selectiveInference {selectiveInference}

Tools for selective inference

Description

Functions to perform post-selection inference for forward stepwise regression, least angle regression, the lasso and the many normal means problem. The lasso function also supports logistic regression and the Cox model.

Details

Package:	selectiveInference
Type:	Package
License:	GPL-2

This package provides tools for inference after selection, in forward stepwise regression, least angle regression, the lasso, and the many normal means problem. The functions compute p-values and selection intervals that properly account for the inherent selection carried out by the procedure. These have exact finite sample type I error and coverage under Gaussian errors. For the logistic and Cox familes (fixedLassoInf), the coverage is asymptotically valid

This R package was developed as part of the selective inference software project in Python and R:

https://github.com/selective-inference

Some of the R code in this work is a modification of Python code from this repository. Here is the current selective inference software team:

Yuval Benjamini, Leonard Blier, Will Fithian, Jason Lee, Joshua Loftus, Joshua Loftus, Stephen Reid, Dennis Sun, Yuekai Sun, Jonathan Taylor, Xiaoying Tian, Ryan Tibshirani, Rob Tibshirani

The main functions included in the package are: fs, fsInf, lar, larInf, fixedLassoInf, manyMeans

Author(s)

Ryan Tibshirani, Rob Tibshirani, Jonathan Taylor, Joshua Loftus, Stephen Reid

Maintainer: Rob Tibshirani <[e-mail]>

References

Ryan Tibshirani, Jonathan Taylor, Richard Lockhart, and Rob Tibshirani (2014). Exact post-selection inference for sequential regression procedures. arXiv:1401.3889.

Jason Lee, Dennis Sun, Yuekai Sun, and Jonathan Taylor (2013). Exact post-selection inference, with application to the lasso. arXiv:1311.6238.

Stephen Reid, Jonathan Taylor, and Rob Tibshirani (2014). Post-selection point and interval estimation of signal sizes in Gaussian samples. arXiv:1405.3340.

Jonathan Taylor and Robert Tibshirani (2016) Post-selection inference for L1-penalized likelihood models. arXiv:1602.07358

Examples

set.seed(33)
n = 50
p = 10
sigma = 1
x = matrix(rnorm(n*p),n,p)
beta = c(3,2,rep(0,p-2))
y = x%*%beta + sigma*rnorm(n)

# run forward stepwise
fsfit = fs(x,y)

# compute sequential p-values and confidence intervals
# (sigma estimated from full model)
out.seq = fsInf(fsfit)
out.seq

# compute p-values and confidence intervals after AIC stopping
out.aic = fsInf(fsfit,type="aic")
out.aic

# compute p-values and confidence intervals after 5 fixed steps
out.fix = fsInf(fsfit,type="all",k=5)
out.fix

## NOT RUN---lasso at fixed lambda- Gaussian family
## first run glmnet
# gfit = glmnet(x,y)

## extract coef for a given lambda; note the 1/n factor!
## (and we don't save the intercept term)
# lambda = .1
# beta = coef(gfit, s=lambda/n, exact=TRUE)[-1]

## compute fixed lambda p-values and selection intervals
# out = fixedLassoInf(x,y,beta,lambda,sigma=sigma)
# out


#lasso at fixed lambda- logistic family
#set.seed(43)
  #   n = 50
  #   p = 10
  #   sigma = 1
     
 #    x = matrix(rnorm(n*p),n,p)
     x=scale(x,TRUE,TRUE)
  #   
#     beta = c(3,2,rep(0,p-2))
 #    y = x%*%beta + sigma*rnorm(n)
 #    y=1*(y>mean(y))
     # first run glmnet
 #    gfit = glmnet(x,y,standardize=FALSE,family="binomial")
     
     # extract coef for a given lambda; note the 1/n factor!
     # (and here  we DO  include the intercept term)
 #    lambda = .8
 #    beta = coef(gfit, s=lambda/n, exact=TRUE)
     
 #    # compute fixed lambda p-values and selection intervals
 #    out = fixedLassoInf(x,y,beta,lambda,family="binomial")
 #    out

##lasso at fixed lambda- Cox family
#set.seed(43)
#     n = 50
 #    p = 10
 #    sigma = 1
     
 #    x = matrix(rnorm(n*p),n,p)
  #   x=scale(x,TRUE,TRUE)
     
 #    beta = c(3,2,rep(0,p-2))
 #    tim = as.vector(x%*%beta + sigma*rnorm(n))
  #   tim= tim-min(tim)+1
#status=sample(c(0,1),size=n,replace=T)
     # first run glmnet
   #  gfit = glmnet(x,Surv(tim,status),standardize=FALSE,family="cox")
     # extract coef for a given lambda; note the 1/n factor!
   
  #   lambda = 1.5
  #   beta = as.numeric(coef(gfit, s=lambda/n, exact=TRUE))
     
     # compute fixed lambda p-values and selection intervals
   #  out = fixedLassoInf(x,tim,beta,lambda,status=status,family="cox")
   #  out
## NOT RUN---many normal means
# set.seed(12345)
# n = 100 
# mu = c(rep(3,floor(n/5)), rep(0,n-floor(n/5))) 
# y = mu + rnorm(n)
# out = manyMeans(y, bh.q=0.1)
# out

## NOT RUN---forward stepwise with groups
# set.seed(1)
# n = 20
# p = 40
# x = matrix(rnorm(n*p), nrow=n)
# index = sort(rep(1:(p/2), 2))
# y = rnorm(n) + 2 * x[,1] - x[,4]
# fit = groupfs(x, y, index, maxsteps = 5)
# out = groupfsInf(fit)
# out

## NOT RUN---estimation of sigma for use in fsInf
## (or larInf or fixedLassoInf)
# set.seed(33)
# n = 50
# p = 10
# sigma = 1
# x = matrix(rnorm(n*p),n,p)
# beta = c(3,2,rep(0,p-2))
# y = x%*%beta + sigma*rnorm(n)

## run forward stepwise
# fsfit = fs(x,y)

## estimate sigma
# sigmahat = estimateSigma(x,y)$sigmahat

## run sequential inference with estimated sigma
# out = fsInf(fit,sigma=sigmahat)
# out