| Title: | Empirical Bayesian Elastic Net |
|---|---|
| Description: | Provides the Empirical Bayesian Elastic Net for handling multicollinearity in generalized linear regression models. As a special case of the 'EBglmnet' package (also available on CRAN), this package encourages a grouping effects to select relevant variables and estimate the corresponding non-zero effects. |
| Authors: | Anhui Huang [aut, cre] |
| Maintainer: | Anhui Huang <[email protected]> |
| License: | GPL |
| Version: | 5.2 |
| Built: | 2024-11-27 06:53:43 UTC |
| Source: | CRAN |
Fast EBEN algorithms.
EBEN implements a normal and generalized gamma hierearchical priors.
( ** ) Two parameters (alpha, lambda) are equivalent with elastic net priors.
( ** ) When parameter alpha = 1, it is equivalent with EBlasso-NE (normal + exponential)
Two models are available for both methods:
( ** ) General linear regression model.
( ** ) Logistic regression model.
Multi-collinearity:
( ** ) for group of high correlated or collinear variables: EBEN identifies the group of variables estimates their effects together.
( ** ) group of variables can be selected together.
*Epistasis (two-way interactions) can be included for all models/priors
*model implemented with memory efficient c code.
*LAPACK/BLAS are used for most linear algebra computations.
| Package: | EBEN |
| Type: | Package |
| Version: | 5.2 |
| Date: | 2015-10-06 |
| License: | gpl |
Anhui Huang
key algorithms:
Cai, X., Huang, A., and Xu, S. (2011). Fast empirical Bayesian LASSO for multiple quantitative trait locus mapping. BMC Bioinformatics 12, 211.
Huang A, Xu S, Cai X. (2013). Empirical Bayesian LASSO-logistic regression for multiple binary trait locus mapping. BMC genetics 14(1):5.
Huang, A., Xu, S., and Cai, X. (2014). Empirical Bayesian elastic net for multiple quantitative trait locus mapping. Heredity 10.1038/hdy.2014.79
Other publications:
Huang, A., E. Martin, et al. (2014). "Detecting genetic interactions in pathway-based genome-wide association studies." Genet Epidemiol 38(4): 300-309.
Huang, A., S. Xu, et al. (2014). "Whole-genome quantitative trait locus mapping reveals major role of epistasis on yield of rice." PLoS ONE 9(1): e87330.
Huang, A. (2014). "Sparse model learning for inferring genotype and phenotype associations." Ph.D Dissertation. University of Miami(1186).
This is a 1000x481 sample feature matrix
data(BASIS)data(BASIS)
The format is: int [1:1000, 1:481] 0 -1 0 0 1 0 1 0 1 0 ...
The data was simulated on a 2400cM chromosome, each column corresponded to an even spaced QTL
Huang, A., Xu, S., and Cai, X. (2014). Empirical Bayesian elastic net for multiple quantitative trait locus mapping. Heredity 10.1038/hdy.2014.79
data(BASIS)data(BASIS)
This is a 500x481 sample feature matrix
data(BASISbinomial)data(BASISbinomial)
The format is: int [1:500, 1:481] 0 -1 0 0 0 0 -1 -1 0 1 ...
The data was simulated on a 2400cM chromosome, each column corresponded to an even spaced QTL
Huang A, Xu S, Cai X: Empirical Bayesian LASSO-logistic regression for multiple binary trait locus mapping. BMC genetics 2013, 14(1):5.
