def test_divergences_to_kl():
"""
Tests that the generalized divergences properly fall back to KL for the appropriate values of alpha, and not otherwise.
"""
test_dists = [get_dists_2(), get_dists_3()]
for dists in test_dists:
for dist1 in dists:
for dist2 in dists:
assert_almost_equal(alpha_divergence(dist1, dist2, alpha=-1),
kullback_leibler_divergence(dist2, dist1))
if dist1 != dist2:
assert_not_equal(alpha_divergence(dist1, dist2, alpha=0),
kullback_leibler_divergence(dist2, dist1))
for divergence in [
renyi_divergence, tsallis_divergence, alpha_divergence,
hellinger_divergence
]:
assert_almost_equal(
divergence(dist1, dist2, alpha=1),
kullback_leibler_divergence(dist1, dist2))
if dist1 != dist2:
assert_not_equal(
alpha_divergence(dist1, dist2, alpha=0),
kullback_leibler_divergence(dist2, dist1))
assert_not_equal(
alpha_divergence(dist1, dist2, alpha=2),
kullback_leibler_divergence(dist2, dist1))
def test_divergences_to_kl(dists):
"""
Tests that the generalized divergences properly fall back to KL for the appropriate values of alpha, and not otherwise.
"""
for dist1, dist2 in combinations(dists, 2):
assert alpha_divergence(dist1, dist2, alpha=-1) == pytest.approx(kullback_leibler_divergence(dist2, dist1))
assert alpha_divergence(dist1, dist2, alpha=0) != pytest.approx(kullback_leibler_divergence(dist2, dist1))
assert alpha_divergence(dist1, dist2, alpha=2) != pytest.approx(kullback_leibler_divergence(dist2, dist1))
def test_alpha_symmetry(alpha, dists):
"""
Tests the alpha -> -alpha symmetry for the alpha divergence, and a similar
symmetry for the Hellinger and Renyi divergences.
"""
for dist1, dist2 in product(dists, repeat=2):
assert alpha_divergence(dist1, dist2, alpha) == pytest.approx(alpha_divergence(dist2, dist1, -alpha))
assert (1.-alpha)*hellinger_divergence(dist1, dist2, alpha) == pytest.approx(alpha*hellinger_divergence(dist2, dist1, 1.-alpha))
assert (1.-alpha)*renyi_divergence(dist1, dist2, alpha) == pytest.approx(alpha*renyi_divergence(dist2, dist1, 1.-alpha))
def test_alpha_symmetry(alpha, dists):
"""
Tests the alpha -> -alpha symmetry for the alpha divergence, and a similar
symmetry for the Hellinger and Renyi divergences.
"""
for dist1, dist2 in product(dists, repeat=2):
assert alpha_divergence(dist1, dist2, alpha) == pytest.approx(alpha_divergence(dist2, dist1, -alpha))
assert (1.-alpha)*hellinger_divergence(dist1, dist2, alpha) == pytest.approx(alpha*hellinger_divergence(dist2, dist1, 1.-alpha))
assert (1.-alpha)*renyi_divergence(dist1, dist2, alpha) == pytest.approx(alpha*renyi_divergence(dist2, dist1, 1.-alpha))
def test_divergences_to_kl(dists):
"""
Tests that the generalized divergences properly fall back to KL for the appropriate values of alpha, and not otherwise.
"""
for dist1, dist2 in combinations(dists, 2):
assert alpha_divergence(dist1, dist2, alpha=-1) == pytest.approx(kullback_leibler_divergence(dist2, dist1))
assert alpha_divergence(dist1, dist2, alpha=0) != pytest.approx(kullback_leibler_divergence(dist2, dist1))
assert alpha_divergence(dist1, dist2, alpha=2) != pytest.approx(kullback_leibler_divergence(dist2, dist1))
def test_alpha_symmetry():
"""
Tests the alpha -> -alpha symmetry for the alpha divergence, and a similar symmetry for the Hellinger divergence.
"""
alphas = [-1, 0, 0.5, 1, 2]
test_dists = [get_dists_2(), get_dists_3()]
for alpha in alphas:
for dists in test_dists:
for dist1 in dists:
for dist2 in dists:
assert_almost_equal(alpha_divergence(dist1, dist2, alpha), alpha_divergence(dist2, dist1, -alpha))
assert_almost_equal((1.-alpha)*hellinger_divergence(dist1, dist2, alpha), alpha*hellinger_divergence(dist2, dist1, 1.-alpha))
def test_divergences_to_kl():
"""
Tests that the generalized divergences properly fall back to KL for the appropriate values of alpha, and not otherwise.
"""
test_dists = [get_dists_2(), get_dists_3()]
for dists in test_dists:
for dist1 in dists:
for dist2 in dists:
assert_almost_equal(alpha_divergence(dist1, dist2, alpha=-1), kullback_leibler_divergence(dist2, dist1))
if dist1 != dist2:
assert_not_equal(alpha_divergence(dist1, dist2, alpha=0), kullback_leibler_divergence(dist2, dist1))
for divergence in [renyi_divergence, tsallis_divergence, alpha_divergence, hellinger_divergence]:
assert_almost_equal(divergence(dist1, dist2, alpha=1), kullback_leibler_divergence(dist1, dist2))
if dist1 != dist2:
assert_not_equal(alpha_divergence(dist1, dist2, alpha=0), kullback_leibler_divergence(dist2, dist1))
assert_not_equal(alpha_divergence(dist1, dist2, alpha=2), kullback_leibler_divergence(dist2, dist1))
def test_divergences_to_kl():
"""
Tests that the generalized divergences properly fall back to KL for the appropriate values of alpha, and not otherwise.
"""
test_dists = [get_dists_2(), get_dists_3()]
for dists in test_dists:
for dist1, dist2 in product(dists, repeat=2):
assert_almost_equal(alpha_divergence(dist1, dist2, alpha=-1), kullback_leibler_divergence(dist2, dist1))
if dist1 is not dist2:
assert_not_equal(alpha_divergence(dist1, dist2, alpha=0), kullback_leibler_divergence(dist2, dist1))
for divergence in divergences:
assert_almost_equal(divergence(dist1, dist2, alpha=1), kullback_leibler_divergence(dist1, dist2))
if dist1 is not dist2:
assert_not_equal(alpha_divergence(dist1, dist2, alpha=0), kullback_leibler_divergence(dist2, dist1))
assert_not_equal(alpha_divergence(dist1, dist2, alpha=2), kullback_leibler_divergence(dist2, dist1))
def test_alpha_symmetry():
"""
Tests the alpha -> -alpha symmetry for the alpha divergence, and a similar
symmetry for the Hellinger and Renyi divergences.
"""
alphas = [-1, 0, 0.5, 1, 2]
test_dists = [get_dists_2(), get_dists_3()]
for alpha in alphas:
for dists in test_dists:
for dist1 in dists:
for dist2 in dists:
assert_almost_equal(alpha_divergence(dist1, dist2, alpha),
alpha_divergence(dist2, dist1, -alpha))
assert_almost_equal(
(1. - alpha) *
hellinger_divergence(dist1, dist2, alpha),
alpha * hellinger_divergence(dist2, dist1, 1. - alpha))
assert_almost_equal(
(1. - alpha) * renyi_divergence(dist1, dist2, alpha),
alpha * renyi_divergence(dist2, dist1, 1. - alpha))
