hierNet.logistic: A logistic regression Lasso for interactions

Description

One of the main functions in the hierNet package. Builds a logistic 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 a alternate algorithm for large scale problems.

Usage

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

Arguments

A matrix of predictors, where the rows are the samples and the columns are the predictors

A vector of observations, with values 0 or 1, 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.

diagonal

Flag specifying whether to include "pure" quadratic terms, th_jjX_j^2, in the model. Default TRUE.

strong

Flag specifying strong hierarchy (TRUE) or weak hierarchy (FALSE). Default FALSE

An *optional* argument, a list with results from a previous call

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 Thresholding 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

Intercept

p-vector of estimated "positive part" main effect (p=#features)

p-vector of estimated "negative part" main effect; overall main effect estimated coefficients are bp-bn

Matrix of estimated interaction coefficients, of dimension p by p

obj

Value of objective function at minimum.

lam

Value of lambda used

type

Type of model fit- "gaussian" or "logistic" (binomial)

p-vector of column means of x

Mean of y

p-vector of column standard deviations of x

mzz

column means of feature product matrix

call

The call to hierNet

References

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

Examples

Run this code

# NOT RUN {
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)
y=1*(y>0)
fit=hierNet.logistic(x,y,lam=5)
print(fit)
# }