lasso.net.grid {LassoNet}

Estimates coefficients and connection signs over the grid of values of penalty parameters \lambda1 and \lambda2.

Description

Fits network regressions over the grid of values of penalty parameters \lambda1 and \lambda2, stores connection signs, number of iterations until convergence and convergence outcome.

Usage

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

Arguments

x

n \times p input data matrix

y

response vector or size n \times 1

beta.0

initial value for \beta. 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 \beta updating; default - 1e5

iscpp

binary choice for using cpp function in coordinate updates; 1 - use C++ (default), 0 - use R

tol

convergence in \beta tolerance level; default - 1e-6

alt.num

alt.num remaining iterataions are stored; default - 12

Details

Fits network regression for the grid values of \lambda1 and \lambda2 using warm starts.

Value

beta

matrix of \beta coefficients, columns are for different \lambda1 parameters, rows \lambda2 parameters

mse

mean squared error value

M

array of connection signs. M[,,i,j] is the connection sign matrix for j-th \lambda1 value and i-th \lambda2 value

iterations

matrix with stored number of steps for sign matrix to converge

update.steps

matrix with stored number of steps for \beta 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 \beta coefficients. If at least one \beta 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

Author(s)

Maintainer: Jonas Striaukas <[e-mail]>

References

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

Examples

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)