Empirical Bayesian Elastic Net (EBEN)

Description

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.

Details

Author(s)

Anhui Huang

References

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).

An Example Data File for the Gauss Model

Description

This is a 1000x481 sample feature matrix

Usage

data(BASIS)

Format

The format is: int [1:1000, 1:481] 0 -1 0 0 1 0 1 0 1 0 ...

Details

The data was simulated on a 2400cM chromosome, each column corresponded to an even spaced QTL

Source

Huang, A., Xu, S., and Cai, X. (2014). Empirical Bayesian elastic net for multiple quantitative trait locus mapping. Heredity 10.1038/hdy.2014.79

Examples

data(BASIS)

An Example Data File for the Binomial Model

Description

This is a 500x481 sample feature matrix

Usage

data(BASISbinomial)

Format

The format is: int [1:500, 1:481] 0 -1 0 0 0 0 -1 -1 0 1 ...

Details

The data was simulated on a 2400cM chromosome, each column corresponded to an even spaced QTL

Source

Huang A, Xu S, Cai X: Empirical Bayesian LASSO-logistic regression for multiple binary trait locus mapping. BMC genetics 2013, 14(1):5.

Examples

data(BASISbinomial)

Internal EBEN functions

Description

Internal EBEN functions

Usage

	ijIndex(trueLoc,K)
	CVonePair(X,y,nFolds,foldId,hyperpara,Epis,prior,family,verbose,group)
	lambdaMax(X,y,Epis)

Details

These are not intended for use by users. ijIndexFunction for looking at the pair of interaction terms. CVonePairFunction performs nFolds CV for the given one pair of hyperparameter. lambdaMaxFunction calculate the maximum lambda for EBlasso-NE and EBEN in CV.

Author(s)

Anhui Huang and Dianting Liu
Dept of Electrical and Computer Engineering, Univ of Miami, Coral Gables, FL

The EB Elastic Net Algorithm for Binomial Model with Normal-Gamma(NG) Prior Distribution

Description

Generalized linear regression, normal-Gxponential (NG) hierarchical prior for regression coefficients

Usage

EBelasticNet.Binomial(BASIS, Target, lambda, alpha,Epis = FALSE,verbose = 0)

Arguments

Details

If Epis=TRUE, the program adds two-way interaction of K*(K-1)/2 more columns to BASIS

Value

Author(s)

Anhui Huang; Dept of Electrical and Computer Engineering, Univ of Miami, Coral Gables, FL

References

Huang A, Xu S, Cai X: Empirical Bayesian LASSO-logistic regression for multiple binary trait locus mapping. BMC genetics 2013, 14(1):5.

Examples

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)

Cross Validation (CV) Function to Determine Hyperparameter of the EB_Elastic Net Algorithm for Binomial Model with Normal-Gamma (NG) Prior Distribution

Description

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)

Usage

EBelasticNet.BinomialCV(BASIS, Target, nFolds,foldId, Epis = FALSE, verbose = 0)

Arguments

Details

If Epis=TRUE, the program adds two-way interaction K*(K-1)/2 more columns to BASIS

Value

Author(s)

Anhui Huang; Dept of Electrical and Computer Engineering, Univ of Miami, Coral Gables, FL

References

Huang A, Xu S, Cai X: Empirical Bayesian LASSO-logistic regression for multiple binary trait locus mapping. BMC genetics 2013, 14(1):5.

Examples

## 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)

The EB Elastic Net Algorithm for Gaussian Model

Description

General linear regression, normal-Gamma (NG) hierarchical prior for regression coefficients

Usage

EBelasticNet.Gaussian(BASIS, Target, lambda, alpha,Epis = FALSE,verbose = 0)

Arguments

Details

If Epis=TRUE, the program adds two-way interaction of K*(K-1)/2 more columns to BASIS

Value

Author(s)

Anhui Huang; Dept of Electrical and Computer Engineering, Univ of Miami, Coral Gables, FL

References

Huang, A., Xu, S., and Cai, X. (2014). Empirical Bayesian elastic net for multiple quantitative trait locus mapping. Heredity 10.1038/hdy.2014.79

