rp_cw {spareg}R Documentation

Sparse embedding matrix

Description

Creates an object class 'randomprojection' using arguments passed by user which in turn can be employed to generate a sparse embedding matrix as in (Clarkson and Woodruff 2013).

Usage

rp_cw(..., control = list())

Arguments

...

includes arguments which can be passed as attributes to the random projection matrix

control

list of arguments to be used in functions generate_fun, update_fun, update_rpm_w_data

Details

The entries of the matrix are generated based on (Clarkson and Woodruff 2013). This matrix is constructed as \Phi=BD\in \mathbb{R}^{m\times p}, where B is a (p\times p) binary matrix, where for each column j an index is uniformly sampled from \{1,\ldots,m\} and the corresponding entry is set to one, and D is a (p\times p) diagonal matrix, with entries d_j \sim \text{Unif}(\{-1, 1\}). If specified as rp_cw(data = TRUE), the random elements on the diagonal are replaced by the ridge coefficients with a small penalty, as introduced in (Parzer et al. 2024).

Value

object of class 'randomprojection' which is a list with elements name, generate_fun, update_fun, control

References

Clarkson KL, Woodruff DP (2013). “Low Rank Approximation and Regression in Input Sparsity Time.” In Proceedings of the Forty-Fifth Annual ACM Symposium on Theory of Computing, STOC '13, 81–90. ISBN 9781450320290, doi:10.1145/2488608.2488620.

Parzer R, Filzmoser P, Vana-Gür L (2024). “Data-Driven Random Projection and Screening for High-Dimensional Generalized Linear Models.” Technical Report 2410.00971, arXiv.org E-Print Archive. doi:10.48550/arXiv.2410.00971..

Examples

example_data <- simulate_spareg_data(n = 200, p = 2000, ntest = 100)
spar_res <- spar(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10, 15, 20, 25, 30),
  rp = rp_cw(data = TRUE))


[Package spareg version 1.0.0 Index]