def test_cosine_analytical(d):
pytest.importorskip('scipy') # beta, betainc, betaincinv
dt = 0.0001
x = np.arange(-1 + dt, 1, dt)
def p(x, d):
# unnormalized CosineSimilarity distribution, derived by Eric H.
return (1 - x * x)**((d - 3) / 2.0)
dist = dists.CosineSimilarity(d)
pdf_exp = dist.pdf(x)
pdf_act = p(x, d)
cdf_exp = dist.cdf(x)
cdf_act = np.cumsum(pdf_act) / np.sum(pdf_act)
# Check that we get the expected pdf after normalization
assert np.allclose(pdf_exp / np.sum(pdf_exp),
pdf_act / np.sum(pdf_act),
atol=0.01)
# Check that this accumulates to the expected cdf
assert np.allclose(cdf_exp, cdf_act, atol=0.01)
# Check that the inverse cdf gives back x
assert np.allclose(dist.ppf(cdf_exp), x, atol=0.01)
def test_cosine_sample_shape(seed):
""""Tests that CosineSimilarity sample has correct shape."""
# sampling (n, d) should be the exact same as sampling (n*d,)
n = 3
d = 4
dist = dists.CosineSimilarity(2)
a = dist.sample(n, d, rng=np.random.RandomState(seed))
b = dist.sample(n * d, rng=np.random.RandomState(seed))
assert np.allclose(a.flatten(), b)
def test_cosine_intercept(d, p, rng):
"""Tests CosineSimilarity inverse cdf for finding intercepts."""
pytest.importorskip('scipy') # betaincinv
num_samples = 250
exp_dist = dists.UniformHypersphere(surface=True)
act_dist = dists.CosineSimilarity(d)
dots = exp_dist.sample(num_samples, d, rng=rng)[:, 0]
# Find the desired intercept so that dots >= c with probability p
c = act_dist.ppf(1 - p)
assert np.allclose(np.sum(dots >= c) / float(num_samples), p, atol=0.05)
def test_cosine_similarity(d, rng):
"""Tests CosineSimilarity sampling."""
num_samples = 2500
num_bins = 5
# Check that it gives a single dimension from UniformHypersphere
exp_dist = dists.UniformHypersphere(surface=True)
act_dist = dists.CosineSimilarity(d)
exp = exp_dist.sample(num_samples, d, rng=rng)[:, 0]
act = act_dist.sample(num_samples, rng=rng)
exp_hist, _ = np.histogram(exp, bins=num_bins)
act_hist, _ = np.histogram(act, bins=num_bins)
assert np.all(np.abs(np.asfarray(exp_hist - act_hist) / num_samples) < 0.1)