Examples

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
betas

Cross Validation (CV) Function to Determine Hyperparameters of the EBEN Algorithm for Gaussian Model

Description

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)

Usage

EBelasticNet.GaussianCV(BASIS, Target, nFolds,foldId, Epis = FALSE, verbose = 0)

Arguments

Details

If Epis=TRUE, the program adds two-way interaction K*(K-1)/2 more columns to BASIS

Value

Author(s)

Anhui Huang; Dept of Electrical and Computer Engineering, Univ of Miami, Coral Gables, FL

References

Huang, A., Xu, S., and Cai, X. (2013). Empirical Bayesian elastic net for multiple quantitative trait locus mapping. submitted.

Examples

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)

The EBlasso Algorithm for Binomial Model with Normal-Exponential-Gamma (NEG) Prior Distribution

Description

Generalized linear regression, normal-exponential-gamma (NEG) hierarchical prior for regression coefficients

Usage

EBlassoNEG.Binomial(BASIS, Target, a_gamma, b_gamma, Epis,verbose,group)

Arguments

Details

If Epis=TRUE, the program adds two-way interaction K*(K-1)/2 more columns to BASIS

Value

Author(s)

Anhui Huang; Dept of Electrical and Computer Engineering, Univ of Miami, Coral Gables, FL

References

Huang, A., Xu, S., and Cai, X.(2012). Empirical Bayesian LASSO-logistic regression for multiple binary trait locus mapping. BMC Genetics. Submitted

Examples

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)

Cross Validation (CV) Function to Determine Hyperparameters of the EBlasso Algorithm for Binomial Model with Normal-Exponential-Gamma (NEG) Prior Distribution

Description

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.)

Usage

EBlassoNEG.BinomialCV(BASIS, Target, nFolds,foldId, Epis,verbose, group)

Arguments

Details

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.

Value

Author(s)

Anhui Huang; Dept of Electrical and Computer Engineering, Univ of Miami, Coral Gables, FL

References

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.

Examples

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)

The EBlasso Algorithm for Gaussian Model with Normal-Exponential-Gamma (NEG) Prior Distribution

Description

General linear regression, normal-exponential-gamma (NEG) hierarchical prior for regression coefficients

Usage

EBlassoNEG.Gaussian(BASIS, Target, a_gamma, b_gamma, Epis, verbose, group)

Arguments

Details

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.

Value

Author(s)

Anhui Huang; Dept of Electrical and Computer Engineering, Univ of Miami, Coral Gables, FL

References

Cai, X., Huang, A., and Xu, S. (2011). Fast empirical Bayesian LASSO for multiple quantitative trait locus mapping. BMC Bioinformatics 12, 211.

Examples

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)

Cross Validation (CV) Function to Determine Hyperparameters of the EBlasso Algorithm for Gaussian Model with Normal-Exponential-Gamma (NEG) Prior Distribution

Description

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.)

Usage

EBlassoNEG.GaussianCV(BASIS, Target, nFolds, foldId, Epis,verbose, group)

Arguments

Details

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.

Value

Author(s)

Anhui Huang; Dept of Electrical and Computer Engineering, Univ of Miami, Coral Gables, FL

References

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.

Examples

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)

Sample Response Data for Gaussian Model

Description

Corresponding to the response of BASIS

Usage

data(y)

Format

The format is: num [1:1000, 1] 113.5 97.1 116.6 96.7 105.5 ...

Source

Huang, A., Xu, S., and Cai, X. (2014). Empirical Bayesian elastic net for multiple quantitative trait locus mapping. Heredity 10.1038/hdy.2014.79

Examples

data(y)

Sample Variable Data for Binomial Model

Description

Corresponding to the class label of BASISbinomial

Usage

data(yBinomial)

Format

The format is: int [1:500, 1] 1 1 1 1 1 1 1 1 1 1 ...

Source

Huang A, Xu S, Cai X: Empirical Bayesian LASSO-logistic regression for multiple binary trait locus mapping. BMC genetics 2013, 14(1):5.

Examples

data(BASISbinomial)