hierNet.path: Fit a path of hierNet models- lasso models with interactions

In hierNet: A Lasso for Hierarchical Interactions

Description

One of the main functions in the hierNet package. Fits a path of hierNet models over different values of the regularization parameter. Calls hierNet, which 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.path(x, y,
             lamlist = NULL, delta=1e-8, minlam = NULL, maxlam = NULL, nlam=20, flmin=.01,
             diagonal = TRUE, strong = FALSE, aa = NULL, zz = NULL,
             stand.main = TRUE, stand.int = FALSE,
             rho = nrow(x), niter = 100, sym.eps = 0.001, 
             step = 1, maxiter = 2000, backtrack = 0.2, tol = 1e-05, 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)
lamlist	Optional vector of values of lambda (the regularization parameter). L1 penalty param is lamdbda * (1-delta).
delta	Elastic Net parameter. Squared L2 penalty param is lambda * delta. Not a tuning parameter: Think of as fixed and small. Default 1e-8.
minlam	Optional minimum value for lambda
maxlam	Optional maximum value for lambda
nlam	Number of values of lambda to be tried
flmin	Fraction of maxlam; minlam= flmin*maxlam. If computation is slow, try increasing flmin to focus on the sparser part of the path
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
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
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

bp	p by nlam matrix of estimated "positive part" main effects (p=#variables)
bn	p by nlam matrix of estimated "negative part" main effects
th	p by p by nlam array of estimated interaction coefficients
obj	nlam values of objective function, one per lambda value
lamlist	Vector of values of lambda used
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

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

hierNet,predict.hierNet, hierNet.cv

Examples

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)
print(fit)

Example output

i,lam= 1 129.72
GG converged in 1 iterations.
i,lam= 2 101.8
GG converged in 20 iterations.
i,lam= 3 79.89
GG converged in 26 iterations.
i,lam= 4 62.69
GG converged in 26 iterations.
i,lam= 5 49.2
GG converged in 26 iterations.
i,lam= 6 38.61
GG converged in 48 iterations.
i,lam= 7 30.3
GG converged in 57 iterations.
i,lam= 8 23.78
GG converged in 62 iterations.
i,lam= 9 18.66
GG converged in 55 iterations.
i,lam= 10 14.64
GG converged in 63 iterations.
i,lam= 11 11.49
GG converged in 60 iterations.
i,lam= 12 9.02
GG converged in 119 iterations.
i,lam= 13 7.08
GG converged in 122 iterations.
i,lam= 14 5.55
GG converged in 139 iterations.
i,lam= 15 4.36
GG converged in 147 iterations.
i,lam= 16 3.42
GG converged in 200 iterations.
i,lam= 17 2.68
GG converged in 374 iterations.
i,lam= 18 2.11
GG converged in 291 iterations.
i,lam= 19 1.65
GG converged in 602 iterations.
i,lam= 20 1.3
GG converged in 657 iterations.
Call:
hierNet.path(x = x, y = y)

      Lambda Objective Number of main effects Number of interactions
 [1,] 129.72    604.54                      1                      0
 [2,] 101.80    596.67                      1                      1
 [3,]  79.89    578.15                      4                      2
 [4,]  62.69    551.28                      4                      2
 [5,]  49.20    521.57                      4                      2
 [6,]  38.61    492.44                      7                      6
 [7,]  30.30    463.48                      8                      7
 [8,]  23.78    434.86                      8                     11
 [9,]  18.66    406.66                      8                     11
[10,]  14.64    380.64                      9                     12
[11,]  11.49    357.57                     10                     13
[12,]   9.02    337.13                     10                     20
[13,]   7.08    316.64                     10                     23
[14,]   5.55    295.96                     10                     24
[15,]   4.36    276.25                     10                     26
[16,]   3.42    258.17                     10                     30
[17,]   2.68    241.73                     10                     33
[18,]   2.11    226.67                     10                     34
[19,]   1.65    212.84                     10                     42
[20,]   1.30    199.61                     10                     45

hierNet documentation built on Feb. 6, 2020, 5:09 p.m.