relaxnet: Relaxation (as in Relaxed Lasso, Meinshausen 2007) applied to...
In relaxnet: Relaxation of glmnet models (as in relaxed lasso, Meinshausen 2007)

Description Usage Arguments Details Value Note Author(s) References See Also Examples

Runs glmnet once on the full x matrix, then again on each distinct subset of columns from along the solution path. The penalty may be lasso (alpha = 1) or elastic net (0 < alpha < 1). The outcome (y) may be continuous or binary.

relaxnet(x, y, family = c("gaussian", "binomial"),
         nlambda = 100,
         alpha = 1,
         relax = TRUE,
         relax.nlambda = 100,
         relax.max.vars = min(nrow(x), ncol(x)) * 0.8,
         lambda = NULL,
         relax.lambda.index = NULL,
         relax.lambda.list = NULL,
         ...)

`x`	Input matrix, of dimension nobs x nvars; each row is an observation vector. Can be in sparse matrix format (inherit from class `"sparseMatrix"` as in package `Matrix`). Must have unique colnames.
`y`	response variable. Quantitative for `family="gaussian"`. For `family="binomial"` should be either a factor with two levels, or a two-column matrix of counts or proportions.
`family`	Response type (see above).
`nlambda`	The number of `lambda` values - default is 100. Determines how fine the grid of lambda values should be.
`alpha`	Elastic net mixing parameter (see `glmnet`).
`relax`	Should the model be relaxed. If FALSE, only the main glmnet model is run and no relaxed models are.
`relax.nlambda`	Like nlambda but for secondary (relaxed) models.
`relax.max.vars`	Maximum number of variables for relaxed models. No relaxation will be done for subsets along the regularization path with number of variables greater than relax.max.vars. If `ncol(x)` > `nrow(x)` and `alpha` < 1, it may make sense to use a value > `nrow(x)`, but this may lead to increased computation time.
`lambda`	See (see `glmnet`). Optional and meant primarily for use by `cv.relaxnet`.
`relax.lambda.index`	Vector which indexes the lambda argument and specifyies the values at which a relaxed model should be fit. Optional and meant primarily for use by `cv.relaxnet`. Ignored if lambda argument is `NULL`.
`relax.lambda.list`	List of lambda values to use for the relaxed models. Optional and meant primarily for use by `cv.relaxnet`. Ignored if lambda argument is `NULL`.
`...`	Further aruments passed to glmnet. Use with caution as this has not yet been tested. For example, setting `standardize = FALSE` will probably work correctly, but setting an offset probably won't.

Version 1.9-5 of glmnet no longer allows single-column x. This broke relaxnet. As a temporary fix, relaxed models containing a single variable now just run glm instead of glmnet, and only the full least squares (or logistic regression, for family = "binomial") solution is considered for that relaxed model. All relaxed models containing more than one variable, as well as the main model, still use the complete glmnet solution path.

Object of class code"relaxnet" with the following components:

`call`	A copy of the call which produced this object
`main.glmnet.fit`	The object resulting from running `glmnet` on the entire `x` matrix.
`relax`	The value of the relax argument. If this is `FALSE`, then several of the other elements of this result will be set to `NA`.
`relax.glmnet.fits`	A list containing the secondary `glmnet` fits gotten by running `glmnet` on the distinct subsets of the columns of `x` resulting along the solution path of lambda values.
`relax.num.vars`	Vector giving the number of variables in each "relaxed" model.
`relax.lambda.index`	This vector indexes result$main.glmnet.fit$lambda and gives the lambda values at which the relax.glmnet.fits were obtained.
`total.time`	Total time in seconds to produce this result.
`main.fit.time`	Time in seconds to produce the main glmnet fit.
`relax.keep`	In certain cases some of the relaxed models are removed after fitting. `relax.fit.times` records times for these removed models as well. This logical vector shows which of the models whose timings are given in `relax.fit.times` were actually kept and have results given in `relax.glmnet.fits` above. Hopefully this will not be necessary in later versions.
`relax.fit.times`	Vector of times in seconds to produce secondary "relaxed" models.

This is a preliminary release and several additional features are planned for later versions.

Stephan Ritter, with design contributions from Alan Hubbard.

Much of the code (and some help file content) is adapted from the glmnet package, whose authors are Jerome Friedman, Trevor Hastie and Rob Tibshirani.

Stephan Ritter and Alan Hubbard, Tech report (forthcoming).

Jerome Friedman, Trevor Hastie, Rob Tibshirani (2010) “Regularization Paths for Generalized Linear Models via Coordinate Descent.” Journal of Statistical Software 33(1)

Nicolai Meinshausen (2007) “Relaxed Lasso” Computational Statistics and Data Analysis 52(1), 374-393

glmnet, cv.relaxnet, predict.relaxnet

## generate predictor matrix

nobs <- 100
nvars <- 200

set.seed(23)

x <- matrix(rnorm(nobs * nvars), nobs, nvars)

## make sure it has unique colnames

colnames(x) <- paste("x", 1:ncol(x), sep = "")

## let y depend on first 5 columns plus noise

y <- rowSums(x[, 1:5]) + rnorm(nrow(x))

## default is family = "gaussian"

result1 <- relaxnet(x, y)

summary(result1)

## now fit family = "binomial" model

y.bin <- rbinom(nrow(x), 1, prob = plogis(0.2 * rowSums(x[, 1:5])))

result2 <- relaxnet(x, y.bin, family = "binomial")

summary(result2)