SBRidgeRSq: R-square Safe-Bayesian Ridge Regression
In SafeBayes: Generalized and Safe-Bayesian Ridge and Lasso Regression
Description
Usage
Arguments
Details
Value
Author(s)
References
Examples
Description
The function SBRidgeRSq (R-square-Safe-Bayesian Ridge Regression) provides a Gibbs sampler together with the R-square-Safe-Bayesian algorithm for Ridge regression models with fixed variance.
Usage
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SBRidgeRSq(y, X = NULL, sigma2 = NULL, etaseq = 1, prior = NULL, nIter = 1100,
burnIn = 100, thin = 10, minAbsBeta = 1e-09, pIter = TRUE)
Arguments
y
Vector of outcome variables, numeric, NA allowed, length n.
X
Design matrix, numeric, dimension n x p, n >= 2.
sigma2
Fixed variance parameter sigma^2, numeric. Default NULL, in which case the variance will be estimated from the data per addition of new data point in the Safe-Bayesian algorithm.
etaseq
Vector of learning rates eta, numeric, 0 <= eta <= 1. Default 1.
prior
List containing the following elements
prior$varE: prior for the variance parameter σ^2 with parameters $df and $S for respectively degrees of freedom and scale parameters for an inverse-chi-square distribution. Default (0,0).
prior$varBR: prior for the variance of the Gaussian prior for the coefficients beta, with parameters $df and $S for respectively degrees of freedom and scale parameters for an inverse-chi-square distribution. Default (0,0).
nIter
Number of iterations, integer. Default 1100.
burnIn
Number of iterations for burn-in, integer. Default 100.
thin
Number of iterations for thinning, integer. Default 10.
minAbsBeta
Minimum absolute value of sampled coefficients beta to avoid numerical problems, numeric. Default 10^-9.
pIter
Print iterations, logical. Default TRUE.
Details
Details on generalized Bayesian regression can be found in (de Heide, 2016). The implementation of the Gibbs sampler is based on the BLR package of (de los Campos et al., 2009).
The Safe-Bayesian algorithm was proposed by Grunwald (2012) as a method to learn the learning rate for the generalized posterior to deal with model misspecification.
Value
$y
Vector of original outcome variables.
$mu
Posterior mean of the intercept.
$varE
Posterior mean of of the variance.
$yHat
Posterior mean of mu + X*beta + epsilon.
$SD.yHat
Corresponding standard deviation.
$whichNa
Vector with indices of missing values of y.
$fit$pD
Estimated number of effective parameters.
$fit$DIC
Deviance Information Criterion.
$bR
Posterior mean of beta.
$SD.bR
Corresponding standard deviation.
$prior
List containing the priors used.
$nIter
Number of iterations.
$burnIn
Number of iterations for burn-in.
$thin
Number of iterations for thinning.
$CMRSEallen
List of cumulative posterior-expected posterior-randomized square-loss per eta.
$eta.min
Learning rate eta minimizing the cumulative posterior-expected posterior-randomized square-loss.
Author(s)
R. de Heide
References
de Heide, R. 2016.
The Safe-Bayesian Lasso. Master Thesis, Leiden University.
de los Campos G., H. Naya, D. Gianola, J. Crossa, A. Legarra, E. Manfredi, K. Weigel and J. Cotes. 2009.
Predicting Quantitative Traits with Regression Models for Dense Molecular Markers and Pedigree. Genetics 182: 375-385.
Grunwald, P.D. 2012.
chapter The Safe Bayesian. Algorithmic Learning Theory: 23rd International Conference, ALT 2012, Lyon, France, October 29-31, 2012. Proceedings. 169-183. Springer Berlin Heidelberg
Examples
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rm(list=ls())
# Simulate data
x <- runif(10, -1, 1) # 10 random uniform x's between -1 and 1
y <- NULL
# for each x, an y that is 0 + Gaussian noise
for (i in 1:10) {
y[i] <- 0 + rnorm(1, mean=0, sd=1/4)
}
plot(x,y)
## Not run:
# Let R-square-SafeBayes learn the learning rate
sbobj <- SBRidgeRSq(y, x, etaseq=c(1, 0.5, 0.25))
# eta
sbobj$eta.min
## End(Not run)
Example output
No prior was provided, improper priors are used.
