def testSamples(self):
"""Tests that samples follow Ornstein-Uhlenbeck process.
This is done by checking that the successive differences
`x_next - (1-theta) * x` have the expected mean and variance.
"""
# Increasing the number of samples can help reduce the variance and make the
# sample mean closer to the distribution mean.
num_samples = 1000
theta, sigma = 0.1, 0.2
ou = common.ornstein_uhlenbeck_process(tf.zeros([10]),
damping=theta,
stddev=sigma)
samples = np.ndarray([num_samples, 10])
self.evaluate(tf.compat.v1.global_variables_initializer())
for i in range(num_samples):
samples[i] = self.evaluate(ou)
diffs = np.ndarray([num_samples - 1, 10])
for i in range(num_samples - 1):
diffs[i] = samples[i + 1] - (1 - theta) * samples[i]
flat_diffs = diffs.reshape([-1])
mean, variance = flat_diffs.mean(), flat_diffs.var()
# To avoid flakiness, we can only expect the sample statistics to match
# the population statistics to one or two decimal places.
self.assertAlmostEqual(mean, 0.0, places=1)
self.assertAlmostEqual(variance, sigma * sigma, places=2)
def testMultipleSamples(self):
"""Tests that creates different samples.
"""
theta, sigma = 0.1, 0.2
ou1 = common.ornstein_uhlenbeck_process(
tf.zeros([10]), damping=theta, stddev=sigma)
ou2 = common.ornstein_uhlenbeck_process(
tf.zeros([10]), damping=theta, stddev=sigma)
samples = np.ndarray([100, 10, 2])
self.evaluate(tf.compat.v1.global_variables_initializer())
for i in range(100):
samples[i, :, 0], samples[i, :, 1] = self.evaluate([ou1, ou2])
diffs = samples[:, :, 0] - samples[:, :, 1]
difference = np.absolute(diffs).mean()
self.assertGreater(difference, 0.0)
