I have a 4 indexes {1,2,3,4} and I want to associate a probability of co-occurrence for index 1 and index 2 as 0.8 and probability of co-occurrence of index 3 and 4 as 0.7 and probability of co-occurrence of index 1 and 3 as 0.1 and probability of co-occurrence of index 2 and 4 as 0.1.
How can I sample 100 instances such that I get tuples of indexes distributed according to the above density ?
How about this?
>>> indices = np.transpose(np.triu_indices(4)) + 1
>>> probs = np.array([0.0, 0.8, 0.1, 0.1, 0.0, 0.1, 0.1, 0.1, 0.7, 0.1])
>>> pairs = indices[np.random.choice(np.arange(10), 1000000, p=probs/probs.sum())]
Note that I created a few more pairs in order to get better statistics:
>>> np.mean((pairs[(pairs == 1).any(1)] == 2).any(1))
0.8011017893563784
>>> np.mean((pairs[(pairs == 3).any(1)] == 4).any(1))
0.7013376446633661
>>> np.mean((pairs[(pairs == 1).any(1)] == 3).any(1))
0.09918417123993356
>>> np.mean((pairs[(pairs == 2).any(1)] == 4).any(1))
0.09942011933775947
