Help for package vennLasso

Type:

Package

Title:

Variable Selection for Heterogeneous Populations

Version:

0.2.0

Description:

Provides variable selection and estimation routines for models with main effects stratified on multiple binary factors. The 'vennLasso' package is an implementation of the method introduced in Huling et al. (2018) <doi:10.1111/biom.12769>.

URL:

https://github.com/jaredhuling/vennLasso

BugReports:

https://github.com/jaredhuling/vennLasso/issues

License:

GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]

Encoding:

UTF-8

Depends:

R (≥ 3.2.0)

Imports:

Rcpp (≥ 0.11.0), foreach, survival, MASS, Matrix, VennDiagram, visNetwork, igraph, methods

LinkingTo:

Rcpp, RcppEigen, RcppNumerical

RoxygenNote:

7.3.3

Suggests:

knitr, rmarkdown, testthat (≥ 3.0.0), glmnet

VignetteBuilder:

knitr

Config/testthat/edition:

NeedsCompilation:

yes

Packaged:

2026-11-13 20:30:13 UTC; huling

Author:

Jared Huling

[aut, cre], Muxuan Liang [ctb], Yixuan Qiu [cph], Gael Guennebaud [cph], Ray Gardner [cph], Jitse Niesen [cph]

Maintainer:

Jared Huling <jaredhuling@gmail.com>

Repository:

CRAN

Date/Publication:

2026-11-14 08:20:08 UTC

Cross Validation for the vennLasso

Description

Cross Validation for the vennLasso

Usage

cv.vennLasso(
  x,
  y,
  groups,
  lambda = NULL,
  compute.se = FALSE,
  conf.int = NULL,
  type.measure = c("mse", "deviance", "class", "auc", "mae", "brier"),
  nfolds = 10,
  foldid,
  grouped = TRUE,
  keep = FALSE,
  parallel = FALSE,
  ...
)

Arguments

x

input matrix or SparseMatrix of dimension nobs x nvars. Each row is an observation, each column corresponds to a covariate

y

numeric response vector of length nobs

groups

A list of length equal to the number of groups containing vectors of integers indicating the variable IDs for each group. For example, groups=list(c(1,2), c(2,3), c(3,4,5)) specifies that Group 1 contains variables 1 and 2, Group 2 contains variables 2 and 3, and Group 3 contains variables 3, 4, and 5. Can also be a matrix of 0s and 1s with the number of columns equal to the number of groups and the number of rows equal to the number of variables. A value of 1 in row i and column j indicates that variable i is in group j and 0 indicates that variable i is not in group j.

lambda

A user-specified sequence of lambda values. Left unspecified, the a sequence of lambda values is automatically computed, ranging uniformly on the log scale over the relevant range of lambda values.

compute.se

logical flag. If TRUE, standard errors will be computed, otherwise if FALSE they will not

conf.int

value between 0 and 1 indicating the level of the confidence intervals to be computed. For example if conf.int = 0.95, 95 percent confidence intervals will be computed.

type.measure

One of c("mse","deviance","class","auc","mae","brier") indicating measure to evaluate for cross-validation. The default is type.measure = "deviance", which uses squared-error for gaussian models (a.k.a type.measure = "mse" there), deviance for logistic regression. type.measure = "class" applies to binomial only. type.measure = "auc" is for two-class logistic regression only. type.measure = "mse" or type.measure = "mae" (mean absolute error) can be used by all models; they measure the deviation from the fitted mean to the response. type.measure = "brier" is for models with family = "coxph" and will compute the Brier score.

nfolds

number of folds for cross-validation. default is 10. 3 is smallest value allowed.

foldid

an optional vector of values between 1 and nfold specifying which fold each observation belongs to.

grouped

Like in glmnet, this is an experimental argument, with default TRUE, and can be ignored by most users. For all models, this refers to computing nfolds separate statistics, and then using their mean and estimated standard error to describe the CV curve. If grouped = FALSE, an error matrix is built up at the observation level from the predictions from the nfold fits, and then summarized (does not apply to type.measure = "auc").

keep

If keep = TRUE, a prevalidated list of arrasy is returned containing fitted values for each observation and each value of lambda for each model. This means these fits are computed with this observation and the rest of its fold omitted. The folid vector is also returned. Default is keep = FALSE

parallel

If TRUE, use parallel foreach to fit each fold. Must register parallel before hand, such as doMC.

...

parameters to be passed to vennLasso

Value

An object with S3 class "cv.vennLasso"

