def test_4d_gaussian(self) -> None:
rng = np.random.default_rng(3)
cov = np.array([[1.0, 0.5, 0.6, -0.2], [0.5, 1.0, 0.7, -0.5],
[0.6, 0.7, 2.0, -0.1], [-0.2, -0.5, -0.1, 0.5]])
data = rng.multivariate_normal([0, 0, 0, 0], cov, size=2000)
actual = _estimate_single_entropy(data, k=3)
expected = 0.5 * log(np.linalg.det(2 * math.pi * math.e * cov))
self.assertAlmostEqual(actual, expected, delta=0.05)
def test_gamma_exponential(self) -> None:
# As in the MI test, the analytical result is due to doi:10.1109/18.825848.
#
# x1 ~ Gamma(rate, shape)
# x2 | x1 ~ Exp(t * x1)
rng = np.random.default_rng(4)
r = 1.2
s = 3.4
t = 0.56
x1 = rng.gamma(shape=s, scale=1 / r, size=1000)
x2 = rng.exponential(x1 * t)
data = np.asarray([x1, x2]).T
raw = _estimate_single_entropy(data)
trans = _estimate_single_entropy(np.log(data))
# The estimate with unlogarithmed data is very bad
expected = 1 + s - s * psi(s) + log(gamma(s)) - log(t)
self.assertAlmostEqual(raw, expected, delta=0.65)
self.assertAlmostEqual(trans, expected, delta=0.01)
def test_uniform(self) -> None:
cases = [ (0, 1, 1000, 3, 0.05),
(1, 2, 1000, 3, 0.05),
(-1, 1, 1000, 3, 0.05),
(-0.1, 0.1, 1000, 3, 0.05), ]
for (a, b, n, k, delta) in cases:
with self.subTest(a=a, b=b, n=n, k=k):
rng = np.random.default_rng(1)
x = rng.uniform(a, b, size=n)
actual = _estimate_single_entropy(x, k=k)
expected = log(b - a)
self.assertAlmostEqual(actual, expected, delta=delta)
def test_univariate_gaussian(self) -> None:
cases = [ (1, 100, 2, 0.2),
(1, 200, 3, 0.05),
(1, 2000, 3, 0.02),
(0.5, 2000, 3, 0.02),
(2.0, 2000, 1, 0.002),
(2.0, 2000, 3, 0.02),
(2.0, 2000, 30, 0.02), ]
for (sd, n, k, delta) in cases:
with self.subTest(sd=sd, n=n, k=k):
rng = np.random.default_rng(0)
x = rng.normal(0, sd, size=n)
actual = _estimate_single_entropy(x, k=k)
expected = 0.5 * log(2 * math.pi * math.e * sd**2)
self.assertAlmostEqual(actual, expected, delta=delta)
def test_bivariate_gaussian(self) -> None:
cases = [ (0, 1, 200, 3, 0.09),
(0, 2, 2000, 3, 0.03),
(0.2, 1, 2000, 3, 0.03),
(0.2, 2, 2000, 5, 0.03),
(0.6, 1, 2000, 1, 0.02),
(0.6, 0.5, 2000, 3, 0.04),
(0.9, 1, 2000, 3, 0.04),
(-0.5, 1, 2000, 5, 0.03), ]
for (rho, var1, n, k, delta) in cases:
with self.subTest(rho=rho, var1=var1, n=n, k=k):
rng = np.random.default_rng(2)
cov = np.array([[var1, rho], [rho, 1]])
data = rng.multivariate_normal([0, 0], cov, size=n)
actual = _estimate_single_entropy(data, k=k)
expected = 0.5 * log(np.linalg.det(2 * math.pi * math.e * cov))
self.assertAlmostEqual(actual, expected, delta=delta)