Distance-based credal set

An ArrayDistanceBasedCredalSet contains every distribution whose total-variation distance to a nominal distribution is at most a given radius. The larger the radius, the wider the uncertainty around the nominal.

This representation is useful when you have a best-guess distribution but want to account for a bounded amount of model mis-specification.

from __future__ import annotations

import matplotlib.pyplot as plt
import numpy as np

from probly.plot import plot_credal_set
from probly.representation.credal_set.array import ArrayDistanceBasedCredalSet

# 2 instances over 3 classes, with a shared radius.
distance_based = ArrayDistanceBasedCredalSet(
    nominal=np.array(
        [
            [0.5, 0.3, 0.2],
            [0.2, 0.6, 0.2],
        ]
    ),
    radius=np.array([0.1, 0.1]),
)

print("Shape (batch dims):", distance_based.shape)
print("Nominal:\n", distance_based.nominal)
print("Radius:", distance_based.radius)
print("Lower envelope (max(0, nominal - r)):\n", distance_based.lower())
print("Upper envelope (min(1, nominal + r)):\n", distance_based.upper())

Shape (batch dims): (2,)
Nominal:
 ArrayCategoricalDistribution(unnormalized_probabilities=array([[0.5, 0.3, 0.2],
       [0.2, 0.6, 0.2]]))
Radius: [0.1 0.1]
Lower envelope (max(0, nominal - r)):
 [[0.4 0.2 0.1]
 [0.1 0.5 0.1]]
Upper envelope (min(1, nominal + r)):
 [[0.6 0.4 0.3]
 [0.3 0.7 0.3]]

On the simplex the feasible region is shown as a filled polygon around the nominal (marked with a dot).

plot_credal_set(distance_based, title="Distance-based credal set")
plt.show()