Examples


library(Matrix)

set.seed(123)
n.obs <- 150
n.vars <- 25

true.beta.mat <- array(NA, dim = c(3, n.vars))
true.beta.mat[1,] <- c(-0.5, -1, 0, 0, 2, rep(0, n.vars - 5))
true.beta.mat[2,] <- c(0.5, 0.5, -0.5, -0.5, 1, -1, rep(0, n.vars - 6))
true.beta.mat[3,] <- c(0, 0, 1, 1, -1, rep(0, n.vars - 5))
rownames(true.beta.mat) <- c("1,0", "1,1", "0,1")
true.beta <- as.vector(t(true.beta.mat))

x.sub1 <- matrix(rnorm(n.obs * n.vars), n.obs, n.vars)
x.sub2 <- matrix(rnorm(n.obs * n.vars), n.obs, n.vars)
x.sub3 <- matrix(rnorm(n.obs * n.vars), n.obs, n.vars)

x <- as.matrix(rbind(x.sub1, x.sub2, x.sub3))

conditions <- as.matrix(cbind(c(rep(1, 2 * n.obs), rep(0, n.obs)),
                              c(rep(0, n.obs), rep(1, 2 * n.obs))))

y <- rnorm(n.obs * 3, sd = 3) + drop(as.matrix(bdiag(x.sub1, x.sub2, x.sub3)) %*% true.beta)

fit <- cv.vennLasso(x = x, y = y, groups = conditions, nfolds = 3)

fitted.coef <- predict(fit$vennLasso.fit, type = "coefficients", s = fit$lambda.min)
(true.coef <- true.beta.mat[match(dimnames(fit$vennLasso.fit$beta)[[1]], 
                                  rownames(true.beta.mat)),])
round(fitted.coef, 2)

## effects smaller for logistic regression

true.beta.mat <- true.beta.mat / 2
true.beta <- true.beta / 2
# logistic regression example#'
y <- rbinom(n.obs * 3, 1, 
       prob = 1 / (1 + exp(-drop(as.matrix(bdiag(x.sub1, x.sub2, x.sub3)) %*% true.beta))))

bfit <- cv.vennLasso(x = x, y = y, groups = conditions, family = "binomial",
                     nfolds = 3)

fitted.coef <- predict(bfit$vennLasso.fit, type = "coefficients", s = bfit$lambda.min)
(true.coef <- true.beta.mat[match(dimnames(bfit$vennLasso.fit$beta)[[1]], 
                                  rownames(true.beta.mat)),])
round(fitted.coef, 2)

function to estimate the hierarchical sparsity parameter for a desired level of sparsity for simulated hierarchical coefficients

Description

function to estimate the hierarchical sparsity parameter for a desired level of sparsity for simulated hierarchical coefficients

Usage

estimate.hier.sparsity.param(
  ncats,
  nvars,
  avg.hier.zeros = 0.3,
  nsims = 150,
  effect.size.max = 0.5,
  misspecification.prop = 0
)

Arguments

ncats

number of categories to stratify on

nvars

number of variables

avg.hier.zeros

desired percent of zero variables among the variables with hierarchical zero patterns.

nsims

number of simulations to estimate the average sparsity. A larger number will be more accurate but take much longer.

effect.size.max

maximum magnitude of the true effect sizes

misspecification.prop

proportion of variables with hierarchical missingness misspecified

Examples

set.seed(123)


# estimate hier.sparsity.param for 0.15 total proportion of nonzero variables
# among vars with hierarchical zero patterns

hsp <- estimate.hier.sparsity.param(ncats = 3, nvars = 25, avg.hier.zeros = 0.15, nsims = 10)

# with nsims = 100, the above results in the following value
hsp <- 0.6341772

# check that this does indeed achieve the desired level of sparsity
mean(replicate(100, mean(genHierSparseBeta(ncats = 3, 
                           nvars = 25, hier.sparsity.param = hsp) != 0)  ))

sparseBeta <- genHierSparseBeta(ncats = 3, nvars = 25, hier.sparsity.param = hsp)



hsp2 <- estimate.hier.sparsity.param(ncats = 2, nvars = 100, 
                        avg.hier.zeros = 0.30, nsims = 10)

# with nsims = 50 and nvars = 100, avg.hier.zeros = 0.30 gives
# 0.5778425 (ncats = 2), 0.4336312 (ncats = 3), 0.2670061 (ncats = 4),
# 0.146682 (ncats = 5) and 0.07551241 (ncats = 6)

function to generate coefficient matrix with hierarchical sparsity

Description

function to generate coefficient matrix with hierarchical sparsity

Usage

genHierSparseBeta(
  ncats,
  nvars,
  hier.sparsity.param = 0.5,
  avg.hier.zeros = NULL,
  effect.size.max = 0.5,
  misspecification.prop = 0
)

Arguments

ncats

number of categories to stratify on

nvars

number of variables

hier.sparsity.param

parameter between 0 and 1 which determines how much hierarchical sparsity there is. To achieve a desired total level of sparsity among the variables with hierarchical sparsity, this parameter can be estimated using the function 'estimate.hier.sparsity.param'

avg.hier.zeros

desired percent of zero variables among the variables with hierarchical zero patterns. If this is specified, it will override the given hier.sparsity.param value and estimate it. This takes a while

effect.size.max

maximum magnitude of the true effect sizes

misspecification.prop

proportion of variables with hierarchical missingness misspecified

Examples

set.seed(123)

# estimate hier.sparsity.param for 0.15 total proportion of nonzero variables
# among vars with hierarchical zero patterns
# NOT RUN: Takes a long time
# hsp <- estimate.hier.sparsity.param(ncats = 3, nvars = 25, avg.hier.zeros = 0.15, nsims = 100)
# the above results in the following value
hsp <- 0.6341772

