import numpy as np
from scipy.special import softmax
from scipy.stats import poisson
[docs]
def get_poisson_soft_labels(J):
"""Get soft labels using poisson distributions for ``J`` classes or splits using the
methodology described in :footcite:t:`liu2020unimodal`.
The :math:`[0,1]` interval is split into ``J`` intervals and the probability for
each interval is computed as the difference between the value of the poisson
probability function for the interval boundaries. The probability for the first
interval is computed as the value of the poisson probability function for the first
interval boundary. Then, a softmax function is applied to each row of the resulting
matrix to obtain valid probabilities.
The poisson probability function is denoted as :math:`\\text{p}(k, \\lambda)`
where :math:`k` is given by the order of the class for which the probability is
computed, and :math:`\\lambda` is given by :math:`k` where :math:`k` is the order
of the target class.
Parameters
----------
J : int
Number of classes or splits.
Raises
------
ValueError
If ``J`` is not a positive integer greater than 1.
Returns
-------
probs : 2d array-like of shape (J, J)
Matrix of probabilities where each row represents the true class
and each column the probability for class j.
Example
-------
>>> from dlordinal.soft_labelling import get_poisson_soft_labels
>>> get_poisson_soft_labels(5)
array([[0.23414552, 0.23414552, 0.19480578, 0.17232403, 0.16457916],
[0.18896888, 0.21635436, 0.21635436, 0.19768881, 0.18063359],
[0.17822335, 0.19688341, 0.21214973, 0.21214973, 0.20059378],
[0.17919028, 0.18931175, 0.20370191, 0.21389803, 0.21389803],
[0.18400408, 0.18903075, 0.19882883, 0.21031236, 0.21782399]])
"""
if J < 2 or not isinstance(J, int):
raise ValueError(f"{J=} must be a positive integer greater than 1")
probs = []
for true_class in range(1, J + 1):
probs.append(poisson.pmf(np.arange(0, J), true_class))
return softmax(np.array(probs), axis=1)