def testSampleGammaLogSpace(self):
concentration = np.linspace(.1, 2., 10)
rate = np.linspace(.5, 2, 10)
np.random.shuffle(rate)
num_samples = int(1e5)
self.assertLess(
self.evaluate(
st.min_num_samples_for_dkwm_cdf_test(discrepancy=0.04,
false_fail_rate=1e-9,
false_pass_rate=1e-9)),
num_samples)
samples = gamma_lib.random_gamma([num_samples],
concentration,
rate,
seed=test_util.test_seed(),
log_space=True)
exp_gamma = tfb.Log()(tfd.Gamma(concentration=concentration,
rate=rate,
validate_args=True))
self.evaluate(
st.assert_true_cdf_equal_by_dkwm(samples,
exp_gamma.cdf,
false_fail_rate=1e-9))
self.assertAllClose(self.evaluate(tf.math.reduce_mean(samples,
axis=0)),
tf.math.digamma(concentration) - tf.math.log(rate),
rtol=0.02,
atol=0.01)
self.assertAllClose(self.evaluate(
tf.math.reduce_variance(samples, axis=0)),
tf.math.polygamma(1., concentration),
rtol=0.05)
def testSamplePoissonHighRates(self):
# High rate (>= log(10.)) samples would use rejection sampling.
rate = [10., 10.5, 11., 11.5, 12.0, 12.5, 13.0, 13.5, 14.0, 14.5]
log_rate = np.log(rate)
num_samples = int(1e5)
self.assertLess(
self.evaluate(
st.min_num_samples_for_dkwm_cdf_test(discrepancy=0.04,
false_fail_rate=1e-9,
false_pass_rate=1e-9)),
num_samples)
samples = poisson_lib._random_poisson_noncpu(
shape=[num_samples],
log_rates=log_rate,
output_dtype=tf.float64,
seed=test_util.test_seed())
poisson = tfd.Poisson(log_rate=log_rate, validate_args=True)
self.evaluate(
st.assert_true_cdf_equal_by_dkwm(
samples,
poisson.cdf,
st.left_continuous_cdf_discrete_distribution(poisson),
false_fail_rate=1e-9))
self.assertAllClose(self.evaluate(tf.math.reduce_mean(samples,
axis=0)),
stats.poisson.mean(rate),
rtol=0.01)
self.assertAllClose(self.evaluate(
tf.math.reduce_variance(samples, axis=0)),
stats.poisson.var(rate),
rtol=0.05)
def testSampleGammaHighConcentration(self):
concentration = np.linspace(10., 20., 10)
rate = np.float64(1.)
num_samples = int(1e5)
self.assertLess(
self.evaluate(
st.min_num_samples_for_dkwm_cdf_test(discrepancy=0.04,
false_fail_rate=1e-9,
false_pass_rate=1e-9)),
num_samples)
samples = gamma_lib._random_gamma_noncpu(shape=[num_samples, 10],
concentration=concentration,
rate=rate,
seed=test_util.test_seed())
gamma = tfd.Gamma(concentration=concentration,
rate=rate,
validate_args=True)
self.evaluate(
st.assert_true_cdf_equal_by_dkwm(samples,
gamma.cdf,
false_fail_rate=1e-9))
self.assertAllClose(self.evaluate(tf.math.reduce_mean(samples,
axis=0)),
sp_stats.gamma.mean(concentration, scale=1 / rate),
rtol=0.01)
self.assertAllClose(self.evaluate(
tf.math.reduce_variance(samples, axis=0)),
sp_stats.gamma.var(concentration, scale=1 / rate),
rtol=0.05)
def testSampleGammaLogRateLogSpaceDerivatives(self):
conc = tf.constant(np.linspace(.8, 1.2, 5), tf.float64)
rate = np.linspace(.5, 2, 5)
np.random.shuffle(rate)
rate = tf.constant(rate, tf.float64)
n = int(1e5)
seed = test_util.test_seed()
# pylint: disable=g-long-lambda
lambdas = [ # Each should sample the same distribution.
