hierNet: A Lasso for interactions

In pejovic/int3D: A Lasso for Hierarchical Interactions

Description

One of the main functions in the hierNet package. Builds a regression model with hierarchically constrained pairwise interactions. Required inputs are an x matrix of features (the columns are the features) and a y vector of values. Reasonably fast for moderate sized problems (100-200 variables). We are currently working on an alternate algorithm for large scale problems.

Usage

hierNet(x, y, lam, delta=1e-8, strong=FALSE, diagonal=TRUE, aa=NULL, zz=NULL,
        center=TRUE, stand.main=TRUE, stand.int=FALSE, 
        rho=nrow(x), niter=100, sym.eps=1e-3,
        step=1, maxiter=2000, backtrack=0.2, tol=1e-5, trace=0)

Arguments

x	A matrix of predictors, where the rows are the samples and the columns are the predictors
y	A vector of observations, where length(y) equals nrow(x)
lam	Regularization parameter (>0). L1 penalty param is lam * (1-delta).
delta	Elastic Net parameter. Squared L2 penalty param is lam * delta. Not a tuning parameter: Think of as fixed and small. Default 1e-8.
strong	Flag specifying strong hierarchy (TRUE) or weak hierarchy (FALSE). Default FALSE.
diagonal	Flag specifying whether to include "pure" quadratic terms, th_jjX_j^2, in the model. Default TRUE.
aa	An *optional* argument, a list with results from a previous call
zz	An *optional* argument, a matrix whose columns are products of features, computed by the function compute.interactions.c
center	Should features be centered? Default TRUE; FALSE should rarely be used. This option is available for special uses only
stand.main	Should main effects be standardized? Default TRUE.
stand.int	Should interactions be standardized? Default FALSE.
rho	ADMM parameter: tuning parameter (>0) for ADMM. If there are convergence problems, try decreasing rho. Default n.
niter	ADMM parameter: number of iterations
sym.eps	ADMM parameter: threshold for symmetrizing with strong=TRUE
step	Stepsize for generalized gradient descent
maxiter	Maximum number of iterations for generalized gradient descent
backtrack	Backtrack parameter for generalized gradient descent
tol	Error tolerance parameter for generalized gradient descent
trace	Output option; trace=1 gives verbose output

Value

bp	p-vector of estimated "positive part" main effect (p=# features)
bn	p-vector of estimated "negative part" main effect; overall main effect estimated coefficients are bp-bn
th	Matrix of estimated interaction coefficients, of dimension p by p. Note: when output from hierNet is printed, th is symmetrized (set to (th+t(th))/2) for simplicity.
obj	Value of objective function at minimum.
lam	Value of lambda used
type	Type of model fit- "gaussian" or "logistic" (binomial)
mx	p-vector of column means of x
sx	p-vector of column standard deviations of x
my	mean of y
mzz	column means of feature product matrix
szz	column standard deviations of feature product matrix
call	The call to hierNet

Author(s)

Jacob Bien and Robert Tibshirani

References

Bien, J., Taylor, J., Tibshirani, R., (2013) "A Lasso for Hierarchical Interactions." Annals of Statistics. 41(3). 1111-1141.

See Also

predict.hierNet, hierNet.cv, hierNet.path

Examples

set.seed(12)
# fit a single hierNet model
x=matrix(rnorm(100*10),ncol=10)
x=scale(x,TRUE,TRUE)
y=x[,1]+2*x[,2]+ x[,1]*x[,2]+3*rnorm(100)
fit=hierNet(x,y,lam=50)
print(fit)

# try strong (rather than weak) hierarchy
fit=hierNet(x,y,lam=50, strong=TRUE)
print(fit)

# a typical analysis including cross-validation
set.seed(12)
x=matrix(rnorm(100*10),ncol=10)
x=scale(x,TRUE,TRUE)
y=x[,1]+2*x[,2]+ x[,1]*x[,2]+3*rnorm(100)
fit=hierNet.path(x,y)
fitcv=hierNet.cv(fit,x,y)
print(fitcv)

lamhat=fitcv$lamhat.1se
fit2=hierNet(x,y,lam=lamhat)
yhat=predict.hierNet(fit2,x)

pejovic/int3D documentation built on May 25, 2019, 12:45 a.m.