softmax function

Softmax transform

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.

softmax(x)

inv_softmax(p)

Arguments

• x: $K-1$ vector of reals
• p: $K$ vector simplex

Returns

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))
sum(p)
inv_softmax(p)