class DeltaMethodAnalyticalExpectedGrads(chex.TestCase):
@chex.all_variants
@parameterized.named_parameters(
chex.params_product([
('_score_function_jacobians', 1.0, 1.0, sge.score_function_jacobians),
('_pathwise_jacobians', 1.0, 1.0, sge.pathwise_jacobians),
('_measure_valued_jacobians', 1.0, 1.0, sge.measure_valued_jacobians),
], [
('estimate_cv_coeffs', True),
('no_estimate_cv_coeffs', False),
],
named=True))
def testQuadraticFunction(self, effective_mean, effective_log_scale,
grad_estimator, estimate_cv_coeffs):
data_dims = 3
num_samples = 10**3
mean = effective_mean * jnp.ones(shape=(data_dims), dtype=jnp.float32)
log_scale = effective_log_scale * jnp.ones(
shape=(data_dims), dtype=jnp.float32)
params = [mean, log_scale]
function = lambda x: jnp.sum(x**2)
rng = jax.random.PRNGKey(1)
jacobians = _cv_jac_variant(self.variant)(
function,
control_variates.control_delta_method,
grad_estimator,
params,
utils.multi_normal, # dist_builder
rng,
num_samples,
None, # No cv state.
estimate_cv_coeffs)[0]
expected_mean_grads = 2 * effective_mean * np.ones(
data_dims, dtype=np.float32)
expected_log_scale_grads = 2 * np.exp(2 * effective_log_scale) * np.ones(
data_dims, dtype=np.float32)
mean_jacobians = jacobians[0]
chex.assert_shape(mean_jacobians, (num_samples, data_dims))
mean_grads_from_jacobian = jnp.mean(mean_jacobians, axis=0)
log_scale_jacobians = jacobians[1]
chex.assert_shape(log_scale_jacobians, (num_samples, data_dims))
log_scale_grads_from_jacobian = jnp.mean(log_scale_jacobians, axis=0)
_assert_equal(mean_grads_from_jacobian, expected_mean_grads,
rtol=1e-1, atol=1e-3)
_assert_equal(log_scale_grads_from_jacobian, expected_log_scale_grads,
rtol=1e-1, atol=1e-3)
@chex.all_variants
@parameterized.named_parameters(
chex.params_product([
('_score_function_jacobians', 1.0, 1.0, sge.score_function_jacobians),
('_pathwise_jacobians', 1.0, 1.0, sge.pathwise_jacobians),
('_measure_valued_jacobians', 1.0, 1.0, sge.measure_valued_jacobians),
], [
('estimate_cv_coeffs', True),
('no_estimate_cv_coeffs', False),
],
named=True))
def testCubicFunction(
self, effective_mean, effective_log_scale, grad_estimator,
estimate_cv_coeffs):
data_dims = 1
num_samples = 10**5
mean = effective_mean * jnp.ones(shape=(data_dims), dtype=jnp.float32)
log_scale = effective_log_scale * jnp.ones(
shape=(data_dims), dtype=jnp.float32)
params = [mean, log_scale]
function = lambda x: jnp.sum(x**3)
rng = jax.random.PRNGKey(1)
jacobians = _cv_jac_variant(self.variant)(
function,
control_variates.control_delta_method,
grad_estimator,
params,
utils.multi_normal,
rng,
num_samples,
None, # No cv state.
estimate_cv_coeffs)[0]
