to_uniform_scale {kldest}

Transform samples to uniform scale

Description

Since Kullback-Leibler divergence is scale-invariant, its sample-based approximations can be computed on a conveniently chosen scale. This helper functions transforms each variable in a way that all marginal distributions of the joint dataset (X,Y) are uniform. In this way, the scales of different variables are rendered comparable, with the idea of a better performance of neighbour-based methods in this situation.

Usage

to_uniform_scale(X, Y)

Arguments

X, Y

n-by-d and m-by-d matrices, representing n samples from the true distribution P and m samples from the approximate distribution Q, both in d dimensions. Vector input is treated as a column matrix. Y can be left blank if q is specified (see below).

Value

A list with fields X and Y, containing the transformed samples.

Examples

# 2D example
n <- 10L
X <- cbind(rnorm(n, mean = 0, sd = 3),
           rnorm(n, mean = 1, sd = 2))
Y <- cbind(rnorm(n, mean = 1, sd = 2),
           rnorm(n, mean = 0, sd = 2))
to_uniform_scale(X, Y)