def df_dtheta():
k, dk = cov.scale(theta[0], cov.se(theta[1])).df_theta(X, Y)
assert_allclose(k[0][0], f())
assert s2*dk[0] == k, 's2*dk[0]=%r k=%r' % (s2*dk[0], k)
if x == y:
assert all(np.all(dki == 0) for dki in dk[1:]), 'dk=%r' % (dk,)
else:
assert all(np.all(dki != 0) for dki in dk[1:])
h, dh = cov.se(theta[1]).df_theta(X, Y)
assert k == s2*h, 'k=%r s2*h=%r' % (k, s2*h)
assert all(dki == s2*dhi for dki, dhi in zip(dk[1:], dh))
return dk
def testTwoSamples_low_covariance(seed):
np_rng = npr.RandomState(seed)
obs_inputs = np.array([1.3, -2.0, 0.0])
obs_outputs = np.array([5.0, 2.3, 8.0])
in_lo_cov = np.array([1.4, -20.0])
sigma = 2.1
l = 1.8
observations = OrderedDict(zip(obs_inputs, obs_outputs))
mean = gp.mean_const(0.)
covariance = cov.scale(sigma**2, cov.se(l**2))
# Fix n = 200, not higher even if we are doing a long-running
# inference quality test, because we're trying to show that a
# Pearson r^2 test of independence will fail to reject the null
# hypothesis that the GP at two points with low covariance are
# simply independent. If we raised the number of samples
# significantly higher, the test is likely to reject the null
# hypothesis.
n = 200
lo_cov_x = []
lo_cov_y = []
for i in range(n):
x, y = gp._gp_sample(mean, covariance, observations, in_lo_cov, np_rng)
lo_cov_x.append(x)
lo_cov_y.append(y)
return reportPearsonIndependence(lo_cov_x, lo_cov_y)
def testOneSample(seed):
np_rng = npr.RandomState(seed)
obs_inputs = np.array([1.3, -2.0, 0.0])
obs_outputs = np.array([5.0, 2.3, 8.0])
test_input = 1.4
expect_mu = 4.6307
expect_sig = 0.0027
sigma = 2.1
l = 1.8
observations = OrderedDict(zip(obs_inputs, obs_outputs))
mean = gp.mean_const(0.)
covariance = cov.scale(sigma**2, cov.se(l**2))
# _gp_sample(..., test_input) should be normally distributed with
# mean expect_mu.
n = default_num_samples(4)
def sample():
s = gp._gp_sample(mean, covariance, observations, [test_input], np_rng)
return s[0]
samples = np.array([sample() for _ in xrange(n)])
assert samples.shape == (n, )
return reportKnownGaussian(expect_mu, np.sqrt(expect_sig), samples)
def df_dtheta():
k, dk = cov.se(theta[0]).df_theta(X, Y)
assert_allclose(k[0][0], f())
if x == y:
assert all(np.all(dki == 0) for dki in dk)
else:
assert all(np.all(dki != 0) for dki in dk)
return dk
def testNormalParameters():
obs_inputs = np.array([1.3, -2.0, 0.0])
obs_outputs = np.array([5.0, 2.3, 8.0])
test_inputs = np.array([1.4, -3.2])
expect_mu = np.array([4.6307, -0.9046])
expect_sig = np.array([[0.0027, -0.0231], [-0.0231, 1.1090]])
sigma = 2.1
l = 1.8
observations = OrderedDict(zip(obs_inputs, obs_outputs))
mean = gp.mean_const(0.)
