sketch function

Sketch

Provides a subsample of data using sketches

sketch(data, m, method = "unif")

Arguments

• data: (n times d)-dimensional matrix of data.
• m: (expected) subsample size that is less than n
• method: method for sketching: "unif" uniform sampling with replacement (default); "unif_without_replacement" uniform sampling without replacement; "bernoulli" Bernoulli sampling; "gaussian" Gaussian projection; "countsketch" CountSketch; "srht" subsampled randomized Hadamard transform; "fft" subsampled randomized trigonometric transforms using the real part of fast discrete Fourier transform (stats::ftt).

Returns

(m times d)-dimensional matrix of data For Bernoulli sampling, the number of rows is not necessarily m.

Examples

## Least squares: sketch and solve
# setup
n <- 1e+6 # full sample size
d <- 5    # dimension of covariates
m <- 1e+3 # sketch size
# generate psuedo-data
X <- matrix(stats::rnorm(n*d), nrow = n, ncol = d)
beta <- matrix(rep(1,d), nrow = d, ncol = 1)
eps <- matrix(stats::rnorm(n), nrow = n, ncol = 1)
Y <- X %*% beta + eps
intercept <- matrix(rep(1,n), nrow = n, ncol = 1)
# full sample including the intercept term
fullsample <- cbind(Y,intercept,X)
# generate a sketch using CountSketch
s_cs <-  sketch(fullsample, m, "countsketch")
# solve without the intercept
ls_cs <- lm(s_cs[,1] ~ s_cs[,2] - 1)
# generate a sketch using SRHT
s_srht <-  sketch(fullsample, m, "srht")
# solve without the intercept
ls_srht <- lm(s_srht[,1] ~ s_srht[,2] - 1)