Convex credal set

An ArrayConvexCredalSet is defined by the convex hull of a set of vertex distributions. Every distribution that can be written as a convex combination of the vertices is considered a member of the set.

This is a common representation in imprecise-probability theory: the vertices are the extreme points of a credal polytope, and the full set is their convex closure.

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 ArrayConvexCredalSet

# 2 instances, each defined by 3 vertex distributions over 3 classes.
# Shape: (instances, vertices, classes) = (2, 3, 3)
convex = ArrayConvexCredalSet(
    array=np.array(
        [
            [[0.7, 0.2, 0.1], [0.1, 0.7, 0.2], [0.1, 0.1, 0.8]],
            [[0.4, 0.4, 0.2], [0.2, 0.2, 0.6], [0.3, 0.1, 0.6]],
        ]
    ),
)

print("Shape (batch dims):", convex.shape)
print("Lower envelope (vertex-wise min):\n", convex.lower())
print("Upper envelope (vertex-wise max):\n", convex.upper())

Shape (batch dims): (2,)
Lower envelope (vertex-wise min):
 [[0.1 0.1 0.1]
 [0.2 0.1 0.2]]
Upper envelope (vertex-wise max):
 [[0.7 0.7 0.8]
 [0.4 0.4 0.6]]

On the simplex the convex hull of the vertices is drawn as a filled polygon.

plot_credal_set(convex, title="Convex credal set")
plt.show()