require(mgc)
require(ggplot2)
n=400
d=1plot_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.
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")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")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")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")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")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")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')