Type: Package
Title: 3CoSE Algorithm
Version: 0.8.3
Date: 2019-12-17
Author: Jonas Striaukas [aut, trl, cre] and Matthias Weber [aut]
Maintainer: Jonas Striaukas <jonas.striaukas@gmail.com>
Description: Contains functions to estimate a penalized regression model using 3CoSE algorithm, see Weber, Striaukas, Schumacher Binder (2018) <doi:10.2139/ssrn.3211163>.
License: GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
Imports: Rcpp (≥ 0.11.5)
Suggests: snowfall
LinkingTo: Rcpp
NeedsCompilation: yes
Packaged: 2020-01-14 12:37:39 UTC; striaukas
Repository: CRAN
Date/Publication: 2020-01-19 15:30:08 UTC

LassoNet: package for 3CoSE algorithm.

Description

LassoNet contains functions to estimate a penalized regression model using 3CoSE algorithm described in the paper Weber, Striaukas, Schumacher and Binder (2018). The main function of the package is the function lasso.net.grid, see the example below.

Details

Package: LassoNet
Type: Package
Version: 0.8.3
Date: 2019-12-16
License: Open source

Author(s)

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

References

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

See Also

Rcpp, glmnet

Updates \beta coefficients.

Description

This function updates \beta for given penalty parameters.

Usage

beta.update.net(x,y,beta,lambda1,lambda2,M1,n.iter,iscpp,tol)

Arguments

x

input data matrix of size n \times p; n - number of observations; p - number of covariates

y

response vector or size n \times 1

beta

initial value for \beta; default - zero vector of size n \times 1

lambda1

lasso penalty parameter

lambda2

network penalty parameter

M1

penalty matrix

n.iter

maximum number of iterations for \beta step; default - 1e5

iscpp

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

tol

convergence tolerance level; default - 1e-6

Details

Updates the coefficient vector \beta given the data and penalty parameters \lambda1 and \lambda2. Convergence criterion is defined as \sum_{i=1}^p |\beta_{i,j} - \beta_{i,j-1}| \leq to.

Value

beta

updated \beta vector

convergence

binary variable; 1 - yes

steps

number of steps until convergence

Author(s)

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

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<-1
lambda2<-1
M1<-diag(p)
updates<-beta.update.net(x, y, beta.0, lambda1, lambda2, M1)

C++ subroutine that updates \beta coefficients.

Description

This function updates \beta for given penalty parameters.

Usage

betanew_lasso_cpp(xx, xy, beta, M, y, Lambda1, Lambda2, iter, tol)

Arguments

xx

Bx matrix

xy

By vector

beta

initial value for \beta; default - zero vector of size p \times 1

M

penalty matrix

y

response vector or size n \times 1

Lambda1

lasso penalty parameter

Lambda2

network penalty parameter

iter

maximum number of iterations for \beta step

tol

convergence tolerance level

Details

See beta.update.net

Value

beta

updated \beta vector

steps

number of steps until convergence

Author(s)

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

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<-1
lambda2<-1
M1<-diag(p)
updates<-beta.update.net(x, y, beta.0, lambda1, lambda2, M1)

Fast least squares estimate.

Description

Computes least squares estimate in an efficient way.

Usage

fastols(y, x)

Arguments

y

dependent variable

x

response variable

Author(s)

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

Examples

p<-10
n<-100
x<-matrix(rnorm(n*p),n,p)
beta<-array(5, c(p,1))
y<-x%*%beta + rnorm(n,mean=0,sd=0.1)
fastols(y,x)

Computes decomposition elements.

Description

Computes matrices B^{ij}_X and B^{ij}_y to speed up estimation of connection signs. These matrices are stored only for indices that have non zero entries in penalty matrix M.

Usage

get.BxBy(x, y, M)

Arguments

x

Input data matrix of size n \times p, n - number of observations, p - number of covariates

y

y Response vector or size n \times 1

M

penalty matrix

Details

Calculates matrices all for i and j indices that have non zero values in a given penalty matrix.

Value

Bx

array of B^{ij}_X stored matrices. Bx[,,k] are the k-th combination of i and j non zero entry in the penalty matrix M

By

array of B^{ij}_y stored matrices. By[,k] are the k-th combination of i and j non zero entry in the penalty matrix M

Author(s)

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

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
x<-matrix(rnorm(n*p),n,p)
y<-rnorm(n,mean=0,sd=1)
M<-diag(p)
get.BxBy(x, y, M)

Vetorizes connection sign matrix.

Description

Stores a matrix of connection signs to a vector.

Usage

get.signs.M(MAT)

Arguments

MAT

matrix of connection signs that contains -1, 1 or 0

Value

vec.out

vectorized MAT matrix

Author(s)

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

Updates the estimates of the connection signs by running mini OLS models.

Description

Updates connection signs \hat{\xi}.

Usage

get.xi(Bx,By,beta,xi,M)

Arguments

Bx

Bx element

By

By element

beta

\hat{\beta} estimated value

xi

\hat{\xi} matrix estimated at the previous step

M

penalty matrix

Value

xi

\hat{\xi} matrix

Author(s)

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

References

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

Estimates coefficients over the grid values of penalty parameters.

Description

See lasso.net.grid

Usage

lasso.net.fixed(x,y,beta.0,lambda1,lambda2,M1,n.iter,iscpp,tol)

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

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

Details

Function loops through the grid of values of penalty parameters \lambda1 and \lambda2 until convergence is reached. Warm starts are stored for each iterator. The warm starts are stored once the coordinate updating converges.

Value

beta

Matrix of \beta coefficients. Columns denote different \lambda1 coefficients, rows - \lambda2 coefficients

mse

Mean squared error 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.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)

Author(s)

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

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.fixed(x, y, beta.0, lambda1, lambda2, M1)

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 <jonas.striaukas@gmail.com>

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)

Computes Laplacian matrix.

Description

Computes Laplacian matrix.

Usage

mat.to.laplacian(M1,type)

Arguments

M1

p \times p matrix

type

Laplacian types: 1) "normalized" (default) - normalized Laplacian, 2) "combinatorial" - combinatorial Laplacian

Value

L

Laplacian

Author(s)

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

Updates connection sign matrix.

Description

Updates M using relation (M)_{ij} = -\hat{\xi}_{ij} |(M_1)|_{ij}.

Usage

matrix.M.update(M, xi)

Arguments

M

penalty matrix

xi

estimated \hat{\xi}_{ij} matrix

Details

Updates M

Value

M

updated M

Author(s)

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

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<-100
M<-diag(p)
xi<-matrix(rnorm(p*p), p, p)
matrix.M.update(M,xi)

Soft thresholding operator.

Description

Soft thresholding operator.

Usage

soft.thresh(x, kappa)

Arguments

x

\beta coordinate

kappa

\kappa value in general or \lambda_1 for covariance updating

Details

Soft thresholding definition: S(x,\kappa) = sign(x) (|x| - \kappa)_{+}

Value

x

value after applying soft thresholding operator

Author(s)

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

Examples

kappa<-0.2
x<-0.7
soft.thresh(x, kappa)