data(BASISbinomial)data(BASISbinomial)
Generalized linear regression, normal-Gxponential (NG) hierarchical prior for regression coefficients
EBelasticNet.Binomial(BASIS, Target, lambda, alpha,Epis = FALSE,verbose = 0)EBelasticNet.Binomial(BASIS, Target, lambda, alpha,Epis = FALSE,verbose = 0)
BASIS |
sample matrix; rows correspond to samples, columns correspond to features |
Target |
Class label of each individual, TAKES VALUES OF 0 OR 1 |
lambda |
Hyperparameter controls degree of shrinkage; can be obtained via Cross Validation; lambda>0 |
alpha |
Hyperparameter controls degree of shrinkage; can be obtained via Cross Validation; 0<alpha<1 |
Epis |
TRUE or FALSE for including two-way interactions |
verbose |
0 or 1; 1: display message; 0 no message |
If Epis=TRUE, the program adds two-way interaction of K*(K-1)/2 more columns to BASIS
weight |
the none-zero regression coefficients: |
logLikelihood |
log likelihood from the final regression coefficients |
WaldScore |
Wald Score |
Intercept |
Intercept |
lambda |
the hyperparameter; same as input lambda |
alpha |
the hyperparameter; same as input alpha |
Anhui Huang; Dept of Electrical and Computer Engineering, Univ of Miami, Coral Gables, FL
Huang A, Xu S, Cai X: Empirical Bayesian LASSO-logistic regression for multiple binary trait locus mapping. BMC genetics 2013, 14(1):5.
library(EBEN) data(BASISbinomial) data(yBinomial) #reduce sample size to speed up the running time n = 50; k = 100; N = length(yBinomial); set = sample(N,n); BASIS = BASISbinomial[set,1:k]; y = yBinomial[set]; output = EBelasticNet.Binomial(BASIS, y,lambda = 0.1,alpha = 0.5, Epis = FALSE,verbose = 5)library(EBEN) data(BASISbinomial) data(yBinomial) #reduce sample size to speed up the running time n = 50; k = 100; N = length(yBinomial); set = sample(N,n); BASIS = BASISbinomial[set,1:k]; y = yBinomial[set]; output = EBelasticNet.Binomial(BASIS, y,lambda = 0.1,alpha = 0.5, Epis = FALSE,verbose = 5)
Hyperparameter controls degree of shrinkage, and is obtained via Cross Validation (CV). This program calculates the maximum lambda that allows one non-zero basis; and performs a search down to 0.001*lambda_max at even steps. (20 steps)
EBelasticNet.BinomialCV(BASIS, Target, nFolds,foldId, Epis = FALSE, verbose = 0)EBelasticNet.BinomialCV(BASIS, Target, nFolds,foldId, Epis = FALSE, verbose = 0)
BASIS |
sample matrix; rows correspond to samples, columns correspond to features |
Target |
Class label of each individual, TAKES VALUES OF 0 OR 1 |
nFolds |
number of n-fold cv |
Epis |
TRUE or FALSE for including two-way interactions |
foldId |
random assign samples to different folds |
verbose |
from 0 to 5; larger verbose displays more messages |
If Epis=TRUE, the program adds two-way interaction K*(K-1)/2 more columns to BASIS
CrossValidation |
col1: hyperparameter; col2: loglikelihood mean; standard ERROR of nfold mean log likelihood |
Lmabda_optimal |
the optimal hyperparameter as computed |
Alpha_optimal |
the optimal hyperparameter as computed |
Anhui Huang; Dept of Electrical and Computer Engineering, Univ of Miami, Coral Gables, FL
Huang A, Xu S, Cai X: Empirical Bayesian LASSO-logistic regression for multiple binary trait locus mapping. BMC genetics 2013, 14(1):5.
