export of randomized and man page

Author: jonathan-taylor

selectiveInference/NAMESPACE

@@ -14,7 +14,8 @@ export(lar,fs,
        TG.pvalue, 
        TG.limits, 
        TG.interval,
-       debiasingMatrix
+       debiasingMatrix,
+       randomizedLassoInf
     )
 
 S3method("coef", "lar")

selectiveInference/man/fixedLassoInf.Rd

@@ -113,7 +113,7 @@ is not allowed.
 
 Note that the coefficients and standard errors reported are unregularized.
 Eg for the Gaussian, they are the usual least squares estimates and standard errors
-for the model fit to the actice set from the lasso.
+for the model fit to the active set from the lasso.
 }
 \value{  
 \item{type}{Type of coefficients tested (partial or full)}

selectiveInference/man/randomizedLassoInf.Rd

@@ -0,0 +1,159 @@
+\name{randomizedLassoInf}
+\alias{randomizedLassoInf}
+
+\title{
+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(X, 
+                   y, 
+                   lam, 
+                   sigma=NULL, 
+                   noise_scale=NULL, 
+                   ridge_term=NULL, 
+                   condition_subgrad=TRUE, 
+                   level=0.9,
+                   nsample=10000,
+                   burnin=2000,
+                   max_iter=100,       
+                   kkt_tol=1.e-4,      
+                   parameter_tol=1.e-8,
+                   objective_tol=1.e-8,
+                   objective_stop=FALSE,
+                   kkt_stop=TRUE,
+                   param_stop=TRUE)
+}
+\arguments{
+  \item{X}{
+Matrix of predictors (n by p); 
+}
+  \item{y}{
+Vector of outcomes (length n)
+}
+  \item{lam}{
+Value of lambda used to compute beta. See the above warning
+ Be careful! This function uses the "standard" lasso objective
+  \deqn{
+    1/2 \|y - x \beta\|_2^2 + \lambda \|\beta\|_1.
+  }
+ In contrast, glmnet multiplies the first term by a factor of 1/n.
+ So after running glmnet, to extract the beta corresponding to a value lambda, 
+ you need to use \code{beta = coef(obj, s=lambda/n)[-1]},
+ where obj is the object returned by glmnet (and [-1] removes the intercept,
+ which glmnet always puts in the first component)
+} 
+\item{sigma}{
+Estimate of error standard deviation. If NULL (default), this is estimated 
+using the mean squared residual of the full least squares based on 
+selected active set.
+}
+\item{noise_scale}{
+Scale of Gaussian noise added to objective. Default is 
+0.5 * sd(y) times the sqrt of the mean of the trace of X^TX.
+}
+\item{ridge_term}{
+A small "elastic net" or ridge penalty is added to ensure
+the randomized problem has a solution. 
+0.5 * sd(y) times the sqrt of the mean of the trace of X^TX divided by
+sqrt(n).
+}
+\item{condition_subgrad}{
+In forming selective confidence intervals and p-values should we condition
+on the inactive coordinates of the subgradient as well?
+Default is TRUE. 
+}
+\item{level}
+{
+Level for confidence intervals.
+}
+\item{nsample}
+{
+Number of samples of optimization variables to sample.
+}
+\item{burnin}
+{
+How many samples of optimization variable to discard (should be less than nsample).
+}
+\item{max_iter}
+{
+How many rounds of updates used of coordinate descent in solving randomized
+LASSO.
+}
+\item{kkt_tol}{
+Tolerance for checking convergence based on KKT conditions.
+}
+\item{parameter_tol}{
+Tolerance for checking convergence based on convergence
+of parameters.
+}
+\item{objective_tol}{
+Tolerance for checking convergence based on convergence
+of objective value.
+}
+\item{kkt_stop}{
+Should we use KKT check to determine when to stop?
+}
+\item{parameter_tol}{
+Should we use convergence of parameters to determine when to stop?
+}
+\item{objective_tol}{
+Should we use convergence of objective value to determine when to stop?
+}
+}
+
+\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{  
+\item{type}{Type of coefficients tested (partial or full)}
+\item{lambda}{Value of tuning parameter lambda used}
+\item{pv}{One-sided P-values for active variables, uses the fact we have conditioned on the sign.}
+\item{ci}{Confidence intervals}
+\item{tailarea}{Realized tail areas (lower and upper) for each confidence interval}
+\item{vlo}{Lower truncation limits for statistics}
+\item{vup}{Upper truncation limits for statistics}
+\item{vmat}{Linear contrasts that define the observed statistics}
+\item{y}{Vector of outcomes}
+\item{vars}{Variables in active set}
+\item{sign}{Signs of active coefficients}
+\item{alpha}{Desired coverage (alpha/2 in each tail)}
+\item{sigma}{Value of error standard deviation (sigma) used}
+\item{call}{The call to lassoInf}
+}
+
+\references{
+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:1609.05609
+
+}
+\author{Jelena Markovic, Jonathan Taylor}
+
+\examples{
+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)
+
+result = randomizedLassoInf(X, y, lam)
+
+}
+