LassoNet_grid: Estimates coefficients and connection signs over the grid of...
In LassoNet: 3CoSE Algorithm

Description Usage Arguments Details Value Author(s) References Examples

Fits network regressions over the grid of values of penalty parameters λ1 and λ2, stores connection signs, number of iterations until convergence and convergence outcome.

1	lasso.net.grid(x,y ,beta.0,lambda1,lambda2,M1,m.iter,n.iter,iscpp=TRUE,tol,alt.num)

`x`	n \times p input data matrix
`y`	response vector or size n \times 1
`beta.0`	initial value for β. default - zero vector of size n \times 1
`lambda1`	lasso penalty coefficient
`lambda2`	network penalty coefficient
`M1`	penalty matrix
`m.iter`	maximum number of iterations for sign matrix updating; default - 100
`n.iter`	maximum number of iterations for β updating; default - 1e5
`iscpp`	binary choice for using cpp function in coordinate updates; 1 - use C++ (default), 0 - use R
`tol`	convergence in β tolerance level; default - 1e-6
`alt.num`	alt.num remaining iterataions are stored; default - 12

Fits network regression for the grid values of λ1 and λ2 using warm starts.

`beta`	matrix of β coefficients, columns are for different λ1 parameters, rows λ2 parameters
`mse`	mean squared error value
`M`	array of connection signs. M[,,i,j] is the connection sign matrix for j-th λ1 value and i-th λ2 value
`iterations`	matrix with stored number of steps for sign matrix to converge
`update.steps`	matrix with stored number of steps for β updates to converge. (only stores the last values from connection signs iterations)
`convergence.in.M`	matrix with stored values for convergence in sign matrix
`convergence.in.grid`	matrix with stored values for convergence in β coefficients. If at least one β did not converge in sign matrix iterations, 0 (false) is stored, otherwise 1 (true)
`xi.conv`	array with stored connection signs changes in each iteration
`beta.alt`	array of coefficient vectors in case connection signs alternate

Maintainer: Jonas Striaukas <jonas.striaukas@gmail.com>

Weber, M., Striaukas, J., Schumacher, M., Binder, H. "Network-Constrained Covariate Coefficient and Connection Sign Estimation" (2018) <doi:10.2139/ssrn.3211163>

p=200
n=100
beta.0=array(1,c(p,1))
x=matrix(rnorm(n*p),n,p)
y=rnorm(n,mean=0,sd=1)
lambda1=c(0,1)
lambda2=c(0,1)
M1=diag(p)
lasso.net.grid(x, y, beta.0, lambda1, lambda2, M1)