## not run library(EBEN) data(BASISbinomial) data(yBinomial) #reduce sample size to speed up the running time n = 50; k = 100; N = length(yBinomial); set.seed(1) set = sample(N,n); BASIS = BASISbinomial[set,1:k]; y = yBinomial[set]; nFolds = 3 ## Not run: CV = EBelasticNet.BinomialCV(BASIS, y, nFolds = 3,Epis = FALSE) ## End(Not run)## not run library(EBEN) data(BASISbinomial) data(yBinomial) #reduce sample size to speed up the running time n = 50; k = 100; N = length(yBinomial); set.seed(1) set = sample(N,n); BASIS = BASISbinomial[set,1:k]; y = yBinomial[set]; nFolds = 3 ## Not run: CV = EBelasticNet.BinomialCV(BASIS, y, nFolds = 3,Epis = FALSE) ## End(Not run)
General linear regression, normal-Gamma (NG) hierarchical prior for regression coefficients
EBelasticNet.Gaussian(BASIS, Target, lambda, alpha,Epis = FALSE,verbose = 0)EBelasticNet.Gaussian(BASIS, Target, lambda, alpha,Epis = FALSE,verbose = 0)
BASIS |
sample matrix; rows correspond to samples, columns correspond to features |
Target |
Response each individual |
lambda |
Hyperparameter controls degree of shrinkage; can be obtained via Cross Validation; lambda>0 |
alpha |
Hyperparameter controls degree of shrinkage; can be obtained via Cross Validation; 0<alpha<1 |
Epis |
TRUE or FALSE for including two-way interactions |
verbose |
0 or 1; 1: display message; 0 no message |
If Epis=TRUE, the program adds two-way interaction of K*(K-1)/2 more columns to BASIS
weight |
the none-zero regression coefficients: |
WaldScore |
Wald Score |
Intercept |
Intercept |
lambda |
the hyperparameter; same as input lambda |
alpha |
the hyperparameter; same as input alpha |
Anhui Huang; Dept of Electrical and Computer Engineering, Univ of Miami, Coral Gables, FL
Huang, A., Xu, S., and Cai, X. (2014). Empirical Bayesian elastic net for multiple quantitative trait locus mapping. Heredity 10.1038/hdy.2014.79
library(EBEN) data(BASIS) data(y) n = 50; k = 100; BASIS = BASIS[1:n,1:k]; y = y[1:n]; Blup = EBelasticNet.Gaussian(BASIS, y,lambda = 0.0072,alpha = 0.95, Epis = FALSE,verbose = 0) betas = Blup$weight betaslibrary(EBEN) data(BASIS) data(y) n = 50; k = 100; BASIS = BASIS[1:n,1:k]; y = y[1:n]; Blup = EBelasticNet.Gaussian(BASIS, y,lambda = 0.0072,alpha = 0.95, Epis = FALSE,verbose = 0) betas = Blup$weight betas
Hyperparameter controls degree of shrinkage, and is obtained via Cross Validation (CV). This program calculates the maximum lambda that allows one non-zero basis; and performs a search down to 0.0001*lambda_max at even steps. (20 steps)
EBelasticNet.GaussianCV(BASIS, Target, nFolds,foldId, Epis = FALSE, verbose = 0)EBelasticNet.GaussianCV(BASIS, Target, nFolds,foldId, Epis = FALSE, verbose = 0)
BASIS |
sample matrix; rows correspond to samples, columns correspond to features |
Target |
Response each individual |
nFolds |
number of n-fold cv |
Epis |
TRUE or FALSE for including two-way interactions |
foldId |
random assign samples to different folds |
verbose |
from 0 to 5; larger verbose displays more messages |
If Epis=TRUE, the program adds two-way interaction K*(K-1)/2 more columns to BASIS
CrossValidation |
col1: hyperparameter; col2: loglikelihood mean; standard ERROR of nfold mean log likelihood |
Lmabda_optimal |
the optimal hyperparameter as computed |
Alpha_optimal |
the optimal hyperparameter as computed |
Anhui Huang; Dept of Electrical and Computer Engineering, Univ of Miami, Coral Gables, FL
Huang, A., Xu, S., and Cai, X. (2013). Empirical Bayesian elastic net for multiple quantitative trait locus mapping. submitted.
