def test_matern52_encoding():
kernel = Matern52(dimension=2, ARD=True)
assert isinstance(kernel.encoding, LogarithmScalarEncoding)
assert isinstance(kernel.squared_distance.encoding,
LogarithmScalarEncoding)
assert kernel.encoding.dimension == 1
assert kernel.squared_distance.encoding.dimension == 2
kernel = Matern52(dimension=2, ARD=True, encoding_type="positive")
assert isinstance(kernel.encoding, PositiveScalarEncoding)
assert isinstance(kernel.squared_distance.encoding, PositiveScalarEncoding)
assert kernel.encoding.dimension == 1
assert kernel.squared_distance.encoding.dimension == 2
def test_gp_regression_with_warping():
def f(x):
return np.sin(3*np.log(x))
np.random.seed(7)
L, U = -5., 12.
input_range = (2.**L, 2.**U)
x_train = np.sort(2.**np.random.uniform(L, U, 250))
x_test = np.sort(2.**np.random.uniform(L, U, 500))
y_train = f(x_train)
y_test = f(x_test)
# to mx.nd
y_train_mx_nd = mx.nd.array(y_train)
x_train_mx_nd = mx.nd.array(x_train)
x_test_mx_nd = mx.nd.array(x_test)
kernels = [
Matern52(dimension=1),
WarpedKernel(
kernel=Matern52(dimension=1),
warping=Warping(dimension=1, index_to_range={0: input_range})
)
]
models = [GaussianProcessRegression(kernel=k, random_seed=0) for k in kernels]
train_errors, test_errors = [], []
for model in models:
model.fit(x_train_mx_nd, y_train_mx_nd)
mu_train, var_train = model.predict(x_train_mx_nd)[0]
mu_test, var_test = model.predict(x_test_mx_nd)[0]
# back to np.array
mu_train = mu_train.asnumpy()
mu_test = mu_test.asnumpy()
# var_train = var_train.asnumpy()
# var_test = var_test.asnumpy()
train_errors.append(np.mean(np.abs((mu_train - y_train))))
test_errors.append(np.mean(np.abs((mu_test - y_test))))
# The two models have similar performance on training points
np.testing.assert_almost_equal(train_errors[0], train_errors[1], decimal=4)
# As expected, the model with warping largely outperforms the model without
assert test_errors[1] < 0.1 * test_errors[0]
def test_likelihood_encoding():
mean = ScalarMeanFunction()
kernel = Matern52(dimension=1)
likelihood = MarginalLikelihood(mean=mean, kernel=kernel)
assert isinstance(likelihood.encoding, LogarithmScalarEncoding)
likelihood = MarginalLikelihood(mean=mean,
kernel=kernel,
encoding_type="positive")
assert isinstance(likelihood.encoding, PositiveScalarEncoding)
def test_matern52_unit_scale():
X = mx.nd.array([[1, 0], [0, 1]], dtype=DATA_TYPE)
kernel = Matern52(dimension=2)
assert kernel.ARD == False
kernel.collect_params().initialize()
K = kernel(X, X).asnumpy()
expected_K = np.array([[mater52(0.0), mater52(2.0)],
[mater52(2.0), mater52(0.0)]])
np.testing.assert_almost_equal(expected_K, K)
def test_set_gp_hps():
mean = ScalarMeanFunction()
kernel = Matern52(dimension=1)
warping = Warping(dimension=1, index_to_range={0: (-4., 4.)})
warped_kernel = WarpedKernel(kernel=kernel, warping=warping)
likelihood = MarginalLikelihood(kernel=warped_kernel, mean=mean, initial_noise_variance=1e-6)
likelihood.initialize(ctx=mx.cpu(), force_reinit=True)
likelihood.hybridize()
hp_values = np.array([1e-2, 1.0, 0.5, 0.3, 0.2, 1.1])
_set_gp_hps(hp_values, likelihood)
np.testing.assert_array_almost_equal(hp_values, _get_gp_hps(likelihood))
def test_get_gp_hps():
mean = ScalarMeanFunction()
kernel = Matern52(dimension=1)
warping = Warping(dimension=1, index_to_range={0: (-4., 4.)})
warped_kernel = WarpedKernel(kernel=kernel, warping=warping)
likelihood = MarginalLikelihood(kernel=warped_kernel, mean=mean, initial_noise_variance=1e-6)
likelihood.initialize(ctx=mx.cpu(), force_reinit=True)
likelihood.hybridize()
hp_values = _get_gp_hps(likelihood)
# the oder of hps are noise, mean, covariance scale, bandwidth, warping a, warping b
np.testing.assert_array_almost_equal(hp_values, np.array([1e-6, 0.0, 1.0, 1.0, 1.0, 1.0]))
def test_matern52_wrongshape():
kernel = Matern52(dimension=3)
kernel.collect_params().initialize()
X1 = mx.nd.random_normal(0.0, 1.0, shape=(5, 2))
with pytest.raises(mx.base.MXNetError):
kmat = kernel(X1, X1)
with pytest.raises(mx.base.MXNetError):
kdiag = kernel.diagonal(mx.nd, X1)
X2 = mx.nd.random_normal(0.0, 1.0, shape=(3, 3))
with pytest.raises(mx.base.MXNetError):
kmat = kernel(X2, X1)
def test_gp_regression_2d_with_ard():
