def test_gp_regression_with_noise():
def f(x):
return anp.sin(x)/x
anp.random.seed(7)
x_train = anp.arange(-5, 5, 0.2)# [-5, -4.8, -4.6,..., 4.8]
x_test = anp.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 = anp.random.normal(0.0, std_noise,size=y_train.shape)
# to anp.ndarray
y_train_np_ndarray = anp.array(y_train)
noise_train_np_ndarray = anp.array(noise_train)
x_train_np_ndarray = anp.array(x_train)
x_test_np_ndarray = anp.array(x_test)
model = GaussianProcessRegression(kernel=Matern52(dimension=1))
model.fit(x_train_np_ndarray, y_train_np_ndarray + noise_train_np_ndarray)
# 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()
numpy.testing.assert_almost_equal(noise_variance, std_noise**2, decimal=4)
mu_train, _ = model.predict(x_train_np_ndarray)[0]
mu_test, _ = model.predict(x_test_np_ndarray)[0]
numpy.testing.assert_almost_equal(mu_train, y_train, decimal=2)
numpy.testing.assert_almost_equal(mu_test, y_test, decimal=2)
def test_gp_regression_no_noise():
def f(x):
return anp.sin(x)/x
x_train = anp.arange(-5, 5, 0.2)# [-5,-4.8,-4.6,...,4.8]
x_test = anp.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 np.ndarray
y_train_np_ndarray = anp.array(y_train)
x_train_np_ndarray = anp.array(x_train)
x_test_np_ndarray = anp.array(x_test)
model = GaussianProcessRegression(kernel=Matern52(dimension=1))
model.fit(x_train_np_ndarray, y_train_np_ndarray)
# 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()
numpy.testing.assert_almost_equal(noise_variance, NOISE_VARIANCE_LOWER_BOUND)
mu_train, var_train = model.predict(x_train_np_ndarray)[0]
mu_test, var_test = model.predict(x_test_np_ndarray)[0]
numpy.testing.assert_almost_equal(mu_train, y_train, decimal=4)
numpy.testing.assert_almost_equal(var_train, [0.0] * len(var_train), decimal=4)
# Fewer decimals imposed for the test points
numpy.testing.assert_almost_equal(mu_test, y_test, decimal=3)
def test_gp_regression_2d_with_ard():
def f(x):
# Only dependent on the first column of x
return anp.sin(x[:,0])/x[:,0]
anp.random.seed(7)
dimension = 3
# 30 train and test points in R^3
x_train = anp.random.uniform(-5, 5, size=(30,dimension))
x_test = anp.random.uniform(-5, 5, size=(30,dimension))
y_train = f(x_train)
y_test = f(x_test)
# to np.ndarray
y_train_np_ndarray = anp.array(y_train)
x_train_np_ndarray = anp.array(x_train)
x_test_np_ndarray = anp.array(x_test)
model = GaussianProcessRegression(kernel=Matern52(dimension=dimension, ARD=True))
model.fit(x_train_np_ndarray, y_train_np_ndarray)
# 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()
numpy.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(sqd.inverse_bandwidths_internal.data())
assert inverse_bandwidths[0] > inverse_bandwidths[1] and inverse_bandwidths[0] > inverse_bandwidths[2]
numpy.testing.assert_almost_equal(inverse_bandwidths[1], INVERSE_BANDWIDTHS_LOWER_BOUND)
numpy.testing.assert_almost_equal(inverse_bandwidths[2], INVERSE_BANDWIDTHS_LOWER_BOUND)
mu_train, _ = model.predict(x_train_np_ndarray)[0]
mu_test, _ = model.predict(x_test_np_ndarray)[0]
numpy.testing.assert_almost_equal(mu_train, y_train, decimal=2)
# Fewer decimals imposed for the test points
numpy.testing.assert_almost_equal(mu_test, y_test, decimal=1)
def test_incremental_update():
def f(x):
return anp.sin(x) / x
numpy.random.seed(298424)
std_noise = 0.01
# Sample data
features_list = []
targets_list = []
num_incr_list = []
for rep in range(10):
num_train = anp.random.randint(low=5, high=15)
num_incr = anp.random.randint(low=1, high=7)
num_incr_list.append(num_incr)
sizes = [num_train, num_incr]
features = []
targets = []
for sz in sizes:
feats = anp.random.uniform(low=-1.0, high=1.0, size=sz).reshape(
(-1, 1))
features.append(feats)
targs = f(feats)
targs += anp.random.normal(0.0, std_noise, size=targs.shape)
targets.append(targs)
features_list.append(features)
targets_list.append(targets)
for rep in range(10):
model = GaussianProcessRegression(kernel=Matern52(dimension=1))
features = features_list[rep]
targets = targets_list[rep]
# Posterior state by incremental updating
train_features = features[0]
train_targets = 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))
num_incr = num_incr_list[rep]
for i in range(num_incr):
state_incr = state_incr.update(features[1][i].reshape((1, -1)),
targets[1][i].reshape((1, -1)))
noise_variance_2 = state_incr.noise_variance[0]
# Posterior state by direct computation
state_comp = GaussProcPosteriorState(
features=anp.concatenate(features, axis=0),
targets=anp.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
chol_fact_comp = state_comp.chol_fact
numpy.testing.assert_almost_equal(chol_fact_incr,
chol_fact_comp,
decimal=2)
pred_mat_incr = state_incr.pred_mat
pred_mat_comp = state_comp.pred_mat
numpy.testing.assert_almost_equal(pred_mat_incr,
pred_mat_comp,
decimal=2)