large-scale regression in R with a sparse feature matrix

Question

I\'d like to do large-scale regression (linear/logistic) in R with many (e.g. 100k) features, where each example is relatively sparse in the feature space---e.g., ~1k non-ze

Answer 1

A belated answer: glmnet will also support sparse matrices and both of the regression models requested. This can use the sparse matrices produced by the Matrix package. I advise looking into regularized models via this package. As sparse data often involves very sparse support for some variables, L1 regularization is useful for knocking these out of the model. It's often safer than getting some very spurious parameter estimates for variables with very low support.

Answer 2

glmnet is a good choice. Supports L1, L2 regularization for linear, logistic, and multinomial regression, among other options.

The only detail is it doesn't have a formula interface, so you have to create your model matrix. But here is where the gain is.

Here is a pseudo-example:

library(glmnet)
library(doMC)
registerDoMC(cores=4)

y_train <- class
x_train <- sparse.model.matrix(~ . -1, data=x_train)

# For example for logistic regression using L1 norm (lasso) 
cv.fit <- cv.glmnet(x=x_train, y=y_train, family='binomial', alpha=1, 
                    type.logistic="modified.Newton", type.measure = "auc",
                    nfolds=5, parallel=TRUE)

plot(cv.fit)

Answer 3

You might also get some mileage by looking here:

• The biglm package.
• The High Performance and Parallel Computing R task view.
• A paper about Sparse Model Matrices for Generalized Linear Models (PDF), by Martin Machler and Douglas Bates from UseR 2010.

Answer 4

Don't know about SparseM but the MatrixModels package has an unexported lm.fit.sparse function that you can use. See ?MatrixModels:::lm.fit.sparse. Here is an example:

Create the data:

y <- rnorm(30)
x <- factor(sample(letters, 30, replace=TRUE))
X <- as(x, "sparseMatrix")
class(X)
# [1] "dgCMatrix"
# attr(,"package")
# [1] "Matrix"
dim(X)
# [1] 18 30

Run the regression:

MatrixModels:::lm.fit.sparse(t(X), y)
#  [1] -0.17499968 -0.89293312 -0.43585172  0.17233007 -0.11899582  0.56610302
#  [7]  1.19654666 -1.66783581 -0.28511569 -0.11859264 -0.04037503  0.04826549
# [13] -0.06039113 -0.46127034 -1.22106064 -0.48729092 -0.28524498  1.81681527

For comparison:

lm(y~x-1)

# Call:
# lm(formula = y ~ x - 1)
# 
# Coefficients:
#       xa        xb        xd        xe        xf        xg        xh        xj  
# -0.17500  -0.89293  -0.43585   0.17233  -0.11900   0.56610   1.19655  -1.66784  
#       xm        xq        xr        xt        xu        xv        xw        xx  
# -0.28512  -0.11859  -0.04038   0.04827  -0.06039  -0.46127  -1.22106  -0.48729  
#       xy        xz  
# -0.28524   1.81682