def f(x):
# Only dependent on the first column of x
return np.sin(x[:, 0]) / x[:, 0]
np.random.seed(7)
dimension = 3
# 30 train and test points in R^3
x_train = np.random.uniform(-5, 5, size=(30, dimension))
x_test = np.random.uniform(-5, 5, size=(30, dimension))
y_train = f(x_train)
y_test = f(x_test)
# to mx.nd
y_train_mx_nd = mx.nd.array(y_train)
x_train_mx_nd = mx.nd.array(x_train)
x_test_mx_nd = mx.nd.array(x_test)
model = GaussianProcessRegression(
kernel=Matern52(dimension=dimension, ARD=True))
model.fit(x_train_mx_nd, y_train_mx_nd)
# Check that the value of the residual noise variance learned by empirical Bayes is in the same order as the smallest allowed value (since there is no noise)
noise_variance = model.likelihood.get_noise_variance()
np.testing.assert_almost_equal(noise_variance, NOISE_VARIANCE_LOWER_BOUND)
# Check that the bandwidths learned by empirical Bayes reflect the fact that only the first column is useful
# In particular, for the useless dimensions indexed by {1,2}, the inverse bandwidths should be close to INVERSE_BANDWIDTHS_LOWER_BOUND
# (or conversely, bandwidths should be close to their highest allowed values)
sqd = model.likelihood.kernel.squared_distance
inverse_bandwidths = sqd.encoding.get(
mx.nd, sqd.inverse_bandwidths_internal.data()).asnumpy()
assert inverse_bandwidths[0] > inverse_bandwidths[
1] and inverse_bandwidths[0] > inverse_bandwidths[2]
np.testing.assert_almost_equal(inverse_bandwidths[1],
INVERSE_BANDWIDTHS_LOWER_BOUND)
np.testing.assert_almost_equal(inverse_bandwidths[2],
INVERSE_BANDWIDTHS_LOWER_BOUND)
mu_train, _ = model.predict(x_train_mx_nd)[0]
mu_test, _ = model.predict(x_test_mx_nd)[0]
# back to np.array
mu_train = mu_train.asnumpy()
mu_test = mu_test.asnumpy()
np.testing.assert_almost_equal(mu_train, y_train, decimal=2)
# Fewer decimals imposed for the test points
np.testing.assert_almost_equal(mu_test, y_test, decimal=1)
def test_incremental_update():
def f(x):
return np.sin(x) / x
np.random.seed(298424)
std_noise = 0.01
for rep in range(10):
model = GaussianProcessRegression(kernel=Matern52(dimension=1))
# Sample data
num_train = np.random.randint(low=5, high=15)
num_incr = np.random.randint(low=1, high=7)
sizes = [num_train, num_incr]
features = []
targets = []
for sz in sizes:
feats = np.random.uniform(low=-1.0, high=1.0, size=sz).reshape((-1, 1))
features.append(feats)
targs = f(feats)
targs += np.random.normal(0.0, std_noise, size=targs.shape)
targets.append(targs)
# Posterior state by incremental updating
train_features = to_nd(features[0])
train_targets = to_nd(targets[0])
model.fit(train_features, train_targets)
noise_variance_1 = model.likelihood.get_noise_variance()
state_incr = IncrementalUpdateGPPosteriorState(
features=train_features, targets=train_targets,
mean=model.likelihood.mean, kernel=model.likelihood.kernel,
noise_variance=model.likelihood.get_noise_variance(as_ndarray=True))
for i in range(num_incr):
state_incr = state_incr.update(
to_nd(features[1][i].reshape((1, -1))),
to_nd(targets[1][i].reshape((1, -1))))
noise_variance_2 = state_incr.noise_variance.asscalar()
# Posterior state by direct computation
state_comp = GaussProcPosteriorState(
features=to_nd(np.concatenate(features, axis=0)),
targets=to_nd(np.concatenate(targets, axis=0)),
mean=model.likelihood.mean, kernel=model.likelihood.kernel,
noise_variance=state_incr.noise_variance)
# Compare them
assert noise_variance_1 == noise_variance_2, \
"noise_variance_1 = {} != {} = noise_variance_2".format(
noise_variance_1, noise_variance_2)
chol_fact_incr = state_incr.chol_fact.asnumpy()
chol_fact_comp = state_comp.chol_fact.asnumpy()
np.testing.assert_almost_equal(chol_fact_incr, chol_fact_comp, decimal=2)
pred_mat_incr = state_incr.pred_mat.asnumpy()
pred_mat_comp = state_comp.pred_mat.asnumpy()
np.testing.assert_almost_equal(pred_mat_incr, pred_mat_comp, decimal=2)
def test_matern52_ard():
X = mx.nd.array([[2., 1.], [1., 2.], [0., 1.]], dtype=DATA_TYPE)
kernel = Matern52(dimension=2, ARD=True)
kernel.collect_params().initialize()
sqd = kernel.squared_distance
assert kernel.ARD == True
assert sqd.ARD == True
sqd.encoding.set(sqd.inverse_bandwidths_internal, [1. / np.sqrt(2.), 1.])