library(EBEN) data(BASIS) data(y) #reduce sample size to speed up the running time n = 50; k = 100; BASIS = BASIS[1:n,1:k]; y = y[1:n]; ## Not run: CV = EBelasticNet.GaussianCV(BASIS, y, nFolds = 3,Epis = FALSE) ## End(Not run)library(EBEN) data(BASIS) data(y) #reduce sample size to speed up the running time n = 50; k = 100; BASIS = BASIS[1:n,1:k]; y = y[1:n]; ## Not run: CV = EBelasticNet.GaussianCV(BASIS, y, nFolds = 3,Epis = FALSE) ## End(Not run)
Generalized linear regression, normal-exponential-gamma (NEG) hierarchical prior for regression coefficients
EBlassoNEG.Binomial(BASIS, Target, a_gamma, b_gamma, Epis,verbose,group)EBlassoNEG.Binomial(BASIS, Target, a_gamma, b_gamma, Epis,verbose,group)
BASIS |
sample matrix; rows correspond to samples, columns correspond to features |
Target |
Class label of each individual, TAKES VALUES OF 0 OR 1 |
a_gamma |
Hyperparameters control degree of shrinkage; can be obtained via Cross Validation; a_gamma>=-1 |
b_gamma |
Hyperparameters control degree of shrinkage; can be obtained via Cross Validation; b_gamma>0 |
Epis |
TRUE or FALSE for including two-way interactions |
verbose |
0 or 1; 1: display message; 0 no message |
group |
0 or 1; 0: No group effect; 1 two-way interaction grouped. Only valid when Epis = TRUE |
If Epis=TRUE, the program adds two-way interaction K*(K-1)/2 more columns to BASIS
weight |
the none-zero regression coefficients: |
logLikelihood |
log likelihood with the final regression coefficients |
WaldScore |
Wald Score |
Intercept |
Intercept |
a_gamma |
the hyperparameter; same as input |
b_gamma |
the hyperparameter; same as input |
Anhui Huang; Dept of Electrical and Computer Engineering, Univ of Miami, Coral Gables, FL
Huang, A., Xu, S., and Cai, X.(2012). Empirical Bayesian LASSO-logistic regression for multiple binary trait locus mapping. BMC Genetics. Submitted
library(EBEN) data(BASISbinomial) data(yBinomial) #reduce sample size to speed up the running time n = 50; k = 100; BASIS = BASISbinomial[1:n,1:k]; y = yBinomial[1:n]; output = EBlassoNEG.Binomial(BASIS,y,0.1,0.1,Epis = FALSE)library(EBEN) data(BASISbinomial) data(yBinomial) #reduce sample size to speed up the running time n = 50; k = 100; BASIS = BASISbinomial[1:n,1:k]; y = yBinomial[1:n]; output = EBlassoNEG.Binomial(BASIS,y,0.1,0.1,Epis = FALSE)
Hyperparameters control degree of shrinkage, and are obtained via Cross Validation. This program performs three steps of CV.
1st: a = b = 0.001, 0.01, 0.1, 1;
2nd: fix b= b1; a=[-0.5, -0.4, -0.3, -0.2, -0.1, -0.01, 0.01, 0.05, 0.1, 0.5, 1];
3rd: fix a = a2; b= 0.01 to 10 with a step size of one for b > 1 and a step size of one on the logarithmic scale for b < 1
In the 2nd step, a can take value from -1 and values in [-1, -0.5] can be added to the set in line 13 of this function (The smaller a is, the less shrinkage.)
EBlassoNEG.BinomialCV(BASIS, Target, nFolds,foldId, Epis,verbose, group)EBlassoNEG.BinomialCV(BASIS, Target, nFolds,foldId, Epis,verbose, group)
BASIS |
sample matrix; rows correspond to samples, columns correspond to features |
Target |
Class label of each individual, TAKES VALUES OF 0 OR 1 |
nFolds |
number of n-fold cv |
foldId |
random assign samples to different folds |
Epis |
TRUE or FALSE for including two-way interactions |
verbose |
from 0 to 5; larger verbose displays more messages |
group |
TRUE or FALSE; FALSE: No group effect; TRUE two-way interaction grouped. Only valid when Epis = TRUE |
If Epis=TRUE, the program adds two-way interaction K*(K-1)/2 more columns to BASIS
Note: Given the fact that degree of shrinkage is a monotonic function of (a,b),
The function implemented a 3-step search as described in Huang, A. 2014, for full
grid search, user needs to modify the function accordingly.