lambda c, r: gamma_lib.random_gamma(
[n], c, r, seed=seed, log_space=True),
lambda c, r: gamma_lib.random_gamma(
[n], c, log_rate=tf.math.log(r), seed=seed, log_space=True),
lambda c, r: tf.math.log(gamma_lib.random_gamma(
[n], c, r, seed=seed)),
lambda c, r: tf.math.log(gamma_lib.random_gamma(
[n], c, log_rate=tf.math.log(r), seed=seed)),
]
# pylint: enable=g-long-lambda
samps = []
dconc = []
drate = []
for fn in lambdas:
# Take samples without the nonlinearity.
samps.append(fn(conc, rate))
# We compute gradient through a nonlinearity to catch a class of errors.
_, (dc_i, dr_i) = tfp.math.value_and_gradient(
lambda c, r: tf.reduce_mean(tf.square(fn(c, r))), (conc, rate)) # pylint: disable=cell-var-from-loop
dconc.append(dc_i)
drate.append(dr_i)
# Assert d rate correctness. Note that the non-logspace derivative for rate
# depends on the realized sample whereas the logspace one does not. Also,
# comparing grads with differently-placed log/exp is numerically perilous.
self.assertAllClose(drate[0], drate[1], rtol=0.06)
self.assertAllClose(drate[0], drate[2], rtol=0.06)
self.assertAllClose(drate[1], drate[3], rtol=0.06)
# Assert sample correctness. If incorrect, dconc will be incorrect.
self.assertLess(
self.evaluate(
st.min_num_samples_for_dkwm_cdf_test(
discrepancy=0.04, false_fail_rate=1e-9, false_pass_rate=1e-9)),
n)
equiv_dist = tfb.Log()(tfd.Gamma(conc, rate))
self.evaluate(st.assert_true_cdf_equal_by_dkwm(
samps[0], equiv_dist.cdf, false_fail_rate=1e-9))
self.evaluate(st.assert_true_cdf_equal_by_dkwm(
samps[1], equiv_dist.cdf, false_fail_rate=1e-9))
self.evaluate(st.assert_true_cdf_equal_by_dkwm(
samps[2], equiv_dist.cdf, false_fail_rate=1e-9))
self.evaluate(st.assert_true_cdf_equal_by_dkwm(
samps[3], equiv_dist.cdf, false_fail_rate=1e-9))
# Assert d concentration correctness. These are sensitive to sample values,
# which are more strongly effected by the log/exp, thus looser tolerances.
self.assertAllClose(dconc[0], dconc[1], rtol=0.06)
self.assertAllClose(dconc[0], dconc[2], rtol=0.06)
self.assertAllClose(dconc[1], dconc[3], rtol=0.06)
def testXLAFriendlySampler(self):
if tf.executing_eagerly():
msg = 'XLA requires tf.function, mode switching is meaningless.'
self.skipTest(msg)
dist = tfd.BetaBinomial(total_count=50,
concentration0=1e-7,
concentration1=1e-5)
seed = test_util.test_seed(sampler_type='stateless')
num_samples = 20000
sample = self.evaluate(
tf.function(jit_compile=True)(dist.sample)(num_samples, seed=seed))
self.assertAllEqual(np.zeros_like(sample), np.isnan(sample))
# Beta(1e-7, 1e-5) should basically always be either 1 or 0, and 1 should
# occur with probability 100/101.
# Ergo, the beta binomial samples should basically always be either 50 or 0,
# and 50 should occur with probability 100/101.
high_samples_mask = sample == 50
low_samples_mask = sample == 0
self.assertAllEqual(np.ones_like(sample),
high_samples_mask | low_samples_mask)
expect = tfd.Bernoulli(probs=100.0 / 101.0)
self.evaluate(
st.assert_true_cdf_equal_by_dkwm(
samples=tf.cast(high_samples_mask, tf.float32),
cdf=expect.cdf,
left_continuous_cdf=st.
left_continuous_cdf_discrete_distribution(expect),
false_fail_rate=1e-9))
self.assertGreater(
num_samples,
self.evaluate(
st.min_num_samples_for_dkwm_cdf_test(0.05,
false_fail_rate=1e-9,
false_pass_rate=1e-9)))
def propSampleCorrectMarginals(self,
dist,
special_class,
under_hypothesis=False):
# Property: When projected on one class, multinomial should sample the
# binomial distribution.
seed = test_util.test_seed()
num_samples = 120000
needed = self.evaluate(
st.min_num_samples_for_dkwm_cdf_test(0.02,
false_fail_rate=1e-9,
false_pass_rate=1e-9))
self.assertGreater(num_samples, needed)
samples = dist.sample(num_samples, seed=seed)
successes = samples[..., special_class]
prob_success = dist._probs_parameter_no_checks()[..., special_class]
if under_hypothesis:
hp.note('Expected probability of success {}'.format(prob_success))
hp.note('Successes obtained {}'.format(successes))
expected_dist = tfd.Binomial(dist.total_count, probs=prob_success)
self.evaluate(
st.assert_true_cdf_equal_by_dkwm(
successes,
expected_dist.cdf,
st.left_continuous_cdf_discrete_distribution(expected_dist),
false_fail_rate=1e-9))
def testSampleHighConcentration(self):
concentration = np.linspace(10., 20., 10)
rate = np.float64(1.)