K = kernel(X, X).asnumpy()
# expected_D is taken from previous test about squared distances
expected_D = np.array([[0., 3. / 2., 2.], [3. / 2., 0., 3. / 2.],
[2.0, 3. / 2., 0.]])
expected_K = mater52(expected_D)
np.testing.assert_almost_equal(expected_K, K)
def test_product_wrongshape():
kernel1 = Matern52(dimension=2)
kernel1.collect_params().initialize()
# A better way to do this is using the `pytest.mark.parametrize`
# decorator. Keeping it simple for now.
kernels = [Matern52(dimension=1), FabolasKernelFunction()]
for kernel2 in kernels:
kernel2.collect_params().initialize()
kernel = ProductKernelFunction(kernel1, kernel2)
X1 = mx.nd.random_normal(0.0, 1.0, shape=(5, 4))
with pytest.raises(mx.base.MXNetError):
kmat = kernel(X1, X1)
with pytest.raises(mx.base.MXNetError):
kdiag = kernel.diagonal(mx.nd, X1)
X2 = mx.nd.random_normal(0.0, 1.0, shape=(3, 3))
with pytest.raises(mx.base.MXNetError):
kmat = kernel(X2, X1)
X1 = mx.nd.random_normal(0.0, 1.0, shape=(5, 2))
with pytest.raises(mx.base.MXNetError):
kmat = kernel(X1, X1)
def test_gp_regression_with_noise():
def f(x):
return np.sin(x) / x
np.random.seed(7)
x_train = np.arange(-5, 5, 0.2) # [-5, -4.8, -4.6,..., 4.8]
x_test = np.arange(
-4.9, 5, 0.2
) # [-4.9, -4.7, -4.5,..., 4.9], note that train and test points do not overlap
y_train = f(x_train)
y_test = f(x_test)
std_noise = 0.01
noise_train = np.random.normal(0.0, std_noise, size=y_train.shape)
# to mx.nd
y_train_mx_nd = mx.nd.array(y_train)
noise_train_mx_nd = mx.nd.array(noise_train)
x_train_mx_nd = mx.nd.array(x_train)
x_test_mx_nd = mx.nd.array(x_test)
model = GaussianProcessRegression(kernel=Matern52(dimension=1))
model.fit(x_train_mx_nd, y_train_mx_nd + noise_train_mx_nd)
# Check that the value of the residual noise variance learned by empirical Bayes is in the same order as std_noise^2
noise_variance = model.likelihood.get_noise_variance()
np.testing.assert_almost_equal(noise_variance, std_noise**2, decimal=4)
mu_train, _ = model.predict(x_train_mx_nd)[0]
mu_test, _ = model.predict(x_test_mx_nd)[0]
# back to np.array
mu_train = mu_train.asnumpy()
mu_test = mu_test.asnumpy()
np.testing.assert_almost_equal(mu_train, y_train, decimal=2)
np.testing.assert_almost_equal(mu_test, y_test, decimal=2)
def test_gp_regression_no_noise():
def f(x):
return np.sin(x) / x
x_train = np.arange(-5, 5, 0.2) # [-5,-4.8,-4.6,...,4.8]
x_test = np.arange(
-4.9, 5, 0.2
) # [-4.9, -4.7, -4.5,...,4.9], note that train and test points do not overlap
y_train = f(x_train)
y_test = f(x_test)
# to mx.nd
y_train_mx_nd = mx.nd.array(y_train)
x_train_mx_nd = mx.nd.array(x_train)
x_test_mx_nd = mx.nd.array(x_test)
model = GaussianProcessRegression(kernel=Matern52(dimension=1))
model.fit(x_train_mx_nd, y_train_mx_nd)
# Check that the value of the residual noise variance learned by empirical Bayes is in the same order
# as the smallest allowed value (since there is no noise)
noise_variance = model.likelihood.get_noise_variance()
np.testing.assert_almost_equal(noise_variance, NOISE_VARIANCE_LOWER_BOUND)
mu_train, var_train = model.predict(x_train_mx_nd)[0]
mu_test, var_test = model.predict(x_test_mx_nd)[0]
# back to np.array
mu_train = mu_train.asnumpy()
mu_test = mu_test.asnumpy()
var_train = var_train.asnumpy()
var_test = var_test.asnumpy()
np.testing.assert_almost_equal(mu_train, y_train, decimal=4)
np.testing.assert_almost_equal(var_train, [0.0] * len(var_train),
decimal=4)
# Fewer decimals imposed for the test points
np.testing.assert_almost_equal(mu_test, y_test, decimal=3)
def build_kernel():
return WarpedKernel(
kernel=Matern52(dimension=1),
warping=Warping(dimension=1, index_to_range={0: (-4., 4.)})
)