generalize.py

from itertools import chain, combinations

def powerset(iterable):
  xs = list(iterable)
  return chain.from_iterable( combinations(xs,n) for n in range(len(xs)+1) )

# Features are binary. An item either has or does not have every feature.
features = 'abcde'

hypotheses_sets = {
    'multiple features': list(powerset(features)),
    'single feature': list(features),
}

# Without loss of generality, the target item is assumed
# to be have all features. We consider one item
# for each possible number of shared features. The item is
# represented as a string of features the item has.
items = [features[:i] for i in range(len(features)+1)]

def compatible(hypothesis, x):
    return all(feature in x for feature in hypothesis)


for name, hypotheses in hypotheses_sets.items():
    print('\n----- {} -----'.format(name))
    print('shared features    p(generalize)')
    for item in items:
        num_compatible = sum(1 for h in hypotheses if compatible(h, item))
        p_gen = num_compatible / len(hypotheses)
        print(len(item), '                ', p_gen)

"""
Output:

----- single feature -----
shared features    p(generalize)
0                  0.0
1                  0.2
2                  0.4
3                  0.6
4                  0.8
5                  1.0

----- multiple features -----
shared features    p(generalize)
0                  0.03125
1                  0.0625
2                  0.125
3                  0.25
4                  0.5
5                  1.0

"""