def joint_information(x, y, n_neighbors=3, random_noise=0.3):
n_samples = x.size
if random_noise:
x = with_added_white_noise(x, random_noise)
y = with_added_white_noise(y, random_noise)
x = x.reshape((-1, 1))
y = y.reshape((-1, 1))
xy = np.hstack((x, y))
# Here we rely on NearestNeighbors to select the fastest algorithm.
nn = NearestNeighbors(metric='chebyshev', n_neighbors=n_neighbors)
nn.fit(xy)
radius = nn.kneighbors()[0]
radius = np.nextafter(radius[:, -1], 0)
# Algorithm is selected explicitly to allow passing an array as radius
# later (not all algorithms support this).
nn.set_params(algorithm='kd_tree')
nn.fit(x)
ind = nn.radius_neighbors(radius=radius, return_distance=False)
nx = np.array([i.size for i in ind])
nn.fit(y)
ind = nn.radius_neighbors(radius=radius, return_distance=False)
ny = np.array([i.size for i in ind])
mi = (digamma(n_samples) + digamma(n_neighbors) -
np.mean(digamma(nx + 1)) - np.mean(digamma(ny + 1)))
return max(0, mi)
