# edgenet-methods: Fit a graph-regularized linear regression model using... In netReg: Network-Regularized Regression Models

## Description

Fit a graph-regularized linear regression model using edge-penalization. The coefficients are computed using graph-prior knowledge in the form of one/two affinity matrices. Graph-regularization is an extension to previously introduced regularization techniques, such as the LASSO. See the vignette for details on the objective function of the model: `vignette("edgenet", package="netReg")`

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43``` ```edgenet( X, Y, G.X = NULL, G.Y = NULL, lambda = 1, psigx = 1, psigy = 1, thresh = 1e-05, maxit = 1e+05, learning.rate = 0.01, family = gaussian ) ## S4 method for signature 'matrix,numeric' edgenet( X, Y, G.X = NULL, G.Y = NULL, lambda = 1, psigx = 1, psigy = 1, thresh = 1e-05, maxit = 1e+05, learning.rate = 0.01, family = gaussian ) ## S4 method for signature 'matrix,matrix' edgenet( X, Y, G.X = NULL, G.Y = NULL, lambda = 1, psigx = 1, psigy = 1, thresh = 1e-05, maxit = 1e+05, learning.rate = 0.01, family = gaussian ) ```

## Arguments

 `X` input matrix, of dimension (`n` x `p`) where `n` is the number of observations and `p` is the number of covariables. Each row is an observation vector. `Y` output matrix, of dimension (`n` x `q`) where `n` is the number of observations and `q` is the number of response variables. Each row is an observation vector. `G.X` non-negativ affinity matrix for `X`, of dimensions (`p` x `p`) where `p` is the number of covariables `G.Y` non-negativ affinity matrix for `Y`, of dimensions (`q` x `q`) where `q` is the number of responses `lambda` `numerical` shrinkage parameter for LASSO. `psigx` `numerical` shrinkage parameter for graph-regularization of `G.X` `psigy` `numerical` shrinkage parameter for graph-regularization of `G.Y` `thresh` `numerical` threshold for optimizer `maxit` maximum number of iterations for optimizer (`integer`) `learning.rate` step size for Adam optimizer (`numerical`) `family` family of response, e.g. gaussian or binomial

## Value

An object of class `edgenet`

 `beta ` the estimated (`p` x `q`)-dimensional coefficient matrix B.hat `alpha ` the estimated (`q` x `1`)-dimensional vector of intercepts `parameters ` regularization parameters `lambda ` regularization parameter lambda) `psigx ` regularization parameter psigx `psigy ` regularization parameter psigy `family ` a description of the error distribution and link function to be used. Can be a `netReg::family` function or a character string naming a family function, e.g. `gaussian` or "gaussian". `call ` the call that produced the object

## References

Cheng, Wei and Zhang, Xiang and Guo, Zhishan and Shi, Yu and Wang, Wei (2014), Graph-regularized dual Lasso for robust eQTL mapping.
Bioinformatics

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```X <- matrix(rnorm(100 * 10), 100, 10) b <- matrix(rnorm(100), 10) G.X <- abs(rWishart(1, 10, diag(10))[, , 1]) G.Y <- abs(rWishart(1, 10, diag(10))[, , 1]) diag(G.X) <- diag(G.Y) <- 0 # estimate the parameters of a Gaussian model Y <- X %*% b + matrix(rnorm(100 * 10), 100) ## dont use affinity matrices fit <- edgenet(X = X, Y = Y, family = gaussian, maxit = 10) ## only provide one matrix fit <- edgenet(X = X, Y = Y, G.X = G.X, psigx = 1, family = gaussian, maxit = 10) ## use two matrices fit <- edgenet(X = X, Y = Y, G.X = G.X, G.Y, family = gaussian, maxit = 10) ## if Y is vectorial, we cannot use an affinity matrix for Y fit <- edgenet(X = X, Y = Y[, 1], G.X = G.X, family = gaussian, maxit = 10) ```

netReg documentation built on Nov. 8, 2020, 5:17 p.m.