# check that this does indeed achieve the desired level of sparsity
mean(replicate(100, mean(genHierSparseBeta(ncats = 3, 
                           nvars = 25, hier.sparsity.param = hsp) != 0)  ))

sparseBeta <- genHierSparseBeta(ncats = 3, nvars = 25, hier.sparsity.param = hsp)

function to generate data with hierarchical sparsity

Description

function to generate data with hierarchical sparsity

Usage

genHierSparseData(
  ncats,
  nvars,
  nobs,
  nobs.test = 100,
  hier.sparsity.param = 0.5,
  avg.hier.zeros = NULL,
  prop.zero.vars = 0.5,
  effect.size.max = 0.5,
  misspecification.prop = 0,
  family = c("gaussian", "binomial", "coxph"),
  sd = 1,
  snr = NULL,
  beta = NULL,
  tau = 10,
  covar = 0
)

Arguments

ncats

number of categories to stratify on

nvars

number of variables

nobs

number of observations per strata to simulate

nobs.test

number of independent test observations per strata to simulate

hier.sparsity.param

avg.hier.zeros

desired percent of zero variables among the variables with hierarchical zero patterns. If this is specified, it will override the given hier.sparsity.param value and estimate it. This takes a while

prop.zero.vars

proportion of all variables that will be zero across all strata

effect.size.max

maximum magnitude of the true effect sizes

misspecification.prop

proportion of variables with hierarchical missingness misspecified

family

family for the response variable

sd

standard devation for gaussian simulations

snr

signal-to-noise ratio (only used for family = "gaussian")

beta

a matrix of true beta values. If given, then no beta will be created and data will be simulated from the given beta

tau

rate parameter for rexp() for generating time-to-event outcomes

covar

scalar, pairwise covariance term for covariates

Examples

set.seed(123)

dat.sim <- genHierSparseData(ncats = 3, nvars = 100, nobs = 200)

# estimate hier.sparsity.param for 0.15 total proportion of nonzero variables
# among vars with hierarchical zero patterns

hsp <- estimate.hier.sparsity.param(ncats = 3, nvars = 50, avg.hier.zeros = 0.15, nsims = 10)

# with nsims = 100, the above results in the following value
hsp <- 0.6270698

# check that this does indeed achieve the desired level of sparsity
mean(replicate(50, mean(genHierSparseBeta(ncats = 3, 
                       nvars = 50, hier.sparsity.param = hsp) != 0)  ))
                           
dat.sim2 <- genHierSparseData(ncats = 3, nvars = 100, nobs = 200, hier.sparsity.param = hsp)

sparseBeta <- genHierSparseBeta(ncats = 3, nvars = 100, hier.sparsity.param = hsp)

## generate data with already generated beta
dat.sim3 <- genHierSparseData(ncats = 3, nvars = 100, nobs = 200, beta = sparseBeta)




## complete example:
## 50% sparsity:
hsp <- 0.2626451

dat.sim <- genHierSparseData(ncats = 3, nvars = 25,
                             nobs = 150, nobs.test = 1000,
                             hier.sparsity.param = hsp,
                             prop.zero.vars = 0.5,
                             effect.size.max = 0.25,
                             family = "gaussian")

x        <- dat.sim$x
x.test   <- dat.sim$x.test
y        <- dat.sim$y
y.test   <- dat.sim$y.test
grp      <- dat.sim$group.ind
grp.test <- dat.sim$group.ind.test

fit.adapt <- cv.vennLasso(x, y,
                          grp,
                          adaptive.lasso = TRUE,
                          nlambda        = 25,
                          family         = "gaussian",
                          abs.tol        = 1e-5,
                          rel.tol        = 1e-5,
                          maxit          = 1000,
                          irls.maxit     = 15L,
                          gamma          = 0.2,
                          standardize    = FALSE,
                          intercept      = TRUE,
                          nfolds         = 3,
                          model.matrix   = TRUE)

preds.a <- predict(fit.adapt$vennLasso.fit, x.test, grp.test, s = fit.adapt$lambda.min,
                   type = 'response')

log likelihood function for fitted vennLasso objects

Description

log likelihood function for fitted vennLasso objects

Usage

## S3 method for class 'vennLasso'
logLik(object, ...)

Arguments

object

fitted "vennLasso" model object.

...

not used

Examples

library(Matrix)

set.seed(123)
n.obs <- 200
n.vars <- 50

true.beta.mat <- array(NA, dim = c(3, n.vars))
true.beta.mat[1,] <- c(-0.5, -1, 0, 0, 2, rep(0, n.vars - 5))
true.beta.mat[2,] <- c(0.5, 0.5, -0.5, -0.5, 1, -1, rep(0, n.vars - 6))
true.beta.mat[3,] <- c(0, 0, 1, 1, -1, rep(0, n.vars - 5))
rownames(true.beta.mat) <- c("1,0", "1,1", "0,1")
true.beta <- as.vector(t(true.beta.mat))

x.sub1 <- matrix(rnorm(n.obs * n.vars), n.obs, n.vars)
x.sub2 <- matrix(rnorm(n.obs * n.vars), n.obs, n.vars)
x.sub3 <- matrix(rnorm(n.obs * n.vars), n.obs, n.vars)

x <- as.matrix(rbind(x.sub1, x.sub2, x.sub3))

conditions <- as.matrix(cbind(c(rep(1, 2 * n.obs), rep(0, n.obs)),
                              c(rep(0, n.obs), rep(1, 2 * n.obs))))

y <- rnorm(n.obs * 3, sd = 3) + drop(as.matrix(bdiag(x.sub1, x.sub2, x.sub3)) %*% true.beta)

fit <- vennLasso(x = x, y = y, groups = conditions)

logLik(fit)

