Type:	Package
Title:	Scalable Spike-and-Slab
Version:	1.0
Date:	2022-05-13
Description:	A scalable Gibbs sampling implementation for high dimensional Bayesian regression with the continuous spike-and-slab prior. Niloy Biswas, Lester Mackey and Xiao-Li Meng, "Scalable Spike-and-Slab" (2022) <doi:10.48550/arXiv.2204.01668>.
License:	GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
Imports:	Rcpp, stats, TruncatedNormal
LinkingTo:	Rcpp, RcppEigen
RoxygenNote:	7.1.2
NeedsCompilation:	yes
Packaged:	2022-05-17 20:40:23 UTC; niloybiswas
Author:	Niloy Biswas [aut, cre], Lester Mackey [aut], Xiao-Li Meng [aut]
Maintainer:	Niloy Biswas <niloy_biswas@g.harvard.edu>
Depends:	R (≥ 3.5.0)
Repository:	CRAN
Date/Publication:	2022-05-18 17:00:07 UTC

Riboflavin GWAS dataset

Description

Dataset of riboflavin production by Bacillus subtilis containing n = 71 observations of a one-dimensional response (riboflavin production) and p = 4088 predictors (gene expressions). The one-dimensional response corresponds to riboflavin production.

Usage

data(riboflavin)

Format

A data frame containing a vector y of length 71 (responses) and a matrix X of dimension 71 by 4088 (gene expressions)

Details

The processed dataset is the same as in the R packages qut and hdi.

References

Buhlmann, P., Kalisch, M. and Meier, L. (2014) High-dimensional statistics with a view towards applications in biology. Annual Review of Statistics and its Applications 1, 255–278

Examples

data(riboflavin)
y <- as.vector(riboflavin$y)
X <- as.matrix(riboflavin$x)

spike_slab_linear

Description

Generates Markov chain targeting the posterior corresponding to Bayesian linear regression with spike and slab priors

Usage

spike_slab_linear(
  chain_length,
  X,
  y,
  tau0,
  tau1,
  q,
  a0 = 1,
  b0 = 1,
  rinit = NULL,
  verbose = FALSE,
  burnin = 0,
  store = TRUE,
  Xt = NULL,
  XXt = NULL,
  tau0_inverse = NULL,
  tau1_inverse = NULL
)

Arguments

Value

Output from Markov chain targeting the posterior corresponding to Bayesian linear regression with spike and slab priors

Examples

# Synthetic dataset
syn_data <- synthetic_data(n=100,p=200,s0=5,error_std=2,type='linear')
X <- syn_data$X
y <- syn_data$y

# Hyperparamters
params <- spike_slab_params(n=nrow(X),p=ncol(X))

# Run S^3
sss_chain <- spike_slab_linear(chain_length=4e3,burnin=1e3,X=X,y=y,
tau0=params$tau0,tau1=params$tau1,q=params$q,a0=params$a0,b0=params$b0,
verbose=FALSE,store=FALSE)

# Use posterior probabilities for variable selection
sss_chain$z_ergodic_avg[1:10]

spike_slab_logistic

Description

Generates Markov chain targeting the posterior corresponding to Bayesian logistic regression with spike and slab priors

Usage

spike_slab_logistic(
  chain_length,
  X,
  y,
  tau0,
  tau1,
  q,
  rinit = NULL,
  verbose = FALSE,
  burnin = 0,
  store = TRUE,
  Xt = NULL,
  XXt = NULL
)

Arguments

Value

Output from Markov chain targeting the posterior corresponding to Bayesian logistic regression with spike and slab priors

Examples

# Synthetic dataset
syn_data <- synthetic_data(n=100,p=200,s0=5,error_std=2,type='logistic')
X <- syn_data$X
y <- syn_data$y

# Hyperparamters
params <- spike_slab_params(n=nrow(X),p=ncol(X))

# Run S^3
sss_chain <- spike_slab_logistic(chain_length=4e3,burnin=1e3,X=X,y=y,
tau0=params$tau0,tau1=params$tau1,q=params$q,verbose=FALSE,store=FALSE)

# Use posterior probabilities for variable selection
sss_chain$z_ergodic_avg[1:10]

spike_slab_params

Description

Generates hyperparameters for spike-and-slab

Usage

spike_slab_params(n, p)

Arguments

Value

spike-and-slab hyperparameters q, tau0, tau1, a0, b0

Examples

hyper_params <- spike_slab_params(n=100,p=200)
print(hyper_params)

spike_slab_probit

Description

Generates Markov chain targeting the posterior corresponding to Bayesian probit regression with spike and slab priors

Usage

spike_slab_probit(
  chain_length,
  X,
  y,
  tau0,
  tau1,
  q,
  rinit = NULL,
  verbose = FALSE,
  burnin = 0,
  store = TRUE,
  Xt = NULL,
  XXt = NULL,
  tau0_inverse = NULL,
  tau1_inverse = NULL
)

Arguments

Value

Output from Markov chain targeting the posterior corresponding to Bayesian logistic regression with spike and slab priors

Examples

# Synthetic dataset
syn_data <- synthetic_data(n=100,p=200,s0=5,error_std=2,type='probit')
X <- syn_data$X
Xt <- t(X)
y <- syn_data$y

# Hyperparamters
params <- spike_slab_params(n=nrow(X),p=ncol(X))

# Run S^3
sss_chain <- spike_slab_probit(chain_length=4e3,burnin=1e3,X=X,y=y,
tau0=params$tau0,tau1=params$tau1,q=params$q,verbose=FALSE,store=FALSE)

# Use posterior probabilities for variable selection
sss_chain$z_ergodic_avg[1:10]

synthetic_data

Description

Generates synthetic linear and logistic regression data

Usage

synthetic_data(
  n,
  p,
  s0,
  error_std,
  type = "linear",
  scale = TRUE,
  signal = "constant"
)

Arguments

Value

Design matrix, response and true signal vector for linear and logistic regression

Examples

syn_data <- synthetic_data(n=100,p=200,s0=5,error_std=2)

# syn_data$X is an n by p design matrix
dim(syn_data$X)

# syn_data$y is a length n response vector
length(syn_data$y) 

# syn_data$true_beta is a length n response vector with only the first s0 entries non-zero
all(syn_data$true_beta[1:5]!=0)
all(syn_data$true_beta[-c(1:5)]==0)