def test_kl_simple():
# verified by hand
# Dhat(P||Q) = \log m/(n-1) + d / n \sum_{i=1}^n \log \nu_k(i)/rho_k(i)
x = np.reshape([0., 1, 3], (3, 1))
y = np.reshape([.2, 1.2, 3.2, 7.2], (4, 1))
n = x.shape[0]
m = y.shape[0]
x_to_y = np.log(
m /
(n - 1)) + 1 / n * (np.log(1.2 / 3) + np.log(.8 / 2) + np.log(1.8 / 3))
y_to_x = np.log(n / (m - 1)) + 1 / m * (np.log(.8 / 3) + np.log(1.2 / 2) +
np.log(2.2 / 3) + np.log(6.2 / 6))
# NOTE: clamping makes this test useless.
x_to_y = max(x_to_y, 0)
y_to_x = max(y_to_x, 0)
res = estimate_divs(Features([x, y]), specs=['kl'], Ks=[2]).squeeze()
assert res[0, 0] == 0
assert res[1, 1] == 0
assert np.allclose(res[1, 0], y_to_x), "{} vs {}".format(res[1, 0], y_to_x)
assert np.allclose(res[0, 1], x_to_y), "{} vs {}".format(res[0, 1], x_to_y)
def generate_gaussians(name, mean_std_nums, dim, min_pts, max_pts):
bags = []
categories = []
for mean, std, num in mean_std_nums:
cat_name = 'mean{}-std{}'.format(mean, std)
for x in range(num):
n_pts = np.random.randint(min_pts, max_pts + 1)
feats = np.random.normal(mean, std, size=(n_pts, dim))
bags.append(feats)
categories.append(cat_name)
features = Features(bags, categories=categories)
features.save_as_hdf5('data/{}.h5'.format(name))
def test_js_simple():
# verified by hand
x = np.reshape([0, 1, 3], (3, 1))
y = np.reshape([.2, 1.2, 3.2, 6.2], (4, 1))
mix_ent = np.log(2) + np.log(3) + psi(2) \
+ (np.log(.2) + np.log(.8) + np.log(1.8) - psi(1) - 2*psi(2)) / 6 \
+ (np.log(.2) + np.log(2) + np.log(3.2) - psi(1) - 3*psi(2)) / 8
x_ent = np.log(2) + (np.log(3) + np.log(2) + np.log(3)) / 3
y_ent = np.log(3) + (np.log(3) + np.log(2) + np.log(3) + np.log(5)) / 4
right_js = mix_ent - (x_ent + y_ent) / 2
expected = np.array([[0, right_js], [right_js, 0]])
# TODO: what about clamping???
est = estimate_divs(Features([x, y]), specs=['js'], Ks=[2],
status_fn=None).squeeze()
assert_close(est, expected, atol=5e-5, msg="JS estimate not as expected")