Overlapping Group Lasso (OGLasso)

Description

Fits the overlapping group lasso, which minimizes

\ell(\beta_0, \beta)/n + \lambda \sum_{g} w_g \|\beta_{G_g}\|_2

over a path of values of \lambda, where the groups G_g may overlap, \ell is the residual sum of squares divided by 2 (family = "gaussian"), the negative log-likelihood (family = "binomial"), or the negative Breslow partial log-likelihood (family = "coxph"), and w_g is the product of group.weights and penalty.factor (and of the adaptive weights when adaptive.lasso = TRUE).

Usage

oglasso(
  x,
  y,
  delta = NULL,
  group,
  fused = NULL,
  family = c("gaussian", "binomial", "coxph"),
  nlambda = 100L,
  lambda = NULL,
  lambda.min.ratio = NULL,
  lambda.fused = 0,
  alpha = NULL,
  group.weights = NULL,
  adaptive.lasso = FALSE,
  adaptive.fused = FALSE,
  penalty.factor = NULL,
  penalty.factor.fused = NULL,
  gamma = 1,
  standardize = TRUE,
  intercept = TRUE,
  compute.se = FALSE,
  rho = NULL,
  dynamic.rho = TRUE,
  maxit = 500L,
  abs.tol = 1e-05,
  rel.tol = 1e-05,
  irls.tol = 1e-05,
  irls.maxit = 100L,
  dfmax = NULL
)

Arguments

x

input matrix of dimension nobs by nvars. Each row is an observation, each column corresponds to a covariate. A sparse matrix is converted to a dense matrix.

y

numeric response vector of length nobs. For family = "binomial" it must take the values 0 and 1; for family = "coxph" it holds the observed times.

delta

vector of length equal to the number of observations with values in 1 and 0, where a 1 indicates the observed time is a death and a 0 indicates the observed time is a censoring event. Required for family = "coxph".

group

A list of length equal to the number of groups containing vectors of integers indicating the variable IDs for each group. For example, group = list(c(1,2), c(2,3), c(3,4,5)) specifies that Group 1 contains variables 1 and 2, Group 2 contains variables 2 and 3, and Group 3 contains variables 3, 4, and 5. Can also be a matrix of 0s and 1s with the number of columns equal to the number of groups and the number of rows equal to the number of variables. A value of 1 in row i and column j indicates that variable i is in group j and 0 indicates that variable i is not in group j. Variables that belong to no group are left unpenalized.

fused

not yet implemented; must be NULL.

family

"gaussian" for least squares problems, "binomial" for binary response, and "coxph" for time-to-event outcomes (Cox proportional hazards model with the Breslow treatment of tied times). The Cox solver forms the nvars x nvars matrix X'WX, which needs 8 * nvars^2 bytes (3.2 GB for 20000 variables)

nlambda

The number of lambda values. Default is 100.

lambda

A user-specified sequence of lambda values. Left unspecified, the a sequence of lambda values is automatically computed, ranging uniformly on the log scale over the relevant range of lambda values.

lambda.min.ratio

Smallest value for lambda, as a fraction of lambda.max, the (data derived) entry value. lambda.max is computed for the problem in which the intercept and any unpenalized variables are fit, and every coefficient in a penalized group is zero at lambda.max. With overlapping groups, lambda.max is a value at which the zero solution is guaranteed, which can be somewhat larger than the smallest such value. The default depends on the sample size nobs relative to the number of variables nvars. If nobs > nvars, the default is 0.0001, close to zero. If nobs < nvars, the default is 0.05. A very small value of lambda.min.ratio will lead to a saturated fit in the nobs < nvars case.

lambda.fused

not used (the fused penalty is not yet implemented)

alpha

currently not used.

group.weights

A vector of values representing multiplicative factors by which each group's penalty is to be multiplied, one value per group. Often, this is a function (such as the square root) of the number of predictors in each group. The default is to use the square root of group size for the group selection methods.

adaptive.lasso

Flag indicating whether or not to use adaptive lasso weights. If set to TRUE and group.weights is unspecified, then this will override group.weights. If a vector is supplied to group.weights, then the adaptive.lasso weights will be multiplied by the group.weights vector

adaptive.fused

not used (the fused penalty is not yet implemented)

penalty.factor

vector of weights to be multiplied to the tuning parameter for the group lasso penalty. A vector of length equal to the number of groups

penalty.factor.fused

not used (the fused penalty is not yet implemented)

gamma

power to raise the MLE estimated weights by for the adaptive lasso. defaults to 1

standardize

Logical flag for x variable standardization, prior to fitting the models. Each column of x is divided by its standard deviation (computed with divisor nobs) and, when an intercept is fit, centered at its mean; constant columns are not scaled. The coefficients are always returned on the original scale. Default is standardize = TRUE. If variables are in the same units already, you might not wish to standardize. The response is never centered or scaled.

