xrnet {xrnet}

Fit hierarchical regularized regression model

Description

Fits hierarchical regularized regression model that enables the incorporation of external data for predictor variables. Both the predictor variables and external data can be regularized by the most common penalties (lasso, ridge, elastic net). Solutions are computed across a two-dimensional grid of penalties (a separate penalty path is computed for the predictors and external variables). Currently support regularized linear and logistic regression, future extensions to other outcomes (i.e. Cox regression) will be implemented in the next major update.

Usage

xrnet(
  x,
  y,
  external = NULL,
  unpen = NULL,
  family = c("gaussian", "binomial"),
  penalty_main = define_penalty(),
  penalty_external = define_penalty(),
  weights = NULL,
  standardize = c(TRUE, TRUE),
  intercept = c(TRUE, FALSE),
  control = list()
)

Arguments

x

predictor design matrix of dimension n x p, matrix options include:

• matrix

• big.matrix

• filebacked.big.matrix

• sparse matrix (dgCMatrix)

y

outcome vector of length n

external

(optional) external data design matrix of dimension p x q, matrix options include:

• matrix

• sparse matrix (dgCMatrix)

unpen

(optional) unpenalized predictor design matrix, matrix options include:

• matrix

family

error distribution for outcome variable, options include:

• "gaussian"

• "binomial"

penalty_main

specifies regularization object for x. See define_penalty for more details.

penalty_external

specifies regularization object for external. See define_penalty for more details.

weights

optional vector of observation-specific weights. Default is 1 for all observations.

standardize

indicates whether x and/or external should be standardized. Default is c(TRUE, TRUE).

intercept

indicates whether an intercept term is included for x and/or external. Default is c(TRUE, FALSE).

control

specifies xrnet control object. See xrnet_control for more details.

Details

This function extends the coordinate descent algorithm of the R package glmnet to allow the type of regularization (i.e. ridge, lasso) to be feature-specific. This extension is used to enable fitting hierarchical regularized regression models, where external information for the predictors can be included in the external= argument. In addition, elements of the R package biglasso are utilized to enable the use of standard R matrices, memory-mapped matrices from the bigmemory package, or sparse matrices from the Matrix package.

Value

A list of class xrnet with components:

beta0

matrix of first-level intercepts indexed by penalty values

betas

3-dimensional array of first-level penalized coefficients indexed by penalty values

gammas

3-dimensional array of first-level non-penalized coefficients indexed by penalty values

alpha0

matrix of second-level intercepts indexed by penalty values

alphas

3-dimensional array of second-level external data coefficients indexed by penalty values

penalty

vector of first-level penalty values

penalty_ext

vector of second-level penalty values

family

error distribution for outcome variable

num_passes

total number of passes over the data in the coordinate descent algorithm

status

error status for xrnet fitting

• 0 = OK

• 1 = Error/Warning

error_msg

description of error

References

Jerome Friedman, Trevor Hastie, Robert Tibshirani (2010). Regularization Paths for Generalized Linear Models via Coordinate Descent. Journal of Statistical Software, 33(1), 1-22. URL http://www.jstatsoft.org/v33/i01/.

Zeng, Y., and Breheny, P. (2017). The biglasso Package: A Memory- and Computation-Efficient Solver for Lasso Model Fitting with Big Data in R. arXiv preprint arXiv:1701.05936. URL https://arxiv.org/abs/1701.05936.

Michael J. Kane, John Emerson, Stephen Weston (2013). Scalable Strategies for Computing with Massive Data. Journal of Statistical Software, 55(14), 1-19. URL http://www.jstatsoft.org/v55/i14/.

Examples

### hierarchical regularized linear regression ###
data(GaussianExample)

## define penalty for predictors and external variables
## default is ridge for predictors and lasso for external
## see define_penalty() function for more details

penMain <- define_penalty(0, num_penalty = 20)
penExt <- define_penalty(1, num_penalty = 20)

## fit model with defined regularization
fit_xrnet <- xrnet(
  x = x_linear,
  y = y_linear,
  external = ext_linear,
  family = "gaussian",
  penalty_main = penMain,
  penalty_external = penExt
)