def test_mvnormal(self):
"""Compare the results to the figure 2 in the paper."""
from numpy.random import multivariate_normal, normal
n = 30000
p = normal(0, 1, size=(n, 2))
np.random.seed(1)
q = multivariate_normal([0.5, -0.5], [[0.5, 0.1], [0.1, 0.3]], size=n)
assert_almost_equal(xca.kldiv(p, q), 1.39, 1)
assert_almost_equal(xca.kldiv(q, p), 0.62, 1)
def accuracy_vs_kth(self, n=100, trials=100):
"""Evalute the accuracy of the algorithm as a function of k.
Parameters
----------
N : int
Number of random samples.
trials : int
Number of independent drawing experiments.
Returns
-------
(err, stddev) The mean error and standard deviation around the
analytical value for different values of k from 1 to 15.
"""
p = stats.norm(0, 1)
q = stats.norm(0.2, 0.9)
k = np.arange(1, 16)
out = []
for i in range(trials):
out.append(xca.kldiv(p.rvs(n), q.rvs(n), k=k))
out = np.array(out)
# Compare with analytical value
err = out - analytical_KLDiv(p, q)
# Return mean and standard deviation
return err.mean(0), err.std(0)
def test_different_sample_size(self):
p = stats.norm(2, 1)
q = stats.norm(2.6, 1.4)
ra = analytical_KLDiv(p, q)
n = 6000
# Same sample size for x and y
re = [xca.kldiv(p.rvs(n), q.rvs(n)) for i in range(30)]
assert_almost_equal(np.mean(re), ra, 2)
# Different sample sizes
re = [xca.kldiv(p.rvs(n * 2), q.rvs(n)) for i in range(30)]
assert_almost_equal(np.mean(re), ra, 2)
re = [xca.kldiv(p.rvs(n), q.rvs(n * 2)) for i in range(30)]
assert_almost_equal(np.mean(re), ra, 2)
def test_against_analytic(self):
p = stats.norm(2, 1)
q = stats.norm(2.6, 1.4)
ra = analytical_KLDiv(p, q)
N = 10000
np.random.seed(2)
# x, y = p.rvs(N), q.rvs(N)
re = xca.kldiv(p.rvs(N), q.rvs(N))
assert_almost_equal(re, ra, 1)