intercept

Should intercept(s) be fitted (default = TRUE) or set to zero (FALSE). Ignored (no intercept) for family = "coxph".

compute.se

not used by oglasso(); see vennLasso

rho

ADMM parameter. must be a strictly positive value. By default, an appropriate value is automatically chosen

dynamic.rho

TRUE/FALSE indicating whether or not the rho value should be updated throughout the course of the ADMM iterations

maxit

integer. Maximum number of ADMM iterations. Default is 500.

abs.tol

absolute convergence tolerance for ADMM iterations for the relative dual and primal residuals. Default is 10^{-5}, which is typically adequate.

rel.tol

relative convergence tolerance for ADMM iterations for the relative dual and primal residuals. Default is 10^{-5}, which is typically adequate.

irls.tol

convergence tolerance for IRLS iterations. Only used if family != "gaussian". Default is 10^{-5}.

irls.maxit

integer. Maximum number of IRLS iterations. Only used if family != "gaussian". Default is 100.

dfmax

limit on the number of nonzero coefficients (not counting the intercept). The path is stopped, with a warning, at the first lambda at which more than dfmax coefficients are nonzero, and only the solutions for the larger values of lambda are returned. The default NULL places no limit, so the whole path is computed.

Value

An object with S3 class "oglasso", a list including

beta

matrix of coefficients on the original scale of x, with one row for the intercept (zero when no intercept is fit) followed by one row per variable, and one column per value of lambda

lambda

the values of lambda used

loss

the loss (residual sum of squares for gaussian, negative log-likelihood for binomial) at each lambda

niter

number of iterations used for each value of lambda

group.weights

the group weights used, including penalty factors and adaptive weights

Examples

library(vennLasso)

set.seed(123)
n.obs <- 200
n.vars <- 50

true.beta <- c(rep(0,2), 1, -1, rep(0, 8), 0.5, -0.5, 1, rep(0, 35))

x <- matrix(rnorm(n.obs * n.vars), n.obs, n.vars)
y <- rnorm(n.obs, sd = 3) + drop(x %*% true.beta)

groups <- c(list(c(1,2), c(2,3), c(3,4,5), 5:10, 6:12, 7:15), lapply(16:50, function(x) x))

fit <- oglasso(x = x, y = y, group = groups, nlambda = 25)
round(fit$beta[1:16, c(1, 10, 25)], 3)

Plot method for cv.vennLasso fitted objects

Description

Plot method for cv.vennLasso fitted objects

Plotting method for vennLasso fitted objects

Usage

## S3 method for class 'cv.vennLasso'
plot(x, sign.lambda = 1, ...)

## S3 method for class 'vennLasso'
plot(
  x,
  which.subpop = 1,
  xvar = c("norm", "lambda", "loglambda", "dev"),
  xlab = iname,
  ylab = "Coefficients",
  ...
)

Arguments

x

fitted vennLasso or cv.vennLasso model object

sign.lambda

Either plot against log(lambda) (default) or its negative if sign.lambda = -1.

...

other graphical parameters for the plot

which.subpop

which row in the coefficient matrix should be plotting? Each row corresponds to a particular combination of the specified stratifying variables

xvar

What is on the X-axis. "norm" plots against the L1-norm of the coefficients, "lambda" against the log-lambda sequence, and "dev" against the percent deviance explained.

xlab

character value supplied for x-axis label

ylab

character value supplied for y-axis label

Examples

set.seed(123)

dat.sim <- genHierSparseData(ncats = 3, nvars = 25,
                             nobs = 100, 
                             hier.sparsity.param = 0.5,
                             prop.zero.vars = 0.5,
                             effect.size.max = 0.25,
                             family = "gaussian")

x        <- dat.sim$x
x.test   <- dat.sim$x.test
y        <- dat.sim$y
y.test   <- dat.sim$y.test
grp      <- dat.sim$group.ind
grp.test <- dat.sim$group.ind.test

fit.adapt <- cv.vennLasso(x, y,
                          grp,
                          adaptive.lasso = TRUE,
                          nlambda        = 25,
                          nfolds         = 4)
                                     
plot(fit.adapt) 

library(Matrix)

set.seed(123)
n.obs <- 200
n.vars <- 50

true.beta.mat <- array(NA, dim = c(3, n.vars))
true.beta.mat[1,] <- c(-0.5, -1, 0, 0, 2, rep(0, n.vars - 5))
true.beta.mat[2,] <- c(0.5, 0.5, -0.5, -0.5, 1, -1, rep(0, n.vars - 6))
true.beta.mat[3,] <- c(0, 0, 1, 1, -1, rep(0, n.vars - 5))
rownames(true.beta.mat) <- c("1,0", "1,1", "0,1")
true.beta <- as.vector(t(true.beta.mat))

x.sub1 <- matrix(rnorm(n.obs * n.vars), n.obs, n.vars)
x.sub2 <- matrix(rnorm(n.obs * n.vars), n.obs, n.vars)
x.sub3 <- matrix(rnorm(n.obs * n.vars), n.obs, n.vars)

x <- as.matrix(rbind(x.sub1, x.sub2, x.sub3))

conditions <- as.matrix(cbind(c(rep(1, 2 * n.obs), rep(0, n.obs)),
                              c(rep(0, n.obs), rep(1, 2 * n.obs))))

y <- rnorm(n.obs * 3, sd = 3) + drop(as.matrix(bdiag(x.sub1, x.sub2, x.sub3)) %*% true.beta)

fit <- vennLasso(x = x, y = y, groups = conditions)

layout(matrix(1:3, ncol = 3))
plot(fit, which.subpop = 1)
plot(fit, which.subpop = 2)
plot(fit, which.subpop = 3)

plotting function to investigate estimated coefficients

Description

plotting function to investigate estimated coefficients

Usage

plotCoefs(object, s = NULL, ...)