num_samples = int(1e5)
self.assertLess(
self.evaluate(
st.min_num_samples_for_dkwm_cdf_test(discrepancy=0.04,
false_fail_rate=1e-9,
false_pass_rate=1e-9)),
num_samples)
d = tfd.ExpGamma(concentration=concentration,
rate=rate,
validate_args=True)
samples = d.sample(num_samples, seed=test_util.test_seed())
self.evaluate(
st.assert_true_cdf_equal_by_dkwm(samples,
d.cdf,
false_fail_rate=1e-9))
self.assertAllClose(self.evaluate(tf.math.reduce_mean(samples,
axis=0)),
d.mean(),
rtol=0.01)
self.assertAllClose(self.evaluate(
tf.math.reduce_variance(samples, axis=0)),
d.variance(),
rtol=0.05)
def testSamplePoissonLowAndHighRates(self):
rate = [1., 3., 5., 6., 7., 10., 13.0, 14., 15., 18.]
log_rate = np.log(rate)
num_samples = int(1e5)
self.assertLess(
self.evaluate(
st.min_num_samples_for_dkwm_cdf_test(discrepancy=0.04,
false_fail_rate=1e-9,
false_pass_rate=1e-9)),
num_samples)
samples = self.evaluate(
poisson_dist.random_poisson_rejection_sampler(
[num_samples, 10], log_rate, seed=test_util.test_seed()))
poisson = tfd.Poisson(log_rate=log_rate, validate_args=True)
self.evaluate(
st.assert_true_cdf_equal_by_dkwm(
samples,
poisson.cdf,
st.left_continuous_cdf_discrete_distribution(poisson),
false_fail_rate=1e-9))
self.assertAllClose(self.evaluate(tf.math.reduce_mean(samples,
axis=0)),
stats.poisson.mean(rate),
rtol=0.01)
self.assertAllClose(self.evaluate(
tf.math.reduce_variance(samples, axis=0)),
stats.poisson.var(rate),
rtol=0.05)
def testSamplePoissonLowRates(self):
# Low log rate (< log(10.)) samples would use Knuth's algorithm.
rate = [1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5]
log_rate = np.log(rate)
num_samples = int(1e5)
self.assertLess(
self.evaluate(
st.min_num_samples_for_dkwm_cdf_test(discrepancy=0.04,
false_fail_rate=1e-9,
false_pass_rate=1e-9)),
num_samples)
samples = self.evaluate(
poisson_dist.random_poisson_rejection_sampler(
[num_samples, 10], log_rate, seed=test_util.test_seed()))
poisson = tfd.Poisson(log_rate=log_rate, validate_args=True)
self.evaluate(
st.assert_true_cdf_equal_by_dkwm(
samples,
poisson.cdf,
st.left_continuous_cdf_discrete_distribution(poisson),
false_fail_rate=1e-9))
self.assertAllClose(self.evaluate(tf.math.reduce_mean(samples,
axis=0)),
stats.poisson.mean(rate),
rtol=0.01)
self.assertAllClose(self.evaluate(
tf.math.reduce_variance(samples, axis=0)),
stats.poisson.var(rate),
rtol=0.05)
def VerifySampleAndPdfConsistency(self, uniform):
"""Verifies samples are consistent with the PDF using importance sampling.
In particular, we verify an estimate the surface area of the n-dimensional
hypersphere, and the surface areas of the spherical caps demarcated by
a handful of survival rates.
Args:
uniform: A `SphericalUniform` distribution instance.
