def w2(self, other):
"""Compute the 2-Wasserstein distance with respect to another normal
distribution.
Args:
other (:class:`.random.Normal`): Other normal.
Returns:
scalar: 2-Wasserstein distance.
"""
root = B.root(B.matmul(B.root(self.var), other.var, B.root(self.var)))
var_part = B.trace(self.var) + B.trace(other.var) - 2 * B.trace(root)
mean_part = B.sum((self.mean - other.mean) ** 2)
# The sum of `mean_part` and `var_par` should be positive, but this
# may not be the case due to numerical errors.
return B.abs(mean_part + var_part) ** .5
def test_marginals():
model = Graph()
p = GP(EQ(), TensorProductMean(lambda x: x ** 2), graph=model)
x = np.linspace(0, 5, 10)
# Check that `marginals` outputs the right thing.
mean, lower, upper = p(x).marginals()
var = B.diag(p.kernel(x))
yield assert_allclose, mean, p.mean(x)[:, 0]
yield assert_allclose, lower, p.mean(x)[:, 0] - 2 * var ** .5
yield assert_allclose, upper, p.mean(x)[:, 0] + 2 * var ** .5
# Test correctness.
y = p(x).sample()
mean, lower, upper = (p | (x, y))(x).marginals()
yield assert_allclose, mean, y[:, 0]
yield le, B.mean(B.abs(upper - lower)), 1e-5
mean, lower, upper = (p | (x, y))(x + 100).marginals()
yield assert_allclose, mean, p.mean(x + 100)[:, 0]
yield assert_allclose, upper - lower, 4 * np.ones(10)