Arguments

object

fitted vennLasso object

s

lambda value for the predictions. Only one can be specified at a time

...

other graphical parameters for the plot

Examples

set.seed(123)

dat.sim <- genHierSparseData(ncats = 3, nvars = 25, nobs = 200)

fit <- vennLasso(x = dat.sim$x, y = dat.sim$y, groups = dat.sim$group.ind)

plotCoefs(fit, s = fit$lambda[22])

plotting function to investigate hierarchical structure of selection

Description

plotting function to investigate hierarchical structure of selection

Usage

plotSelections(object, s = NULL, type = c("d3.tree"), ...)

Arguments

object

fitted vennLasso object

s

lambda value for the predictions. Only one can be specified at a time

type

type of plot to make. Currently only "d3.tree" and "igraph.tree" available

...

other graphical parameters for the plot

Examples

set.seed(123)

dat.sim <- genHierSparseData(ncats = 3, nvars = 25, nobs = 200)

fit <- vennLasso(x = dat.sim$x, y = dat.sim$y, groups = dat.sim$group.ind)

plotSelections(fit, s = fit$lambda[32])

plotting function for venn diagrams of overlapping conditions

Description

plotting function for venn diagrams of overlapping conditions

Usage

plotVenn(
  conditions,
  condition.names = NULL,
  lty = "blank",
  fill.colors = c("royalblue1", "goldenrod1", "mediumvioletred", "turquoise3",
    "firebrick1"),
  ...
)

Arguments

conditions

condition matrix such as the one given to vennLasso() function. It can have up to 5 conditions

condition.names

names of the conditions (equal to the number of columns of conditions)

lty

standard 'lty' graphical parameter for line type around circles. default is no lines

fill.colors

vector of colors for plotting. Set fill.colors = NULL for no colors

...

other graphical parameters for the plot

Examples

library(Matrix)

set.seed(123)
n.obs <- 200
n.vars <- 50

true.beta.mat <- array(NA, dim = c(3, n.vars))
true.beta.mat[1,] <- c(-0.5, -1, 0, 0, 2, rep(0, n.vars - 5))
true.beta.mat[2,] <- c(0.5, 0.5, -0.5, -0.5, 1, -1, rep(0, n.vars - 6))
true.beta.mat[3,] <- c(0, 0, 1, 1, -1, rep(0, n.vars - 5))
rownames(true.beta.mat) <- c("1,0", "1,1", "0,1")
true.beta <- as.vector(t(true.beta.mat))

x.sub1 <- matrix(rnorm(n.obs * n.vars), n.obs, n.vars)
x.sub2 <- matrix(rnorm(n.obs * n.vars), n.obs, n.vars)
x.sub3 <- matrix(rnorm(n.obs * n.vars), n.obs, n.vars)

x <- as.matrix(rbind(x.sub1, x.sub2, x.sub3))

conditions <- as.matrix(cbind(c(rep(1, 2 * n.obs), rep(0, n.obs)),
                              c(rep(0, n.obs), rep(1, 2 * n.obs))))

y <- rnorm(n.obs * 3, sd = 3) + drop(as.matrix(bdiag(x.sub1, x.sub2, x.sub3)) %*% true.beta)

fit <- vennLasso(x = x, y = y, groups = conditions)

vennobj <- plotVenn(conditions)

Prediction for Cross Validation Hierarchical Lasso Object

Description

Prediction for Cross Validation Hierarchical Lasso Object

Usage

## S3 method for class 'cv.vennLasso'
predict(object, newx, group.mat, s = c("lambda.min"), use.refit = FALSE, ...)

Arguments

object

fitted cv.vennLasso object

newx

new matrix for predictions

group.mat

A matrix of the group memberships for now. Ignore the rest: A list of length equal to the number of groups containing vectors of integers indicating the variable IDs for each group. For example, groups=list(c(1,2), c(2,3), c(3,4,5)) specifies that Group 1 contains variables 1 and 2, Group 2 contains variables 2 and 3, and Group 3 contains variables 3, 4, and 5. Can also be a matrix of 0s and 1s with the number of columns equal to the number of groups and the number of rows equal to the number of variables. A value of 1 in row i and column j indicates that variable i is in group j and 0 indicates that variable i is not in group j.

s

lambda value for the predictions. defaults to all values computed in the vennLasso object

use.refit

Should the refitted beta estimates be used for prediction? Defaults to FALSE. If TRUE then the beta estimates from the model refit on just the selected covariates are used

...

