LassoNet (version 0.8.3)

lasso.net.grid: Estimates coefficients and connection signs over the grid of values of penalty parameters \(\lambda\)1 and \(\lambda\)2.

Description

Fits network regressions over the grid of values of penalty parameters \(\lambda\)1 and \(\lambda\)2, 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

Value

beta

matrix of \(\beta\) coefficients, columns are for different \(\lambda\)1 parameters, rows \(\lambda\)2 parameters

mse

mean squared error value

M

array of connection signs. \(M[,,i,j]\) is the connection sign matrix for j-th \(\lambda\)1 value and i-th \(\lambda\)2 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

Details

Fits network regression for the grid values of \(\lambda\)1 and \(\lambda\)2 using warm starts.

References

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

Examples

# NOT RUN {
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)
# }