BayesBridgeSMU: Unified Bayesian Regularization via Scale Mixture of Uniform...

In himelmallick/UBeRr: Unified Bayesian Regularization via Scale Mixture of Uniform Distributions

Description

Bayesian Bridge Regression

Usage

BayesBridgeSMU(
  x,
  y,
  alpha = 0.5,
  max.steps = 20000,
  n.burn = 10000,
  n.thin = 1,
  eps = 1e-06,
  r = 1,
  delta = 0.1,
  posterior.summary.beta = "mean",
  posterior.summary.lambda = "mean",
  posterior.summary.alpha = "mean",
  beta.ci.level = 0.95,
  lambda.ci.level = 0.95,
  alpha.ci.level = 0.95,
  seed = 1234
)

Arguments

x	A numeric matrix with standardized predictors in columns and samples in rows.
y	A mean-centered continuous response variable with matched sample rows with x.
alpha	Concavity parameter of the bridge penalty (the exponent to which the L1 norm of the coefficients are raised). Default is 0.5, the square root. Must be in (0,1].
max.steps	Number of MCMC iterations. Default is 20000.
n.burn	Number of burn-in iterations. Default is 10000.
n.thin	Lag at which thinning should be done. Default is 1 (no thinning).
eps	Small tolerance parameter to be used when inverting X, if it is less than full rank. Default is 1e-06.
r	Shape hyperparameter for the Gamma prior on lambda. Default is 1.
delta	Rate hyperparameter for the Gamma prior on lambda. Default is 0.1.
posterior.summary.beta	Posterior summary measure for beta (mean, median, or mode). Default is 'mean'.
posterior.summary.lambda	Posterior summary measure for lambda (mean or median). Default is 'mean'.
beta.ci.level	Credible interval level for beta. Default is 0.95 (95%).
lambda.ci.level	Credible interval level for lambda. Default is 0.95 (95%).
seed	Seed value for reproducibility. Default is 1234.

Value

A list containing the following components is returned:

time	Computational time in minutes.
beta	Posterior mean or median estimates of beta.
lowerbeta	Lower limit credible interval of beta.
upperbeta	Upper limit credible interval of beta.
lambda	Posterior estimate of lambda.
lambdaci	Posterior credible interval of lambda.
beta.post	Post-burn-in posterior samples of beta.
sigma2.post	Post-burn-in posterior samples of sigma2.
lambda.post	Post-burn-in posterior samples of lambda

Examples

## Not run: 

#########################
# Load Diabetes dataset #
#########################

library(ElemStatLearn)
prost<-prostate

###########################################
# Scale data and prepare train/test split #
###########################################

prost.std <- data.frame(cbind(scale(prost[,1:8]),prost$lpsa))
names(prost.std)[9] <- 'lpsa'
data.train <- prost.std[prost$train,]
data.test <- prost.std[!prost$train,]

##################################
# Extract standardized variables #
##################################

y.train   = data.train$lpsa - mean(data.train$lpsa)
y.test <- data.test$lpsa - mean(data.test$lpsa)
x.train = scale(as.matrix(data.train[,1:8], ncol=8))
x.test = scale(as.matrix(data.test[,1:8], ncol=8))

##############################################
# Bayesian Bridge with alpha = 0.5 using SMU #
##############################################

library(UBR)
BayesBridge<- BayesBridgeSMU(as.data.frame(x.train), y.train, alpha = 0.5)
y.pred.BayesBridge<-x.test%*%BayesBridge$beta
mean((y.pred.BayesBridge - y.test)^2) # Performance on test data

#############################################################
# Bayesian Bridge with alpha = 1 using SMU (Bayesian LASSO) #
#############################################################

BayesLASSO<- BayesBridgeSMU(as.data.frame(x.train), y.train, alpha = 1)
y.pred.BayesLASSO<-x.test%*%BayesLASSO$beta
mean((y.pred.BayesLASSO - y.test)^2) # Performance on test data

########################################################
# Visualization of Posterior Samples (Bayesian Bridge) #
########################################################

##############
# Trace Plot #
##############

library(coda)
plot(mcmc(BayesBridge$beta.post),density=FALSE,smooth=TRUE)

#############
# Histogram #
#############

library(psych)
multi.hist(BayesBridge$beta.post,density=TRUE,main="")


## End(Not run)

himelmallick/UBeRr documentation built on June 4, 2020, 7:18 a.m.