parameters to be passed to predict.vennLasso

Value

predictions or coefficients

Prediction for Hierarchical Shared Lasso

Description

Prediction for Hierarchical Shared Lasso

Usage

## S3 method for class 'vennLasso'
predict(
  object,
  newx,
  group.mat,
  s = NULL,
  use.refit = FALSE,
  type = c("link", "response", "coefficients", "nonzero", "class", "nvars", "median",
    "survival"),
  ...
)

Arguments

object

fitted vennLasso object

newx

new matrix for predictions

group.mat

s

lambda value for the predictions. defaults to all values computed in the vennLasso object

use.refit

Should the refitted beta estimates be used for prediction? Defaults to FALSE. If TRUE then the beta estimates from the model refit on just the selected covariates are used

type

type of predictions to be made. type = "median" is for the median survival time and type = "survival" is for the predicted hazard function

...

parameters to be passed to vennLasso

Value

predictions or coefficients

Fitting vennLasso models

Description

Fitting vennLasso models

Usage

vennLasso(
  x,
  y,
  groups,
  family = c("gaussian", "binomial"),
  nlambda = 100L,
  lambda = NULL,
  lambda.min.ratio = NULL,
  lambda.fused = NULL,
  penalty.factor = NULL,
  group.weights = NULL,
  adaptive.lasso = FALSE,
  adaptive.fused = FALSE,
  gamma = 1,
  standardize = FALSE,
  intercept = TRUE,
  one.intercept = FALSE,
  compute.se = FALSE,
  conf.int = NULL,
  rho = NULL,
  dynamic.rho = TRUE,
  maxit = 500L,
  abs.tol = 1e-05,
  rel.tol = 1e-05,
  irls.tol = 1e-05,
  irls.maxit = 100L,
  model.matrix = FALSE,
  ...
)

Arguments

x

input matrix of dimension nobs by nvars. Each row is an observation, each column corresponds to a covariate

y

numeric response vector of length nobs

groups

A list of length equal to the number of groups containing vectors of integers indicating the variable IDs for each group. For example, groups = list(c(1,2), c(2,3), c(3,4,5)) specifies that Group 1 contains variables 1 and 2, Group 2 contains variables 2 and 3, and Group 3 contains variables 3, 4, and 5. Can also be a matrix of 0s and 1s with the number of columns equal to the number of groups and the number of rows equal to the number of variables. A value of 1 in row i and column j indicates that variable i is in group j and 0 indicates that variable i is not in group j.

family

"gaussian" for least squares problems, "binomial" for binary response, and "coxph" for time-to-event outcomes (not yet available)

nlambda

The number of lambda values. Default is 100.

lambda

A user-specified sequence of lambda values. Left unspecified, the a sequence of lambda values is automatically computed, ranging uniformly on the log scale over the relevant range of lambda values.

lambda.min.ratio

Smallest value for lambda, as a fraction of lambda.max, the (data derived) entry value (i.e. the smallest value for which all parameter estimates are zero). The default depends on the sample size nobs relative to the number of variables nvars. If nobs > nvars, the default is 0.0001, close to zero. If nobs < nvars, the default is 0.05. A very small value of lambda.min.ratio can lead to a saturated fit when nobs < nvars.

lambda.fused

tuning parameter for fused lasso penalty

penalty.factor

vector of weights to be multiplied to the tuning parameter for the group lasso penalty, one per variable and subpopulation before empty groups are removed: a vector of length (ncol(x) + 1) * M (without the 1 when one.intercept = TRUE), where M is the number of combinations of conditions present in the data, ordered by variable and then by combination. The penalty factors of the subpopulation intercepts are always set to zero.

group.weights

A vector of values representing multiplicative factors by which each group's penalty is to be multiplied. Often, this is a function (such as the square root) of the number of predictors in each group. The default is to use the square root of group size for the group selection methods.

adaptive.lasso

adaptive.fused

Flag indicating whether or not to use adaptive fused lasso weights.

gamma

power to raise the MLE estimated weights by for the adaptive lasso. defaults to 1

standardize

Should the data be standardized? Defaults to FALSE. If TRUE, each column of the expanded (stratum-specific) design matrix is scaled by its standard deviation before fitting, and the coefficients are returned on the original scale; see oglasso. Each stratum-specific column is zero outside its stratum, and its standard deviation is computed over all observations, so the scaling (and hence the effective penalty) depends on the size of the stratum; to standardize within strata instead, scale x within each stratum before calling vennLasso().

intercept

Should an intercept be fit? Defaults to TRUE

one.intercept

Should a single intercept be fit for all subpopulations instead of one for each subpopulation? Defaults to FALSE.

compute.se

Should standard errors be computed? If TRUE, then models are re-fit with no penalization and the standard errors are computed from the refit models. These standard errors are only theoretically valid for the adaptive lasso (when adaptive.lasso is set to TRUE)

conf.int

level for confidence intervals. Defaults to NULL (no confidence intervals). Should be a value between 0 and 1. If confidence intervals are to be computed, compute.se will be automatically set to TRUE

rho

ADMM parameter. must be a strictly positive value. By default, an appropriate value is automatically chosen

dynamic.rho

TRUE/FALSE indicating whether or not the rho value should be updated throughout the course of the ADMM iterations

maxit

integer. Maximum number of ADMM iterations. Default is 500.

abs.tol

absolute convergence tolerance for ADMM iterations for the relative dual and primal residuals. Default is 10^{-5}, which is typically adequate.

rel.tol

relative convergence tolerance for ADMM iterations for the relative dual and primal residuals. Default is 10^{-5}, which is typically adequate.

irls.tol

convergence tolerance for IRLS iterations. Only used if family != "gaussian". Default is 10^{-5}.

irls.maxit

integer. Maximum number of IRLS iterations. Only used if family != "gaussian". Default is 100.

model.matrix

logical flag. Should the design matrix used be returned?