"""
dim = tf.compat.dimension_value(uniform.event_shape[-1])
nsamples = int(6e4)
self.assertLess(
self.evaluate(
st.min_num_samples_for_dkwm_cdf_test(discrepancy=0.04,
false_fail_rate=1e-9,
false_pass_rate=1e-9)),
nsamples)
samples = uniform.sample(sample_shape=[nsamples],
seed=test_util.test_seed())
samples = tf.debugging.check_numerics(samples, 'samples')
log_prob = uniform.log_prob(samples)
log_prob = self.evaluate(
tf.debugging.check_numerics(log_prob, 'log_prob'))
true_sphere_surface_area = 2 * (np.pi)**(dim / 2) * self.evaluate(
tf.exp(-tf.math.lgamma(dim / 2)))
true_sphere_surface_area += np.zeros_like(log_prob)
# Check the log prob is a constant and is the reciprocal of the surface
# area.
self.assertAllClose(np.exp(log_prob), 1. / true_sphere_surface_area)
# For sampling, let's check the marginals. x_i**2 ~ Beta(0.5, d - 1 / 2)
beta_dist = tfp.distributions.Beta(self.dtype(0.5),
self.dtype((dim - 1.) / 2.))
for i in range(dim):
self.evaluate(
st.assert_true_cdf_equal_by_dkwm(samples[..., i]**2,
cdf=beta_dist.cdf,
false_fail_rate=1e-9))
def testSamplePoissonLowAndHighRates(self):
rate = [1., 3., 5., 6., 7., 10., 13.0, 14., 15., 18.]
log_rate = np.log(rate)
num_samples = int(1e5)
poisson = tfd.Poisson(log_rate=log_rate, validate_args=True)
self.assertLess(
self.evaluate(
st.min_num_samples_for_dkwm_cdf_test(
discrepancy=0.04, false_fail_rate=1e-9, false_pass_rate=1e-9)),
num_samples)
samples = poisson_lib._random_poisson_noncpu(
shape=[num_samples],
log_rates=log_rate,
output_dtype=tf.float64,
seed=test_util.test_seed())
self.evaluate(
st.assert_true_cdf_equal_by_dkwm(
samples,
poisson.cdf,
st.left_continuous_cdf_discrete_distribution(poisson),
false_fail_rate=1e-9))
def testSampleMarginals(self):
# Verify that the marginals of the LKJ distribution are distributed
# according to a (scaled) Beta distribution. The LKJ distributed samples are
# obtained by sampling a CholeskyLKJ distribution using HMC and the
# CorrelationCholesky bijector.
dim = 4
concentration = np.array(2.5, dtype=np.float64)
beta_concentration = np.array(.5 * dim + concentration - 1, np.float64)
beta_dist = beta.Beta(
concentration0=beta_concentration, concentration1=beta_concentration)
inner_kernel = hmc.HamiltonianMonteCarlo(
target_log_prob_fn=cholesky_lkj.CholeskyLKJ(
dimension=dim, concentration=concentration).log_prob,
num_leapfrog_steps=3,
step_size=0.3)
kernel = transformed_kernel.TransformedTransitionKernel(
inner_kernel=inner_kernel, bijector=tfb.CorrelationCholesky())
num_chains = 10
num_total_samples = 30000
# Make sure that we have enough samples to catch a wrong sampler to within
# a small enough discrepancy.
self.assertLess(
self.evaluate(
st.min_num_samples_for_dkwm_cdf_test(
discrepancy=0.04, false_fail_rate=1e-9, false_pass_rate=1e-9)),
num_total_samples)
@tf.function # Ensure that MCMC sampling is done efficiently.
def sample_mcmc_chain():
return sample.sample_chain(
num_results=num_total_samples // num_chains,
num_burnin_steps=1000,
current_state=tf.eye(dim, batch_shape=[num_chains], dtype=tf.float64),
trace_fn=lambda _, pkr: pkr.inner_results.is_accepted,
kernel=kernel,
seed=test_util.test_seed())
# Draw samples from the HMC chains.
chol_lkj_samples, is_accepted = self.evaluate(sample_mcmc_chain())
# Ensure that the per-chain acceptance rate is high enough.
self.assertAllGreater(np.mean(is_accepted, axis=0), 0.8)
# Transform from Cholesky LKJ samples to LKJ samples.
lkj_samples = tf.matmul(chol_lkj_samples, chol_lkj_samples, adjoint_b=True)
lkj_samples = tf.reshape(lkj_samples, shape=[num_total_samples, dim, dim])
# Only look at the entries strictly below the diagonal which is achieved by
# the OutputToUnconstrained bijector. Also scale the marginals from the
# range [-1,1] to [0,1].
scaled_lkj_samples = .5 * (OutputToUnconstrained().forward(lkj_samples) + 1)
# Each of the off-diagonal marginals should be distributed according to a
# Beta distribution.
for i in range(dim * (dim - 1) // 2):
self.evaluate(
st.assert_true_cdf_equal_by_dkwm(
scaled_lkj_samples[..., i],
cdf=beta_dist.cdf,
false_fail_rate=1e-9))
