softmax {bmm}

Softmax and logsoftmax functions and their inverse functions

Description

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)

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

Value

Value of the softmax function or its inverse

Examples

softmax(5:7)
softmaxinv(softmax(5:7))