LR_GradientConjugate_gpumatrix {GPUmatrix}

Logistic Regression with Conjugate Gradient method

Description

The developed function performs the logistic regression using the Conjugate Gradient method. This method has shown to be very effective for logistic regression of big models [1]. The code is general enough to accommodate standard R matrices, sparse matrices from the 'Matrix' package and, more interestingly, gpu.matrix-class objects from the GPUmatrix package.

Usage

LR_GradientConjugate_gpumatrix(X, y, beta = NULL,
                               lambda = 0, iterations = 100,
                               tol = 1e-08)

Arguments

X

the design matrix. Could be either a object of class gpu.matrix, matrix, or Matrix.

y

vector of observations.

beta

initial solution.

lambda

numeric. Penalty factor also known as the L2 norm or L2 penalty, which is computed as the sum of the squared coefficients: \lambda||\beta_i||_2^2

iterations

maximum number of iterations.

tol

tolerance to be used for the estimation.

Details

If the input gpu.matrix-class object(s) are stored on the GPU, then the operations will be performed on the GPU. See gpu.matrix.

Value

The function returns a vector containing the values of the coefficients. This returned vector will be a 'matrix', 'Matrix' or 'gpu.matrix-class' object depending on the class of the object X.

Author(s)

Angel Rubio and Cesar Lobato.

References

[1] Minka TP (2003). “A comparison of numerical optimizers for logistic regression.” URL: https://tminka.github.io/papers/logreg/minka-logreg.pdf.

See Also

See also: GPUglm

Examples

## Not run: 

#toy example:
set.seed(123)
m <- 1000
n <- 100
x <- matrix(runif(m*n),m,n)
sol <- rnorm(n)
y <- rbinom(m, 1, prob = plogis(x%*%sol))
s2_granConj <- LR_GradientConjugate_gpumatrix(X = x,y = y)

#the following compares LR_GradientConjugate_gpumatrix
# with glm and GPUglm:

require(MASS)
require(stats,quietly = TRUE)
#logistic:
data(menarche)
glm.out <- glm(cbind(Menarche, Total-Menarche) ~ Age, family=binomial(), data=menarche)
summary(glm.out)

glm.out_gpu <- GPUglm(cbind(Menarche, Total-Menarche) ~ Age, family=binomial(), data=menarche)
summary(glm.out_gpu)

#can be also called using glm.fit.gpu:
new_menarche <- data.frame(Age=rep(menarche$Age,menarche$Total))
observations <- c()
for(i in 1:nrow(menarche)){
  observations <- c(observations,rep(c(0,1),c(menarche$Total[i]-menarche$Menarche[i],
                                              menarche$Menarche[i])))
}
new_menarche$observations <- observations
x <- model.matrix(~Age,data=new_menarche)
head(new_menarche)
glm.fit_gpu <- glm.fit.GPU(x=x,y=new_menarche$observations, family=binomial())
summary(glm.fit_gpu)

#GPUmatrix package also include the function 'LR_GradientConjugate_gpumatrix'
lr_gran_sol <- LR_GradientConjugate_gpumatrix(X = x,y = observations)

#check results
glm.out$coefficients
glm.out_gpu$coefficients
glm.fit_gpu$coefficients
lr_gran_sol


## End(Not run)