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Iter: 819 time/iter: 0 varE: 0
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Iter: 821 time/iter: 0 varE: 0
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Iter: 822 time/iter: 0.001 varE: 0
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Iter: 824 time/iter: 0 varE: 0
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Iter: 825 time/iter: 0 varE: 0
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Iter: 828 time/iter: 0 varE: 0
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Iter: 829 time/iter: 0 varE: 0
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Iter: 830 time/iter: 0.001 varE: 0
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Iter: 831 time/iter: 0 varE: 0
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Iter: 832 time/iter: 0 varE: 0
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Iter: 873 time/iter: 0 varE: 0
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Iter: 883 time/iter: 0 varE: 0
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Iter: 886 time/iter: 0 varE: 0
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Iter: 907 time/iter: 0 varE: 0
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Iter: 908 time/iter: 0 varE: 0
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Iter: 909 time/iter: 0 varE: 0
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Iter: 991 time/iter: 0 varE: 0
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Iter: 992 time/iter: 0 varE: 0
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Iter: 993 time/iter: 0 varE: 0
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Iter: 994 time/iter: 0 varE: 0
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Iter: 995 time/iter: 0 varE: 0
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Iter: 1010 time/iter: 0 varE: 0
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Sigma^2 is not provided and will be estimated from the dataIter: 1 time/iter: 0.001 varE: 0.013
------------------------------------------------------------
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Iter: 1100 time/iter: 0 varE: 0.022
------------------------------------------------------------
Sigma^2 is not provided and will be estimated from the dataIter: 1 time/iter: 0 varE: 0.021
------------------------------------------------------------
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Iter: 1100 time/iter: 0 varE: 0.036
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Sigma^2 is not provided and will be estimated from the dataIter: 1 time/iter: 0 varE: 0
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Iter: 826 time/iter: 0 varE: 0
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Iter: 827 time/iter: 0 varE: 0
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Iter: 828 time/iter: 0.001 varE: 0
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Iter: 829 time/iter: 0 varE: 0
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Iter: 830 time/iter: 0 varE: 0
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Iter: 831 time/iter: 0 varE: 0
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Iter: 848 time/iter: 0.001 varE: 0
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Iter: 849 time/iter: 0 varE: 0
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Iter: 870 time/iter: 0.001 varE: 0
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Iter: 873 time/iter: 0 varE: 0
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Iter: 880 time/iter: 0 varE: 0
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Iter: 882 time/iter: 0 varE: 0
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Iter: 883 time/iter: 0 varE: 0
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Iter: 884 time/iter: 0 varE: 0
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Iter: 886 time/iter: 0 varE: 0
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Iter: 892 time/iter: 0 varE: 0
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Iter: 901 time/iter: 0 varE: 0
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Iter: 905 time/iter: 0 varE: 0
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Iter: 910 time/iter: 0.001 varE: 0
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Iter: 914 time/iter: 0 varE: 0
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Iter: 932 time/iter: 0 varE: 0
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Iter: 993 time/iter: 0.001 varE: 0
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Iter: 994 time/iter: 0 varE: 0
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Iter: 995 time/iter: 0 varE: 0
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Iter: 996 time/iter: 0 varE: 0
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Iter: 1013 time/iter: 0 varE: 0
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Iter: 1024 time/iter: 0 varE: 0
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Iter: 1031 time/iter: 0.001 varE: 0
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Iter: 1032 time/iter: 0 varE: 0
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Sigma^2 is not provided and will be estimated from the dataIter: 1 time/iter: 0.001 varE: 0.013
------------------------------------------------------------
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SafeBayes documentation built on May 1, 2019, 9:23 p.m.
R Package Documentation
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Description Usage Arguments Details Value Author(s) References Examples
Description
The function SBRidgeRSq (R-square-Safe-Bayesian Ridge Regression) provides a Gibbs sampler together with the R-square-Safe-Bayesian algorithm for Ridge regression models with fixed variance.
