def __init__(self, var, mean=None):
var = B.array(var)
# Consider all various ranks of `var` and `mean` for convenient
# broadcasting behaviour.
if mean is not None:
mean = B.array(mean)
if B.rank(var) == 1:
if B.rank(mean) == 0:
mean = mean * \
B.ones([B.shape(var)[0], 1], dtype=B.dtype(var))
elif B.rank(mean) == 1:
mean = mean[:, None]
else:
raise ValueError('Invalid rank {} of mean.'
''.format(B.rank(mean)))
var = Diagonal(var)
elif B.rank(var) == 0:
if B.rank(mean) == 0:
mean = mean * B.ones([1, 1], dtype=B.dtype(var))
var = UniformlyDiagonal(var, 1)
elif B.rank(mean) == 1:
mean = mean[:, None]
var = UniformlyDiagonal(var, B.shape(mean)[0])
else:
raise ValueError('Invalid rank {} of mean.'
''.format(B.rank(mean)))
else:
raise ValueError('Invalid rank {} of variance.'
''.format(B.rank(var)))
else:
if B.rank(var) == 0:
var = UniformlyDiagonal(var, 1)
elif B.rank(var) == 1:
var = Diagonal(var)
else:
raise ValueError('Invalid rank {} of variance.'
''.format(B.rank(var)))
Normal.__init__(self, var, mean)
def test_derivative():
B.backend_to_tf()
s = B.Session()
m = TensorProductMean(lambda x: x**2)
m2 = TensorProductMean(lambda x: x**3)
x = B.array(np.random.randn(10, 1))
yield assert_allclose, s.run(m.diff(0)(x)), s.run(2 * x)
yield assert_allclose, s.run(m2.diff(0)(x)), s.run(3 * x**2)
s.close()
B.backend_to_np()
def logpdf(self, x):
"""Compute the log-pdf.
Args:
x (input): Values to compute the log-pdf of.
Returns:
list[tensor]: Log-pdf for every input in `x`. If it can be
determined that the list contains only a single log-pdf,
then the list is flattened to a scalar.
"""
# Convert to numeric type if necessary.
x = B.array(x) if isinstance(x, (list, tuple)) else x
logpdfs = -(B.logdet(self.var) + B.cast(self.dim, dtype=self.dtype) *
B.cast(B.log_2_pi, dtype=self.dtype) +
B.qf_diag(self.var,
uprank(x) - self.mean)) / 2
return logpdfs[0] if B.shape_int(logpdfs) == (1, ) else logpdfs
def dense(a):
return B.array(a)
def test_derivative():
# First, check properties.
k = EQ().diff(0)
yield eq, k.stationary, False
yield raises, RuntimeError, lambda: k.length_scale
yield raises, RuntimeError, lambda: k.var
yield raises, RuntimeError, lambda: k.period
# Test equality.
yield eq, EQ().diff(0), EQ().diff(0)
yield neq, EQ().diff(0), EQ().diff(1)
yield neq, Matern12().diff(0), EQ().diff(0)
yield raises, RuntimeError, lambda: EQ().diff(None, None)(1)
# Third, check computation.
B.backend_to_tf()
s = B.Session()
# Test derivative of kernel EQ.
k = EQ()
x1 = B.array(np.random.randn(10, 1))
x2 = B.array(np.random.randn(5, 1))
# Test derivative with respect to first input.
ref = s.run(-dense(k(x1, x2)) * (x1 - B.transpose(x2)))
yield assert_allclose, s.run(dense(k.diff(0, None)(x1, x2))), ref
ref = s.run(-dense(k(x1)) * (x1 - B.transpose(x1)))
yield assert_allclose, s.run(dense(k.diff(0, None)(x1))), ref
# Test derivative with respect to second input.
ref = s.run(-dense(k(x1, x2)) * (B.transpose(x2) - x1))
yield assert_allclose, s.run(dense(k.diff(None, 0)(x1, x2))), ref
ref = s.run(-dense(k(x1)) * (B.transpose(x1) - x1))
yield assert_allclose, s.run(dense(k.diff(None, 0)(x1))), ref
# Test derivative with respect to both inputs.
ref = s.run(dense(k(x1, x2)) * (1 - (x1 - B.transpose(x2))**2))
yield assert_allclose, s.run(dense(k.diff(0, 0)(x1, x2))), ref
yield assert_allclose, s.run(dense(k.diff(0)(x1, x2))), ref
ref = s.run(dense(k(x1)) * (1 - (x1 - B.transpose(x1))**2))
yield assert_allclose, s.run(dense(k.diff(0, 0)(x1))), ref
yield assert_allclose, s.run(dense(k.diff(0)(x1))), ref
# Test derivative of kernel Linear.
k = Linear()
x1 = B.array(np.random.randn(10, 1))
x2 = B.array(np.random.randn(5, 1))
# Test derivative with respect to first input.
ref = s.run(B.ones((10, 5), dtype=np.float64) * B.transpose(x2))
yield assert_allclose, s.run(dense(k.diff(0, None)(x1, x2))), ref
ref = s.run(B.ones((10, 10), dtype=np.float64) * B.transpose(x1))
yield assert_allclose, s.run(dense(k.diff(0, None)(x1))), ref
# Test derivative with respect to second input.
ref = s.run(B.ones((10, 5), dtype=np.float64) * x1)
yield assert_allclose, s.run(dense(k.diff(None, 0)(x1, x2))), ref
ref = s.run(B.ones((10, 10), dtype=np.float64) * x1)
yield assert_allclose, s.run(dense(k.diff(None, 0)(x1))), ref
# Test derivative with respect to both inputs.
ref = s.run(B.ones((10, 5), dtype=np.float64))
yield assert_allclose, s.run(dense(k.diff(0, 0)(x1, x2))), ref
yield assert_allclose, s.run(dense(k.diff(0)(x1, x2))), ref
ref = s.run(B.ones((10, 10), dtype=np.float64))
yield assert_allclose, s.run(dense(k.diff(0, 0)(x1))), ref
yield assert_allclose, s.run(dense(k.diff(0)(x1))), ref
s.close()
B.backend_to_np()