CrossValidation |
col1: hyperparameters; col2: loglikelihood mean; standard ERROR of nfold mean log likelihood |
a_optimal |
the optimal hyperparameter as computed |
b_optimal |
the optimal hyperparameter as computed |
Anhui Huang; Dept of Electrical and Computer Engineering, Univ of Miami, Coral Gables, FL
Huang A, Xu S, Cai X: Empirical Bayesian LASSO-logistic regression for multiple binary trait locus mapping. BMC genetics 2013, 14(1):5.
Huang, A., S. Xu, et al. Whole-genome quantitative trait locus mapping reveals major role of epistasis on yield of rice. PLoS ONE 2014, 9(1): e87330.
library(EBEN) data(BASISbinomial) data(yBinomial) #reduce sample size to speed up the running time n = 50; k = 100; BASIS = BASISbinomial[1:n,1:k]; y = yBinomial[1:n]; ## Not run: CV = EBlassoNEG.BinomialCV(BASIS, y, nFolds = 3,Epis = FALSE, verbose = 0) ## End(Not run)library(EBEN) data(BASISbinomial) data(yBinomial) #reduce sample size to speed up the running time n = 50; k = 100; BASIS = BASISbinomial[1:n,1:k]; y = yBinomial[1:n]; ## Not run: CV = EBlassoNEG.BinomialCV(BASIS, y, nFolds = 3,Epis = FALSE, verbose = 0) ## End(Not run)
General linear regression, normal-exponential-gamma (NEG) hierarchical prior for regression coefficients
EBlassoNEG.Gaussian(BASIS, Target, a_gamma, b_gamma, Epis, verbose, group)EBlassoNEG.Gaussian(BASIS, Target, a_gamma, b_gamma, Epis, verbose, group)
BASIS |
sample matrix; rows correspond to samples, columns correspond to features |
Target |
Response each individual |
a_gamma |
Hyperparameters control degree of shrinkage; can be obtained via Cross Validation |
b_gamma |
Hyperparameters control degree of shrinkage; can be obtained via Cross Validation |
Epis |
TRUE or FALSE for including two-way interactions |
verbose |
from 0 to 5; larger verbose displays more messages |
group |
0 or 1; 0: No group effect; 1 two-way interaction grouped. Only valid when Epis = TRUE |
If Epis=TURE, the program adds two-way interaction K*(K-1)/2 more columns to BASIS
for memory efficient, the function pass n_effect to C. n_effect > n_true effects, which is
a rough guess on how many variables will be selected by the function
by providing a relative 'small' n_effect, the function will not allocate
a large trunck of memory during computation.
weight |
the none-zero regression coefficients: |
WaldScore |
Wald Score |
Intercept |
Intercept |
residVar |
residual variance |
a_gamma |
the hyperparameter; same as input |
b_gamma |
the hyperparameter; same as input |
Anhui Huang; Dept of Electrical and Computer Engineering, Univ of Miami, Coral Gables, FL
Cai, X., Huang, A., and Xu, S. (2011). Fast empirical Bayesian LASSO for multiple quantitative trait locus mapping. BMC Bioinformatics 12, 211.
library(EBEN) data(BASIS) data(y) n = 50; k = 100; BASIS = BASIS[1:n,1:k]; y = y[1:n]; output = EBlassoNEG.Gaussian(BASIS, y, a_gamma = 0.1, b_gamma = 0.1)library(EBEN) data(BASIS) data(y) n = 50; k = 100; BASIS = BASIS[1:n,1:k]; y = y[1:n]; output = EBlassoNEG.Gaussian(BASIS, y, a_gamma = 0.1, b_gamma = 0.1)
Hyperparameters control degree of shrinkage, and are obtained
via Cross Validation. This program performs three steps of CV.
