def test_pinskers_inequality(dist1, dist2):
"""
DKL(p||q) >= V(p||q)**2 / (2log(2))
"""
dkl = relative_entropy(dist1, dist2)
vd = variational_distance(dist1, dist2)
assert dkl >= vd**2 / (2 * np.log(2)) - epsilon
def test_pinskers_inequality(dist1, dist2):
"""
DKL(p||q) >= V(p||q)**2 / (2log(2))
"""
dkl = relative_entropy(dist1, dist2)
vd = variational_distance(dist1, dist2)
assert dkl >= vd**2 / (2 * np.log(2)) - epsilon
def test_hellinger_variational(dist1, dist2):
"""
H^2(p||q) <= V(p||q) <= sqrt(2)*H(p||q)
"""
h = hellinger_distance(dist1, dist2)
v = variational_distance(dist1, dist2)
assert h**2 <= v + epsilon
assert v <= np.sqrt(2) * h + epsilon
def test_hellinger_variational(dist1, dist2):
"""
H^2(p||q) <= V(p||q) <= sqrt(2)*H(p||q)
"""
h = hellinger_distance(dist1, dist2)
v = variational_distance(dist1, dist2)
assert h**2 <= v + epsilon
assert v <= np.sqrt(2)*h + epsilon
def test_vd2():
"""
Test against known value
"""
d1 = Distribution(['0', '1'], [1 / 2, 1 / 2])
d2 = Distribution(['1', '2'], [1 / 4, 3 / 4])
v = variational_distance(d1, d2)
assert v == pytest.approx(0.75)
def test_vd2():
"""
Test against known value.
"""
vd = variational_distance(d1, d3)
assert vd == pytest.approx(0.75)
def test_vd2():
"""
Test against known value.
"""
vd = variational_distance(d1, d3)
assert vd == pytest.approx(0.75)
