result <- CBPLinearE(X, y, lambda = lambda)
print(result)
Correlation-based Estimator for Logistic Regression Models
Description
This function computes the correlation-based estimator for logistic regression models.
Usage
CBPLogisticE(X, y, lambda, max_iter = 100, tol = 1e-06)
Arguments
X |
A numeric matrix of predictors where rows represent observations and columns represent variables. |
y |
A numeric vector of binary outcomes (0 or 1). |
lambda |
A regularization parameter. |
max_iter |
An integer specifying the maximum number of iterations for the logistic regression algorithm. Default is 100. |
tol |
A numeric value specifying the convergence tolerance for the logistic regression algorithm. Default is 1e-10. |
Details
The correlation-based penalized logistic estimator is calculated as:
\hat{\beta} = \text{argmin}\left\{ \sum_{i=1}^n \left( y_i \ln(\pi_i) + (1 - y_i) \ln(1 - \pi_i) \right) + \lambda \sum_{i=1}^{p-1} \sum_{j>i} \left( \frac{(\beta_i - \beta_j)^2}{1 - \rho_{ij}} + \frac{(\beta_i + \beta_j)^2}{1 + \rho_{ij}} \right) \right\}
where \pi_i = \text{Pr}(y_i = 1|\mathbf{x}_i) and \rho_{ij} denotes the (empirical) correlation between the ith and the jth predictor.
Value
A numeric vector of the estimated coefficients for the specified model.
References
Algamal, Z. Y., & Lee, M. H. (2015). Penalized logistic regression with the adaptive LASSO for gene selection in high-dimensional cancer classification. Expert Systems with Applications, 42(23), 9326-9332.
Examples
set.seed(42)
n <- 100
p <- 4
X <- matrix(rnorm(n * p), n, p)
beta_true <- c(0.5, -1, 2, 5)
y <- rbinom(n, 1, 1 / (1 + exp(-X %*% beta_true)))
lambda <- 0.1
result <- CBPLogisticE(X, y, lambda)
print(result)