Usage
1 2 | SBRidgeRSq(y, X = NULL, sigma2 = NULL, etaseq = 1, prior = NULL, nIter = 1100,
burnIn = 100, thin = 10, minAbsBeta = 1e-09, pIter = TRUE)
|
Arguments
y |
Vector of outcome variables, numeric, NA allowed, length n. |
X |
Design matrix, numeric, dimension n x p, n >= 2. |
sigma2 |
Fixed variance parameter sigma^2, numeric. Default NULL, in which case the variance will be estimated from the data per addition of new data point in the Safe-Bayesian algorithm. |
etaseq |
Vector of learning rates eta, numeric, 0 <= eta <= 1. Default 1. |
prior |
List containing the following elements
|
nIter |
Number of iterations, integer. Default 1100. |
burnIn |
Number of iterations for burn-in, integer. Default 100. |
thin |
Number of iterations for thinning, integer. Default 10. |
minAbsBeta |
Minimum absolute value of sampled coefficients beta to avoid numerical problems, numeric. Default 10^-9. |
pIter |
Print iterations, logical. Default TRUE. |
Details
Details on generalized Bayesian regression can be found in (de Heide, 2016). The implementation of the Gibbs sampler is based on the BLR package of (de los Campos et al., 2009).
The Safe-Bayesian algorithm was proposed by Grunwald (2012) as a method to learn the learning rate for the generalized posterior to deal with model misspecification.
Value
$y |
Vector of original outcome variables. |
$mu |
Posterior mean of the intercept. |
$varE |
Posterior mean of of the variance. |
$yHat |
Posterior mean of mu + X*beta + epsilon. |
$SD.yHat |
Corresponding standard deviation. |
$whichNa |
Vector with indices of missing values of y. |
$fit$pD |
Estimated number of effective parameters. |
$fit$DIC |
Deviance Information Criterion. |
$bR |
Posterior mean of beta. |
$SD.bR |
Corresponding standard deviation. |
$prior |
List containing the priors used. |
$nIter |
Number of iterations. |
$burnIn |
Number of iterations for burn-in. |
$thin |
Number of iterations for thinning. |
$CMRSEallen |
List of cumulative posterior-expected posterior-randomized square-loss per eta. |
$eta.min |
Learning rate eta minimizing the cumulative posterior-expected posterior-randomized square-loss. |
Author(s)
R. de Heide
References
de Heide, R. 2016. The Safe-Bayesian Lasso. Master Thesis, Leiden University.
de los Campos G., H. Naya, D. Gianola, J. Crossa, A. Legarra, E. Manfredi, K. Weigel and J. Cotes. 2009. Predicting Quantitative Traits with Regression Models for Dense Molecular Markers and Pedigree. Genetics 182: 375-385.
Grunwald, P.D. 2012. chapter The Safe Bayesian. Algorithmic Learning Theory: 23rd International Conference, ALT 2012, Lyon, France, October 29-31, 2012. Proceedings. 169-183. Springer Berlin Heidelberg
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | rm(list=ls())
# Simulate data
x <- runif(10, -1, 1) # 10 random uniform x's between -1 and 1
y <- NULL
# for each x, an y that is 0 + Gaussian noise
for (i in 1:10) {
y[i] <- 0 + rnorm(1, mean=0, sd=1/4)
}
plot(x,y)
## Not run:
# Let R-square-SafeBayes learn the learning rate
sbobj <- SBRidgeRSq(y, x, etaseq=c(1, 0.5, 0.25))
# eta
sbobj$eta.min
## End(Not run)
|
Example output
No prior was provided, improper priors are used.
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Sigma^2 is not provided and will be estimated from the dataIter: 1 time/iter: 0.001 varE: 0.013
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Iter: 1008 time/iter: 0 varE: 0.023
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Iter: 1017 time/iter: 0.001 varE: 0.023
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Iter: 959 time/iter: 0.001 varE: 0.036
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Sigma^2 is not provided and will be estimated from the dataIter: 1 time/iter: 0.001 varE: 0.013
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