The hardware and bandwidth for this mirror is donated by METANET, the Webhosting and Full Service-Cloud Provider.
If you wish to report a bug, or if you are interested in having us mirror your free-software or open-source project, please feel free to contact us at mirror[@]metanet.ch.

Canonical Dependence Simulations

Eric Bridgeford

2020-06-22

require(mgc)
require(ggplot2)
n=400
d=1

plot_sim <- function(X, Y, name) {
  if (!is.null(dim(Y))) {
    Y <- Y[, 1]
  }
  data <- data.frame(x1=X[,1], y=Y)
  ggplot(data, aes(x=x1, y=y)) +
    geom_point() +
    xlab("x") +
    ylab("y") +
    ggtitle(name) +
    theme_bw()
}

plot_sim_func <- function(X, Y, Xf, Yf, name, geom='line') {
  if (!is.null(dim(Y))) {
    Y <- Y[, 1]
    Yf <- Yf[, 1]
  }
  if (geom == 'points') {
    funcgeom <- geom_point
  } else {
    funcgeom <- geom_line
  }
  data <- data.frame(x1=X[,1], y=Y)
  data_func <- data.frame(x1=Xf[,1], y=Yf)
  ggplot(data, aes(x=x1, y=y)) +
    funcgeom(data=data_func, aes(x=x1, y=y), color='red', size=3) +
    geom_point() +
    xlab("x") +
    ylab("y") +
    ggtitle(name) +
    theme_bw()
}

In this notebook, we will review the simulation algorithms provided in the mgc paper. All simulations will be n=400 examples in d=1 dimensions, since some of the plots do not look obviously of the given simulation type in higher dimensions. The simulation is plotted along with the true distribution of the given simulation where possible.

Linear

data <- mgc.sims.linear(n, d)
X <- data$X; Y <- data$Y
func <- mgc.sims.linear(n, d, eps=0)
Xf <- func$X; Yf <- func$Y
plot_sim_func(X, Y, Xf, Yf, "Linear Simulation")

Exponential

data <- mgc.sims.exp(n, d)
X <- data$X; Y <- data$Y
func <- mgc.sims.exp(n, d, eps=0)
Xf <- func$X; Yf <- func$Y
plot_sim_func(X, Y, Xf, Yf, "Exponential Simulation")

Cubic

data <- mgc.sims.cubic(n, d)
X <- data$X; Y <- data$Y
func <- mgc.sims.cubic(n, d, eps=0)
Xf <- func$X; Yf <- func$Y
plot_sim_func(X, Y, Xf, Yf, "Cubic Simulation")

Joint-Normal

data <- mgc.sims.joint(n, d)
X <- data$X; Y <- data$Y
plot_sim(X, Y, "Joint-Normal Simulation")

# Step

data <- mgc.sims.step(n, d)
X <- data$X; Y <- data$Y
func <- mgc.sims.step(n, d, eps=0)
Xf <- func$X; Yf <- func$Y
plot_sim_func(X, Y, Xf, Yf, "Step-Fn Simulation")

Quadratic

data <- mgc.sims.quad(n, d)
X <- data$X; Y <- data$Y
func <- mgc.sims.quad(n, d, eps=0)
Xf <- func$X; Yf <- func$Y
plot_sim_func(X, Y, Xf, Yf, "Quadratic Simulation")

W-Shape

data <- mgc.sims.wshape(n, d)
X <- data$X; Y <- data$Y
func <- mgc.sims.wshape(n, d, eps=0)
Xf <- func$X; Yf <- func$Y
plot_sim_func(X, Y, Xf, Yf, "W Simulation")

Spiral

data <- mgc.sims.spiral(n, d)
X <- data$X; Y <- data$Y
func <- mgc.sims.spiral(n=1000, d, eps=0)
Xf <- func$X; Yf <- func$Y
plot_sim_func(X, Y, Xf, Yf, "Spiral Simulation", geom='points')

Uncorrelated Bernoulli

data <- mgc.sims.ubern(n, d)
X <- data$X; Y <- data$Y
plot_sim(X, Y, "Uncorrelated Bernoulli Simulation")

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.