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, ref_position = length(p), ref_value = 0)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)
- ref_position
The reference position that should be used to calculate the inverse softmax function. The default is the last position.
- ref_value
The value the reference position will be set to. The default is 0.
Details
The softmax function is a bijective function that maps a real vector with length m 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:
$$\Large P(\eta_i) = \frac{e^{\lambda \eta_i}}{\sum_{j=1}^m e^{\lambda \eta_j}}$$