Statisfaction

Moustache target distribution and Wes Anderson

Posted in Art, Geek, R by Pierre Jacob on 31 March 2014

Today I am going to introduce the moustache target distribution (moustarget distribution for brievety). Load some packages first.

library(wesanderson) # on CRAN
library(RShapeTarget) # available on https://github.com/pierrejacob/RShapeTarget/
library(PAWL) # on CRAN

Let’s invoke the moustarget distribution.

 shape <- create_target_from_shape(
file_name=system.file(package = "RShapeTarget", "extdata/moustache.svg"),
lambda=5)
rinit <- function(size) matrix(rnorm(2*size), ncol = 2)
moustarget <- target(name = "moustache", dimension = 2,
rinit = rinit, logdensity = shape$logd,
parameters = shape$algo_parameters)

This defines a target distribution represented by a SVG file using RShapeTarget. The target probability density function is defined on \mathbb{R}^2 and is proportional to 1 on the segments described in the SVG files, and decreases exponentially fast to 0 away from the segments. The density function of the moustarget is plotted below, a picture being worth a thousand words.

Joint work with the Department of Facial Hair

Moustarget distribution, joint work with the Department of Facial Hair

ranges <- apply(shape$bounding_box, 2, range)
gridx <- seq(from=ranges[1,1], to=ranges[2,1], length.out=300)
gridy <- seq(from=ranges[1,2], to=ranges[2,2], length.out=300)
grid.df <- expand.grid(gridx, gridy)
grid.df$logdensity <- 
moustarget@logdensity(cbind(grid.df$Var1, grid.df$Var2), moustarget@parameters)
names(grid.df) <- c("x", "y", "z")
g2d <- ggplot(grid.df) + geom_raster(aes(x=x, y=y, fill=exp(z))) + 
xlab("X") + ylab("Y")
g2d <- g2d + xlim(ranges[,1]) + ylim(ranges[,2])
pal <- wes.palette(name = "GrandBudapest", type = "continuous")
g2d <- g2d + scale_fill_gradientn(name = "density", colours = pal(50))
g2d <- g2d + 
theme(legend.position = "bottom", legend.text = element_text(size = 10))
g2d

There are various interesting aspects to note about this distribution. First it is very multi-modal and strongly non-Gaussian, thus providing an interesting toy problem for testing MCMC algorithms. Furthermore, sampling from the moustarget can be made arbitrarily difficult by pulling the moustache down, thus separating the moustache mode from the remaining probability mass around the eyes, ears and hat. Finally, note that the colours chosen to represent the density above approximately match the principal colours used in Grand Budapest Hotel by Wes Anderson. This is thanks to the awesome wesanderson package on CRAN. Obviously it is now very tempting to launch the Wang-Landau algorithm on this target with a spatial binning strategy, in order to try out the various palettes provided in wesanderson.

mhparameters <- tuningparameters(nchains = 10, 
niterations = 10000, storeall = TRUE)
getPos <- function(points, logdensity) points[,2]
explore_range <- c(-700,0)
ncuts <- 20
positionbinning <- binning(position = getPos, name = "position",
 binrange = explore_range,
 ncuts = ncuts, useLearningRate = TRUE, autobinning = FALSE)
pawlresults <- pawl(target = moustarget, binning = positionbinning, 
 AP = mhparameters, verbose = TRUE)
pawlchains <- ConvertResults(pawlresults, verbose = FALSE)
locations <- positionbinning@getLocations(pawlresults$finalbins, pawlchains$X2)
pawlchains$locations <- factor(locations)
g <- ggplot(subset(pawlchains), 
aes(x=X1, y = X2, alpha = exp(logdens), 
size = exp(logdens), colour = locations)) +
 geom_point() + theme(legend.position="none") + xlab("X") + ylab("Y")
g <- g + geom_hline(yintercept = pawlresults$finalbins)
pal <- wes.palette(name = "GrandBudapest", type = "continuous")
print(g + scale_color_manual(values = pal(21)) + 
labs(title = "Moustarget in Grand Budapest colours"))
pal <- wes.palette(name = "Darjeeling", type = "continuous")
print(g + scale_color_manual(values = pal(21)) + 
labs(title = "Moustarget in Darjeeling colours"))
pal <- wes.palette(name = "Zissou", type = "continuous")
print(g + scale_color_manual(values = pal(21)) + 
labs(title = "Moustarget in Zissou colours"))

sample_LA sample_GB sample_DJ

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3 Responses

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  1. […] article was first published on Statisfaction » R, and kindly contributed to […]

  2. xi'an said, on 12 May 2014 at 20:29

    c’était en préparation de l’Eurovision???

    • Pierre Jacob said, on 13 May 2014 at 11:44

      Haha oui apparemment la delegation francaise suit Statisfaction.


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