MHLS: Metropolis-Hastings sampler for lasso estimator under the...

In EAlasso: Simulation Based Inference of Lasso Estimator

Description

Metropolis-Hastings sampler for lasso estimator under the fixed active set.

Usage

MHLS(X, PE, sig2, lbd, weights = rep(1, ncol(X)), B0, S0, A = which(B0 !=
  0), tau = rep(1, ncol(X)), niter = 2000, burnin = 0, PEtype = "coeff",
  updateS.itv = 1, verbose = FALSE, ...)

Arguments

X	predictor matrix.
PE, sig2, lbd	parameters of target distribution. (point estimate of beta or E(y) depends on PEtype, variance estimate of error and lambda).
weights	weight vector with length p(the number of covariates). Default is weights = rep(1, p).
B0	numeric vector with length p. Initial value of lasso estimator.
S0	numeric vector with length p. Initial value of subgradients. If not given, this will be generated in a default way.
A	numeric vector. Active coefficient index. Every active coefficient index in B0 must be included. Default is A = which(B0 != 0).
tau	numeric vector with length p. Standard deviaion of proposal distribution for each coefficient.
niter	integer. The number of iterations. Default is niter = 2000
burnin	integer. The length of burin-in periods. Default is burnin = 0
PEtype	Type of PE which is needed to characterize the target distribution. Users can choose either "coeff" or "mu".
updateS.itv	integer. Update subgradients every updateS.itv iterations. Set this value larger than niter if one wants to skip updating subgradients.
verbose	logical. If true, print out the progress step.
...	complementary arguments. FlipSA : optional parameter. This has to be a subset of active set, A. If the index is not listed in FlipSA, the sign of coefficients which correspond to the listed index will remain fixed. The default is FlipSA=A SFindex : optional parameter. subgradient index for the free coordinate. randomSFindex : logical. If true, resample SFindex every updateSF.itv iterations. updateSF.itv : integer. In every updateSF.itv iterations, randomize SFindex.

Details

Given appropriate initial value, provides Metropolis-Hastings samples under the fixed active set.

Value

MHLS returns an object of class "MHLS". The functions summary.MHLS and plot.MHLS provide a brief summary and generate plots.

beta	lasso samples.
subgrad	subgradient samples.
acceptHistory	numbers of acceptance and proposal.
niter, burnin, PE, type	same as function arguments.

References

Zhou, Q. (2014), "Monte Carlo simulation for Lasso-type problems by estimator augmentation," Journal of the American Statistical Association, 109, 1495-1516.

Zhou, Q. and Min, S. (2017), "Estimator augmentation with applications in high-dimensional group inference," Electronic Journal of Statistics, 11(2), 3039-3080.

Examples

#-------------------------
# Low dim
#-------------------------
set.seed(123)
n <- 10
p <- 5
X <- matrix(rnorm(n * p), n)
Y <- X %*% rep(1, p) + rnorm(n)
sigma2 <- 1
lbd <- .37
weights <- rep(1, p)
LassoResult <- Lasso.MHLS(X = X, Y = Y, lbd = lbd, type = "lasso", weights = weights)
B0 <- LassoResult$B0
S0 <- LassoResult$S0
MHLS(X = X, PE = rep(0, p), sig2 = 1, lbd = 1,
     weights = weights, B0 = B0, S0 = S0, niter = 50, burnin = 0,
     PEtype = "coeff")
MHLS(X = X, PE = rep(0, n), sig2 = 1, lbd = 1,
     weights = weights, B0 = B0, S0 = S0, niter = 50, burnin = 0,
     PEtype = "mu")

#-------------------------
# High dim
#-------------------------
set.seed(123)
n <- 5
p <- 10
X <- matrix(rnorm(n*p),n)
Y <- X %*% rep(1,p) + rnorm(n)
weights <- rep(1,p)
LassoResult <- Lasso.MHLS(X = X,Y = Y,lbd = lbd, type = "lasso", weights = weights)
B0 <- LassoResult$B0
S0 <- LassoResult$S0
MHLS(X = X, PE = rep(0, p), sig2 = 1, lbd = 1,
     weights = weights, B0 = B0, S0 = S0, niter = 50, burnin = 0,
     PEtype = "coeff")
MHLS(X = X, PE = rep(0, n), sig2 = 1, lbd = 1,
     weights = weights, B0 = B0, S0 = S0, niter = 50, burnin = 0,
     PEtype = "mu")

EAlasso documentation built on Sept. 1, 2017, 9:03 a.m.