Softmax and logsoftmax functions and their inverse functions

softmax returns the value of the softmax function softmaxinv returns the value of the inverse-softmax function

Usage

softmax(eta, lambda = 1)

softmaxinv(p, lambda = 1)

Arguments

eta

A numeric vector input

lambda

Tuning parameter (a single positive value)

p

A probability vector (i.e., numeric vector of non-negative values that sum to one)

Value

Value of the softmax function or its inverse

Details

The softmax function is a bijective function that maps a real vector with length m-1 to a probability vector with length m with all non-zero probabilities. The present functions define the softmax function and its inverse, both with a tuning parameter.

The current functions define the softmax as:

$$\Large P(\eta_i) = \frac{e^{\lambda \eta_i}}{1+ \sum_{j=1}^m e^{\lambda \eta_j}}$$

Code adapted from the utilities package

Examples

softmax(5:7)
#> [1] 0.0899759918 0.2445801036 0.6648376511 0.0006062535
softmaxinv(softmax(5:7))
#> [1] 5 6 7