mgc (version 2.0.2)

mgc.sims.linear: Linear Simulation

Description

A function for Generating a linear simulation.

Usage

mgc.sims.linear(n, d, eps = 1, ind = FALSE, a = -1, b = 1)

Arguments

n

the number of samples for the simulation.

d

the number of dimensions for the simulation setting.

eps

the noise level for the simulation. Defaults to 1.

ind

whether to sample x and y independently. Defaults to FALSE.

a

the lower limit for the range of the data matrix. Defaults to -1.

b

the upper limit for the range of the data matrix. Defaults to 1.

Value

a list containing the following:

X

[n, d] the data matrix with n samples in d dimensions.

Y

[n] the response array.

Details

Given: \(w_i = \frac{1}{i}\) is a weight-vector that scales with the dimensionality. Simulates \(n\) points from \(Linear(X, Y) \in \mathbf{R}^d \times \mathbf{R}\), where: $$X \sim {U}(a, b)^d$$ $$Y = w^TX + \kappa \epsilon$$ and \(\kappa = 1\textrm{ if }d = 1, \textrm{ and 0 otherwise}\) controls the noise for higher dimensions.

Examples

# NOT RUN {
library(mgc)
result  <- mgc.sims.linear(n=100, d=10)  # simulate 100 samples in 10 dimensions
X <- result$X; Y <- result$Y
# }