1st: a = b = 0.001, 0.01, 0.1, 1;
2nd: fix b= b1; a=[-0.5, -0.4, -0.3, -0.2, -0.1, -0.01, 0.01, 0.05, 0.1, 0.5, 1];
3rd: fix a = a2; b= 0.01 to 10 with a step size of one for b > 1 and a step size of one on the logarithmic scale for b < 1
In the 2nd step, a can take value from -1 and values in [-1, -0.5] can be added to the set in line 13 of this function (The smaller a is, the less shrinkage.)
EBlassoNEG.GaussianCV(BASIS, Target, nFolds, foldId, Epis,verbose, group)EBlassoNEG.GaussianCV(BASIS, Target, nFolds, foldId, Epis,verbose, group)
BASIS |
sample matrix; rows correspond to samples, columns correspond to features |
Target |
Class label of each individual, TAKES VALUES OF 0 OR 1 |
nFolds |
number of n-fold cv |
foldId |
random assign samples to different folds |
Epis |
TRUE or FALSE for including two-way interactions |
verbose |
from 0 to 5; larger verbose displays more messages |
group |
TRUE or FALSE; FALSE: No group effect; TRUE two-way interaction grouped. Only valid when Epis = TRUE |
If Epis= TRUE, the program adds two-way interaction K*(K-1)/2 more columns to BASIS
Note: Given the fact that degree of shrinkage is a monotonic function of (a,b),
The function implemented a 3-step search as described in Huang, A. 2014, for full
grid search, user needs to modify the function accordingly.
CrossValidation |
col1: hyperparameters; col2: loglikelihood mean; standard ERROR of nfold mean log likelihood |
a_optimal |
the optimal hyperparameter as computed |
b_optimal |
the optimal hyperparameter as computed |
Anhui Huang; Dept of Electrical and Computer Engineering, Univ of Miami, Coral Gables, FL
Huang A, Xu S, Cai X: Empirical Bayesian LASSO-logistic regression for multiple binary trait locus mapping. BMC genetics 2013, 14(1):5.
Huang, A., S. Xu, et al. Whole-genome quantitative trait locus mapping reveals major role of epistasis on yield of rice. PLoS ONE 2014, 9(1): e87330.
library(EBEN) data(BASIS) data(y) #reduce sample size to speed up the running time n = 50; k = 100; BASIS = BASIS[1:n,1:k]; y = y[1:n]; ## Not run: CV = EBlassoNEG.GaussianCV(BASIS, y, nFolds = 3,Epis = FALSE) ## End(Not run)library(EBEN) data(BASIS) data(y) #reduce sample size to speed up the running time n = 50; k = 100; BASIS = BASIS[1:n,1:k]; y = y[1:n]; ## Not run: CV = EBlassoNEG.GaussianCV(BASIS, y, nFolds = 3,Epis = FALSE) ## End(Not run)
Corresponding to the response of BASIS
data(y)data(y)
The format is: num [1:1000, 1] 113.5 97.1 116.6 96.7 105.5 ...
Huang, A., Xu, S., and Cai, X. (2014). Empirical Bayesian elastic net for multiple quantitative trait locus mapping. Heredity 10.1038/hdy.2014.79
data(y)data(y)
Corresponding to the class label of BASISbinomial
data(yBinomial)data(yBinomial)
The format is: int [1:500, 1] 1 1 1 1 1 1 1 1 1 1 ...
Huang A, Xu S, Cai X: Empirical Bayesian LASSO-logistic regression for multiple binary trait locus mapping. BMC genetics 2013, 14(1):5.
data(BASISbinomial)data(BASISbinomial)