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-zero features per example.

It seems like the SparseM package slm should do this, but I'm having difficulty converting from the sparseMatrix format to a slm-friendly format.

I have a numeric vector of labels y and a sparseMatrix of features X \in {0,1}. When I try

model <- slm(y ~ X)

I get the following error:

Error in model.frame.default(formula = y ~ X) : 
invalid type (S4) for variable 'X'

presumably because slm wants a SparseM object instead of a sparseMatrix.

Is there an easy way to either a) populate a SparseM object directly or b) convert a sparseMatrix to a SparseM object? Or perhaps there's a better/simpler way to do this?

(I suppose I could explicitly code the solutions for linear regression using X and y, but it would be nice to have slm working.)

Answer 1

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