mgc.sims.exp {mgc}

Exponential Simulation

Description

A function for Generating an exponential simulation.

Usage

mgc.sims.exp(n, d, eps = 10, ind = FALSE, a = 0, b = 3)

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 10.

ind

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

a

the lower limit for the range of the data matrix. Defaults to 0.

b

the upper limit for the range of the data matrix. Defaults to 3.

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 = e^{w^TX} + \kappa \epsilon

and \kappa = 1\textrm{ if }d = 1, \textrm{ and 0 otherwise} controls the noise for higher dimensions.

Author(s)

Eric Bridgeford

Examples

library(mgc)
result  <- mgc.sims.exp(n=100, d=10)  # simulate 100 samples in 10 dimensions
X <- result$X; Y <- result$Y