Kullback-Leibler Divergence
Estimate the Kullback-Leibler divergence of several distributions.
## S4 method for signature 'matrix'
KLdiv(object, eps = 10^-4, overlap = TRUE,...)
## S4 method for signature 'flexmix'
KLdiv(object, method = c("continuous", "discrete"), ...)object |
See Methods section below. |
method |
The method to be used; "continuous" determines the Kullback-Leibler divergence between the unweighted theoretical component distributions and the unweighted posterior probabilities at the observed points are used by "discrete". |
eps |
Probabilities below this threshold are replaced by this threshold for numerical stability. |
overlap |
Logical, do not determine the KL divergence for
those pairs where for each point at least one of the densities has a
value smaller than |
... |
Passed to the matrix method. |
Estimates
\int f(x) (\log f(x) - \log g(x)) dx
for distributions with densities f() and g().
A matrix of KL divergences where the rows correspond to using the respective distribution as f() in the formula above.
Takes as input a matrix of density values with one row per observation and one column per distribution.
Returns the Kullback-Leibler divergence of the mixture components.
The density functions are modified to have equal support.
A weight of at least eps is given to each
observation point for the modified densities.
Friedrich Leisch and Bettina Gruen
S. Kullback and R. A. Leibler. On information and sufficiency.The Annals of Mathematical Statistics, 22(1), 79–86, 1951.
Friedrich Leisch. Exploring the structure of mixture model components. In Jaromir Antoch, editor, Compstat 2004–Proceedings in Computational Statistics, 1405–1412. Physika Verlag, Heidelberg, Germany, 2004. ISBN 3-7908-1554-3.
## Gaussian and Student t are much closer to each other than
## to the uniform:
x <- seq(-3, 3, length = 200)
y <- cbind(u = dunif(x), n = dnorm(x), t = dt(x, df = 10))
matplot(x, y, type = "l")
KLdiv(y)
if (require("mlbench")) {
set.seed(2606)
x <- mlbench.smiley()$x
model1 <- flexmix(x ~ 1, k = 9, model = FLXmclust(diag = FALSE),
control = list(minprior = 0))
plotEll(model1, x)
KLdiv(model1)
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