The softmax transform is a multivariate generalisation of the logit
transform. softmax() maps a vector of \(K-1\) values on the real line to a
\(K\)-simplex (i.e. values between 0 and 1, that sum to 1). inv_softmax()
provides the inverse transform, mapping a \(K\)-simplex vector to a vector of
\(K-1\) real values.
Usage
softmax(x)
inv_softmax(p)
Arguments
- x
\(K-1\) vector of reals
- p
\(K\) vector simplex
Value
softmax() returns a vector of length \(K\) that is a simplex.
inv_softmax() returns a vector of reals of length \(K-1\).
Examples
x <- c(-1, 3, -0.5, 2)
(p <- softmax(x))
#> [1] 0.03395701 0.01249208 0.68204471 0.02059597 0.25091023
sum(p)
#> [1] 1
inv_softmax(p)
#> [1] -1.0 3.0 -0.5 2.0