...

further arguments passed to oglasso, for example dfmax

Value

An object with S3 class "vennLasso", a list including

beta

array of coefficients with dimensions (combinations of conditions) x (variables) x (lambda values)

lambda

the values of lambda used

df

nobs minus the effective number of parameters at each lambda. The effective number of parameters is tr\{(H_S + N\lambda A_S)^{-1} H_S\} over the active set S (nonzero and unpenalized coefficients), where H is the Hessian of the loss and A_j = \sum_{g \ni j} w_g / \|\beta_g\|_2 is the local quadratic approximation of the penalty (Section 3.3 of Huling et al., 2018); unpenalized coefficients such as the intercepts count fully

aic, bic, aicc, mbic

information criteria based on that effective number of parameters

Examples

library(Matrix)

# first simulate heterogeneous data using
# genHierSparseData
set.seed(123)
dat.sim <- genHierSparseData(ncats = 2, nvars = 25,
                             nobs = 200, 
                             hier.sparsity.param = 0.5,
                             prop.zero.vars = 0.5,
                             family = "gaussian")

x          <- dat.sim$x
conditions <- dat.sim$group.ind
y          <- dat.sim$y

true.beta.mat <- dat.sim$beta.mat

fit <- vennLasso(x = x, y = y, groups = conditions)

## coefficients at the value of lambda selected by BIC
(true.coef <- true.beta.mat[match(dimnames(fit$beta)[[1]], rownames(true.beta.mat)),])
round(fit$beta[,,which.min(fit$bic)], 2)

## fit adaptive version and compute confidence intervals
afit <- vennLasso(x = x, y = y, groups = conditions, conf.int = 0.95, adaptive.lasso = TRUE)

aic.idx <- which.min(afit$aic)
bic.idx <- which.min(afit$bic)

## first ten variables (column 1 of the coefficient arrays is the intercept)
round(true.coef[,1:10], 2)
round(afit$beta[,2:11,aic.idx], 2)
round(afit$lower.ci[,2:11,aic.idx], 2)
round(afit$upper.ci[,2:11,aic.idx], 2)

# actual coverage
mean(true.coef[afit$beta[,-1,aic.idx] != 0] >= 
             afit$lower.ci[,-1,aic.idx][afit$beta[,-1,aic.idx] != 0] &
         true.coef[afit$beta[,-1,aic.idx] != 0] <= 
             afit$upper.ci[,-1,aic.idx][afit$beta[,-1,aic.idx] != 0])

(covered <- true.coef >= afit$lower.ci[,-1,aic.idx] & true.coef <= afit$upper.ci[,-1,aic.idx])
mean(covered)


# logistic regression example

set.seed(123)
dat.sim <- genHierSparseData(ncats = 2, nvars = 25,
                             nobs = 200, 
                             hier.sparsity.param = 0.5,
                             prop.zero.vars = 0.5,
                             family = "binomial",
                             effect.size.max = 0.5) # don't make any 
                                                    # coefficients too big

x           <- dat.sim$x
conditions  <- dat.sim$group.ind
y           <- dat.sim$y
true.beta.b <- dat.sim$beta.mat

bfit <- vennLasso(x = x, y = y, groups = conditions, family = "binomial")

(true.coef.b <- -true.beta.b[match(dimnames(fit$beta)[[1]], rownames(true.beta.b)),])
round(bfit$beta[,,which.min(bfit$bic)], 2)

Package {vennLasso}

Cross Validation for the vennLasso

Description

Usage

Arguments

Value

Examples

function to estimate the hierarchical sparsity parameter for a desired level of sparsity for simulated hierarchical coefficients

Description

Usage

Arguments

Examples

function to generate coefficient matrix with hierarchical sparsity

Description

Usage

Arguments

Examples

function to generate data with hierarchical sparsity

Description

Usage

Arguments

Examples

log likelihood function for fitted vennLasso objects

Description

Usage

Arguments

Examples

Overlapping Group Lasso (OGLasso)

Description

Usage

Arguments

Value

Examples

Plot method for cv.vennLasso fitted objects

Description

Usage

Arguments

Examples

plotting function to investigate estimated coefficients

Description

Usage

Arguments

Examples

plotting function to investigate hierarchical structure of selection

Description

Usage

Arguments

Examples

plotting function for venn diagrams of overlapping conditions

Description

Usage

Arguments

Examples

Prediction for Cross Validation Hierarchical Lasso Object

Description

Usage

Arguments

Value

Prediction for Hierarchical Shared Lasso

Description

Usage

Arguments

Value

Fitting vennLasso models

Description

Usage

Arguments

Value

Examples