def test_empty_arrays(self):
"""Check that computing the IB on a pair of empty arrays raises an exception"""
for alpha in self.alphas:
with self.subTest(alpha=alpha):
with self.assertRaises(
ValueError,
msg="If pxy is not specified, x and y can't be empty."):
eb = embo.InformationBottleneck(self.empty, self.empty, alpha=alpha)
def test_array_with_inf(self):
"""Check that an error is raised in presence of infinities"""
for alpha in self.alphas:
with self.subTest(alpha=alpha):
with self.assertRaises(
ValueError,
msg="The observation data contains NaNs or Infs."):
embo.InformationBottleneck(self.x_with_inf, self.y, alpha=alpha)
def test_asymptote(x, y, maxbeta=30, alpha=1):
"""Check that the IB/DIB bound saturates at MI(X:Y) for large beta.
This should be true with the default setting that the cardinality
of M is the same as that of X.
Note that the reference value of MI(X,Y) is computed using embo's
internal facility for this.
"""
eb = embo.InformationBottleneck(x, y, maxbeta=maxbeta, alpha=alpha)
i_y = eb.get_iy()
mi = eb.get_saturation_point()
np.testing.assert_allclose(i_y[-1], mi, rtol=1e-7, atol=1e-6)
def test_random_distributions(self):
"""Run IB/DIB on many random distributions of various shapes and check β→∞ limit"""
for X in range(2, self.Xmax):
for Y in range(2, self.Ymax):
for alpha in self.alphas:
with self.subTest(X=X, Y=Y, alpha=alpha):
for each in range(self.N):
#pxy = self.rng.dirichlet(np.full(X*Y,1/2)).reshape(X,Y)
pxy = self.sample_pxy(X,Y)
eb = embo.InformationBottleneck(pxy=pxy, maxbeta=20, numbeta=5, alpha=alpha, restarts=10, rtol=1e-5, iterations=1000, ensure_monotonic_bound=False)
ix, iy, hm, _, ixy, hx, hy = eb.get_bottleneck(return_entropies=True)
self.assertTrue(
# note the relatively large
# tolerances: they help ignoring
# uninteresting cases where I(X:Y) is
# very small
np.testing.assert_allclose(iy[-1], ixy, rtol=1e-1, atol=1e-1) is None,
msg='Check asymptote')
def test_origin(x, y, alpha=1):
"""Check that the IB bound starts at (0,0) for small beta"""
eb = embo.InformationBottleneck(x, y, alpha=alpha)
i_x = eb.get_ix()
i_y = eb.get_iy()
np.testing.assert_allclose((i_x[0], i_y[0]), (0,0), rtol=1e-7, atol=1e-6)