Description Usage Arguments Value Author(s) Examples
Transformations applied to each marginal component sample to map given data to a different range.
1 2  range_trafo(x, lower, upper, inverse = FALSE)
logis_trafo(x, mean = 0, sd = 1, slope = 1, intercept = 0, inverse = FALSE)

x 
(n, d)matrix of data (typically before training or after sampling). 
lower 
value or dvector typically
containing the smallest value of each column of 
upper 
value or dvector typically
containing the largest value of each column of 
mean 
value or dvector. 
sd 
value or dvector. 
slope 
value or dvector of slopes
of the linear transformations applied after applying

intercept 
value or dvector of intercepts
of the linear transformations applied after applying

inverse 

An object as x
containing the componentwise transformed data.
Marius Hofert
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69  ## Generate data
n < 100
set.seed(271)
x < cbind(rnorm(n), (1runif(n))^(1/2)1) # normal and Pareto(2) margins
plot(x)
## Range transformation
ran < apply(x, 2, range) # column j = range of the jth column of x
x.ran < range_trafo(x, lower = ran[1,], upper = ran[2,]) # marginally transform to [0,1]
plot(x.ran) # => now range [0,1] but points a bit clustered around small yvalues
x. < range_trafo(x.ran, lower = ran[1,], upper = ran[2,], inverse = TRUE) # transform back
stopifnot(all.equal(x., x)) # check
## Logistic transformation
x.logis < logis_trafo(x) # marginally transform to [0,1] via plogis()
plot(x.logis) # => yrange is [1/2, 1] which can be harder to train
x. < logis_trafo(x.logis, inverse = TRUE) # transform back
stopifnot(all.equal(x., x)) # check
## Logistic transformation with scaling to all of [0,1] in the second coordinate
x.logis.scale < logis_trafo(x, slope = 2, intercept = 1)
plot(x.logis.scale) # => now yrange is scaled to [0,1]
x. < logis_trafo(x.logis.scale, slope = 2, intercept = 1, inverse = TRUE) # transform back
stopifnot(all.equal(x., x)) # check
## Logistic transformation with sample mean and standard deviation and then
## transforming the range to [0,1] with a range transformation (note that
## slope = 2, intercept = 1 would not help here as the yrange is not [1/2, 1])
mu < colMeans(x)
sig < apply(x, 2, sd)
x.logis.fit < logis_trafo(x, mean = mu, sd = sig) # marginally plogis(, location, scale)
plot(x.logis.fit) # => yrange is not [1/2, 1] => use range transformation
ran < apply(x.logis.fit, 2, range)
x.logis.fit.ran < range_trafo(x.logis.fit, lower = ran[1,], upper = ran[2,])
plot(x.logis.fit.ran) # => now yrange is [1/2, 1]
x. < logis_trafo(range_trafo(x.logis.fit.ran, lower = ran[1,], upper = ran[2,],
inverse = TRUE),
mean = mu, sd = sig, inverse = TRUE) # transform back
stopifnot(all.equal(x., x)) # check
## Note that for heavytailed data, plogis() can fail to stay inside (0,1)
## even with adapting to sample mean and standard deviation. We now present
## a case where we see that using a fitted logistic distribution function
## is *just* good enough to numerically keep the data inside (0,1).
set.seed(271)
x < cbind(rnorm(n), (1runif(n))^(2)1) # normal and Pareto(1/2) margins
plot(x) # => heavytailed in ycoordinate
## Transforming with standard logistic distribution function
x.logis < logis_trafo(x)
stopifnot(any(x.logis[,2] == 1))
## => There is value numerically indistinguishable from 1 to which applying
## the inverse transform will lead to Inf
stopifnot(any(is.infinite(logis_trafo(x.logis, inverse = TRUE))))
## Now adapt the logistic distribution to share the mean and standard deviation
## with the data
mu < colMeans(x)
sig < apply(x, 2, sd)
x.logis.scale < logis_trafo(x, mean = mu, sd = sig)
stopifnot(all(x.logis.scale[,2] != 1)) # => no values equal to 1 anymore
## Alternatively, log() the data first, thus working with a loglogistic
## distribution as transformation
lx < cbind(x[,1], log(x[,2])) # 2nd coordinate only
lmu < c(mu[1], mean(lx[,2]))
lsig < c(sig[1], sd(lx[,2]))
x.llogis < logis_trafo(lx, mean = lmu, sd = lsig)
x. < logis_trafo(x.llogis, mean = lmu, sd = lsig, inverse = TRUE)
x.. < cbind(x.[,1], exp(x.[,2])) # undo log()
stopifnot(all.equal(x.., x))

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