randomizedLassoInf {selectiveInference} | R Documentation |
Inference for the randomized lasso, with a fixed lambda
Description
Compute p-values and confidence intervals based on selecting an active set with the randomized lasso, at a fixed value of the tuning parameter lambda and using Gaussian randomization.
Usage
randomizedLassoInf(rand_lasso_soln,
targets=NULL,
level=0.9,
sampler=c("norejection", "adaptMCMC"),
nsample=10000,
burnin=2000,
opt_samples=NULL)
Arguments
rand_lasso_soln |
A randomized lasso solution as returned by |
targets |
If not NULL, should be a list with entries
For example, this cross-covariance could be estimated by jointly bootstrapping the target of interest and the above vector. |
level |
Level for confidence intervals. |
sampler |
Which sampler to use – default is a no-rejection sampler. Otherwise use MCMC from the adaptMCMC package. |
nsample |
Number of samples of optimization variables to sample. |
burnin |
How many samples of optimization variable to discard (should be less than nsample). |
opt_samples |
Optional sample of optimization variables. If not NULL then no MCMC will be run. |
Details
This function computes selective p-values and confidence intervals for a randomized version of the lasso, given a fixed value of the tuning parameter lambda.
Value
targets |
A list with entries |
pvalues |
P-values testing hypotheses that each specific target is 0. |
ci |
Confidence interval for parameters determined by |
Author(s)
Jelena Markovic, Jonathan Taylor
References
Jelena Markovic and Jonathan Taylor (2016). Bootstrap inference after using multiple queries for model selection. arxiv.org:1612.07811
Xiaoying Tian and Jonathan Taylor (2015). Selective inference with a randomized response. arxiv.org:1507.06739
Xiaoying Tian, Snigdha Panigrahi, Jelena Markovic, Nan Bi and Jonathan Taylor (2016). Selective inference after solving a convex problem. arxiv.org:1609.05609
Examples
set.seed(43)
n = 50
p = 10
sigma = 0.2
lam = 0.5
X = matrix(rnorm(n*p), n, p)
X = scale(X, TRUE, TRUE) / sqrt(n-1)
beta = c(3,2,rep(0,p-2))
y = X%*%beta + sigma*rnorm(n)
result = randomizedLasso(X, y, lam)
inf_result = randomizedLassoInf(result)