def test_radial_basis_function_kernel(
x1, x2, amplitude, length_scale, exact
) -> None:
tol = 1e-5
batch_size = amplitude.shape[0]
history_length_1 = x1.shape[0]
history_length_2 = x2.shape[0]
num_features = x1.shape[1]
if batch_size > 1:
x1 = nd.tile(x1, reps=(batch_size, 1, 1))
x2 = nd.tile(x2, reps=(batch_size, 1, 1))
for i in range(1, batch_size):
x1[i, :, :] = (i + 1) * x1[i, :, :]
x2[i, :, :] = (i - 3) * x2[i, :, :]
else:
x1 = x1.reshape(batch_size, history_length_1, num_features)
x2 = x2.reshape(batch_size, history_length_2, num_features)
amplitude = amplitude.reshape(batch_size, 1, 1)
length_scale = length_scale.reshape(batch_size, 1, 1)
rbf = RBFKernel(amplitude, length_scale)
exact = amplitude * nd.exp(-0.5 * exact / length_scale ** 2)
res = rbf.kernel_matrix(x1, x2)
assert nd.norm(exact - res) < tol
def test_jitter_synthetic(
jitter_method, float_type, ctx=mx.Context('cpu')
) -> None:
# Initialize problem parameters
batch_size = 1
prediction_length = 50
context_length = 5
num_samples = 3
# Initialize test data to generate Gaussian Process from
lb = -5
ub = 5
dx = (ub - lb) / (prediction_length - 1)
x_test = nd.arange(lb, ub + dx, dx, ctx=ctx, dtype=float_type).reshape(
-1, 1
)
x_test = nd.tile(x_test, reps=(batch_size, 1, 1))
# Define the GP hyper parameters
amplitude = nd.ones((batch_size, 1, 1), ctx=ctx, dtype=float_type)
length_scale = math.sqrt(0.4) * nd.ones_like(amplitude)
sigma = math.sqrt(1e-5) * nd.ones_like(amplitude)
# Instantiate desired kernel object and compute kernel matrix
rbf_kernel = RBFKernel(amplitude, length_scale)
# Generate samples from 0 mean Gaussian process with RBF Kernel and plot it
gp = GaussianProcess(
sigma=sigma,
kernel=rbf_kernel,
prediction_length=prediction_length,
context_length=context_length,
num_samples=num_samples,
ctx=ctx,
float_type=float_type,
jitter_method=jitter_method,
sample_noise=False, # Returns sample without noise
)
# Generate training set on subset of interval using the sine function
x_train = nd.array([-4, -3, -2, -1, 1], ctx=ctx, dtype=float_type).reshape(
context_length, 1
)
x_train = nd.tile(x_train, reps=(batch_size, 1, 1))
y_train = nd.sin(x_train.squeeze(axis=2))
# Predict exact GP using the GP predictive mean and covariance using the same fixed hyper-parameters
samples, predictive_mean, predictive_std = gp.exact_inference(
x_train, y_train, x_test
)
assert (
np.sum(np.isnan(samples.asnumpy())) == 0
), 'NaNs in predictive samples!'
def test_inference(gp_params, mean_exact, std_exact, x_full, y_train) -> None:
# Initialize problem parameters
tol = 1e-2
num_samples = 100
context_length = y_train.shape[1]
prediction_length = mean_exact.shape[1]
# Extract training and test set
x_train = x_full[:, :context_length, :]
x_test = x_full[:, context_length : context_length + prediction_length, :]
amplitude = gp_params[:, 0, :].expand_dims(axis=2)
length_scale = gp_params[:, 1, :].expand_dims(axis=2)
sigma = gp_params[:, 2, :].expand_dims(axis=2)
# Instantiate RBFKernel with its hyper-parameters
kernel = RBFKernel(amplitude, length_scale)
# Instantiate gp_inference object and hybridize
gp = GaussianProcess(
sigma=sigma,
kernel=kernel,
context_length=context_length,
prediction_length=prediction_length,
num_samples=num_samples,
float_type=np.float32,
)
# Compute predictive mean and covariance
_, mean, std = gp.exact_inference(x_train, y_train, x_test)
# This test compares to the predictive mean and std generated from MATLAB's fitrgp, which
# outputs the sample with the noise, i.e. adds :math:`sigma^2` to the diagonal of
# the predictive covariance matrix.
assert relative_error(mean, mean_exact) <= tol
assert relative_error(std, std_exact) <= tol
def main():
# Initialize problem parameters
batch_size = 1
prediction_length = 50
context_length = 5
axis = [-5, 5, -3, 3]
float_type = np.float64
ctx = mx.Context("gpu")
num_samples = 3
ts_idx = 0
# Initialize test data to generate Gaussian Process from
lb = -5
ub = 5
dx = (ub - lb) / (prediction_length - 1)
x_test = nd.arange(lb, ub + dx, dx, ctx=ctx,
dtype=float_type).reshape(-1, 1)
x_test = nd.tile(x_test, reps=(batch_size, 1, 1))
# Define the GP hyper parameters
amplitude = nd.ones((batch_size, 1, 1), ctx=ctx, dtype=float_type)
length_scale = math.sqrt(0.4) * nd.ones_like(amplitude)
sigma = math.sqrt(1e-5) * nd.ones_like(amplitude)
# Instantiate desired kernel object and compute kernel matrix
rbf_kernel = RBFKernel(amplitude, length_scale)
# Generate samples from 0 mean Gaussian process with RBF Kernel and plot it
gp = GaussianProcess(
sigma=sigma,
kernel=rbf_kernel,
prediction_length=prediction_length,
context_length=context_length,
num_samples=num_samples,
ctx=ctx,
float_type=float_type,
sample_noise=False, # Returns sample without noise
)
mean = nd.zeros((batch_size, prediction_length), ctx=ctx, dtype=float_type)
covariance = rbf_kernel.kernel_matrix(x_test, x_test)
gp.plot(x_test=x_test, samples=gp.sample(mean, covariance), ts_idx=ts_idx)
# Generate training set on subset of interval using the sine function
x_train = nd.array([-4, -3, -2, -1, 1], ctx=ctx,
dtype=float_type).reshape(context_length, 1)
x_train = nd.tile(x_train, reps=(batch_size, 1, 1))
y_train = nd.sin(x_train.squeeze(axis=2))
# Predict exact GP using the GP predictive mean and covariance using the same fixed hyper-parameters
samples, predictive_mean, predictive_std = gp.exact_inference(
x_train, y_train, x_test)
assert (np.sum(np.isnan(
samples.asnumpy())) == 0), "NaNs in predictive samples!"
gp.plot(
x_train=x_train,
y_train=y_train,
x_test=x_test,
ts_idx=ts_idx,
mean=predictive_mean,
std=predictive_std,
samples=samples,
axis=axis,
)