covariance = cov.scale(sigma**2, cov.se(l**2))
actual_mu, actual_sig = gp._gp_mvnormal(mean, covariance, observations,
test_inputs)
np.testing.assert_almost_equal(actual_mu, expect_mu, decimal=4)
np.testing.assert_almost_equal(actual_sig, expect_sig, decimal=4)
def test_se():
for x in [-1, 0, 1]:
X = np.array([x])
for y in [-1, 0, 1]:
Y = np.array([y])
for l2 in [.01, 1, 10, 100]:
check_ddx(cov.se(l2), x, Y)
theta = [l2]
def f():
return cov.se(theta[0]).f(X, Y)[0][0]
def df_dtheta():
k, dk = cov.se(theta[0]).df_theta(X, Y)
assert_allclose(k[0][0], f())
if x == y:
assert all(np.all(dki == 0) for dki in dk)
else:
assert all(np.all(dki != 0) for dki in dk)
return dk
check_ddtheta(f, df_dtheta, theta)
def interpret_covariance_kernel(ast):
if ast[0]['value'] == 'gp_cov_bump':
min_tolerance = ast[1]['value']
max_tolerance = ast[2]['value']
return covariance.bump(min_tolerance, max_tolerance)
elif ast[0]['value'] == 'gp_cov_scale':
s2 = ast[1]['value']
K = interpret_covariance_kernel(ast[2])
return covariance.scale(s2, K)
elif ast[0]['value'] == 'gp_cov_wn':
s2 = ast[1]['value']
K = covariance.bump(1e-9, 1e-11)
return covariance.scale(s2, K)
elif ast[0]['value'] == 'gp_cov_const':
c = ast[1]['value']
return covariance.const(c)
elif ast[0]['value'] == 'gp_cov_linear':
c = ast[1]['value']
return covariance.linear(c)
elif ast[0]['value'] == 'gp_cov_se':
l2 = ast[1]['value']
return covariance.se(l2)
elif ast[0]['value'] == 'gp_cov_periodic':
l2 = ast[1]['value']
T = ast[2]['value']
return covariance.periodic(l2, T)
elif ast[0]['value'] == 'gp_cov_sum':
K = interpret_covariance_kernel(ast[1])
H = interpret_covariance_kernel(ast[2])
return covariance.sum(K, H)
elif ast[0]['value'] == 'gp_cov_product':
K = interpret_covariance_kernel(ast[1])
H = interpret_covariance_kernel(ast[2])
return covariance.product(K, H)
elif ast[0]['value'] == 'gp_cov_cp':
location = ast[1]['value']
scale = ast[2]['value']
K = interpret_covariance_kernel(ast[3])
H = interpret_covariance_kernel(ast[4])
return change_point(location, scale, K, H)
else:
assert False, 'Failed to interpret AST'
def test_sum_se_bump():
for x in [-1, 0, 1]:
X = np.array([x])
for y in [-1, 0, 1]:
Y = np.array([y])
for l2 in [.1, 1, 10]:
for mint in [.4, 1.4, 2.4]:
for maxt in [.6, 1.6, 2.6]:
if maxt < mint:
continue
check_ddx(cov.sum(cov.se(l2), cov.bump(mint, maxt)), x, Y)
theta = [l2, mint, maxt]
def f():
K = cov.se(theta[0])
H = cov.bump(theta[1], theta[2])
return cov.sum(K, H).f(X, Y)[0][0]
def df_dtheta():
K = cov.se(theta[0])
H = cov.bump(theta[1], theta[2])
k, dk = cov.sum(K, H).df_theta(X, Y)
assert_allclose(k[0][0], f())
return dk
check_ddtheta(f, df_dtheta, theta)
def test_se_scaled():
for x in [-1, 0, 1]:
X = np.array([x])
for y in [-1, 0, 1]:
Y = np.array([y])
for s2 in [.1, 1, 10, 100]:
for l2 in [.1, 1, 10]:
check_ddx(cov.scale(s2, cov.se(l2)), x, Y)
theta = [s2, l2]
def f():
return cov.scale(theta[0], cov.se(theta[1])).f(X, Y)[0][0]
def df_dtheta():
k, dk = cov.scale(theta[0], cov.se(theta[1])).df_theta(X, Y)
assert_allclose(k[0][0], f())
assert s2*dk[0] == k, 's2*dk[0]=%r k=%r' % (s2*dk[0], k)
if x == y:
assert all(np.all(dki == 0) for dki in dk[1:]), 'dk=%r' % (dk,)
else:
assert all(np.all(dki != 0) for dki in dk[1:])
h, dh = cov.se(theta[1]).df_theta(X, Y)
assert k == s2*h, 'k=%r s2*h=%r' % (k, s2*h)
assert all(dki == s2*dhi for dki, dhi in zip(dk[1:], dh))
return dk
check_ddtheta(f, df_dtheta, theta)
def df_dtheta(): K = cov.se(theta[0]) H = cov.bump(theta[1], theta[2]) k, dk = cov.sum(K, H).df_theta(X, Y) assert_allclose(k[0][0], f()) return dk
def f(): K = cov.se(theta[0]) H = cov.bump(theta[1], theta[2]) return cov.sum(K, H).f(X, Y)[0][0]
def f(): return cov.scale(theta[0], cov.se(theta[1])).f(X, Y)[0][0]
def f(): return cov.se(theta[0]).f(X, Y)[0][0]