Numpy has the random.choice function, which allows you to sample from a categorical distribution. How would you repeat this over an axis? To illustrate what I mean, here is my current code:
categorical_distributions = np.array([
[.1, .3, .6],
[.2, .4, .4],
])
_, n = categorical_distributions.shape
np.array([np.random.choice(n, p=row)
for row in categorical_distributions])
Ideally, I would like to eliminate the for loop.
Here's one vectorized way to get the random indices per row, with a as the 2D array of probabilities -
(a.cumsum(1) > np.random.rand(a.shape[0])[:,None]).argmax(1)
Generalizing to cover both along the rows and columns for 2D array -
def random_choice_prob_index(a, axis=1):
r = np.expand_dims(np.random.rand(a.shape[1-axis]), axis=axis)
return (a.cumsum(axis=axis) > r).argmax(axis=axis)
Let's verify with the given sample by running it over a million times -
In [589]: a = np.array([
...: [.1, .3, .6],
...: [.2, .4, .4],
...: ])
In [590]: choices = [random_choice_prob_index(a)[0] for i in range(1000000)]
# This should be close to first row of given sample
In [591]: np.bincount(choices)/float(len(choices))
Out[591]: array([ 0.099781, 0.299436, 0.600783])
Runtime test
Original loopy way -
def loopy_app(categorical_distributions):
m, n = categorical_distributions.shape
out = np.empty(m, dtype=int)
for i,row in enumerate(categorical_distributions):
out[i] = np.random.choice(n, p=row)
return out
Timings on bigger array -
In [593]: a = np.array([
...: [.1, .3, .6],
...: [.2, .4, .4],
...: ])
In [594]: a_big = np.repeat(a,100000,axis=0)
In [595]: %timeit loopy_app(a_big)
1 loop, best of 3: 2.54 s per loop
In [596]: %timeit random_choice_prob_index(a_big)
100 loops, best of 3: 6.44 ms per loop