# The third order uncentered moment of the Gaussian distribution is
# mu**3 + 2 mu * sigma **2. We use that to compute the expected value
# of the gradients. Note: for the log scale we need use the chain rule.
expected_mean_grads = (
3 * effective_mean**2 + 3 * np.exp(effective_log_scale)**2)
expected_mean_grads *= np.ones(data_dims, dtype=np.float32)
expected_log_scale_grads = (
6 * effective_mean * np.exp(effective_log_scale) ** 2)
expected_log_scale_grads *= np.ones(data_dims, dtype=np.float32)
mean_jacobians = jacobians[0]
chex.assert_shape(mean_jacobians, (num_samples, data_dims))
mean_grads_from_jacobian = jnp.mean(mean_jacobians, axis=0)
log_scale_jacobians = jacobians[1]
chex.assert_shape(log_scale_jacobians, (num_samples, data_dims))
log_scale_grads_from_jacobian = jnp.mean(log_scale_jacobians, axis=0)
_assert_equal(mean_grads_from_jacobian, expected_mean_grads,
rtol=1e-1, atol=1e-3)
_assert_equal(log_scale_grads_from_jacobian, expected_log_scale_grads,
rtol=1e-1, atol=1e-3)
@chex.all_variants
@parameterized.named_parameters(
chex.params_product([
('_score_function_jacobians', 1.0, 1.0, sge.score_function_jacobians),
('_pathwise_jacobians', 1.0, 1.0, sge.pathwise_jacobians),
('_measure_valued_jacobians', 1.0, 1.0, sge.measure_valued_jacobians),
], [
('estimate_cv_coeffs', True),
('no_estimate_cv_coeffs', False),
],
named=True))
def testForthPowerFunction(
self, effective_mean, effective_log_scale, grad_estimator,
estimate_cv_coeffs):
data_dims = 1
num_samples = 10**5
mean = effective_mean * jnp.ones(shape=(data_dims), dtype=jnp.float32)
log_scale = effective_log_scale * jnp.ones(
shape=(data_dims), dtype=jnp.float32)
params = [mean, log_scale]
function = lambda x: jnp.sum(x**4)
rng = jax.random.PRNGKey(1)
jacobians = _cv_jac_variant(self.variant)(
function,
control_variates.control_delta_method,
grad_estimator,
params,
utils.multi_normal,
rng,
num_samples,
None, # No cv state
estimate_cv_coeffs)[0]
# The third order uncentered moment of the Gaussian distribution is
# mu**4 + 6 mu **2 sigma **2 + 3 sigma**4. We use that to compute the
# expected value of the gradients.
# Note: for the log scale we need use the chain rule.
expected_mean_grads = (
3 * effective_mean**3
+ 12 * effective_mean * np.exp(effective_log_scale)**2)
expected_mean_grads *= np.ones(data_dims, dtype=np.float32)
expected_log_scale_grads = 12 * (
effective_mean**2 * np.exp(effective_log_scale) +
np.exp(effective_log_scale) ** 3) * np.exp(effective_log_scale)
expected_log_scale_grads *= np.ones(data_dims, dtype=np.float32)
mean_jacobians = jacobians[0]
chex.assert_shape(mean_jacobians, (num_samples, data_dims))
mean_grads_from_jacobian = jnp.mean(mean_jacobians, axis=0)
log_scale_jacobians = jacobians[1]
chex.assert_shape(log_scale_jacobians, (num_samples, data_dims))
log_scale_grads_from_jacobian = jnp.mean(log_scale_jacobians, axis=0)
_assert_equal(mean_grads_from_jacobian, expected_mean_grads,
rtol=1e-1, atol=1e-3)
_assert_equal(log_scale_grads_from_jacobian, expected_log_scale_grads,
rtol=1e-1, atol=1e-3)
class ConsistencyWithStandardEstimators(chex.TestCase):
@chex.all_variants
@parameterized.named_parameters(
chex.params_product([
('_score_function_jacobians', 1, 1, sge.score_function_jacobians,
10**6),
('_pathwise_jacobians', 1, 1, sge.pathwise_jacobians, 10**5),
('_measure_valued_jacobians', 1, 1, sge.measure_valued_jacobians,
10**5),
], [
('control_delta_method', control_variates.control_delta_method),
('moving_avg_baseline', control_variates.moving_avg_baseline),
],
named=True))
def testWeightedLinearFunction(self, effective_mean, effective_log_scale,
grad_estimator, num_samples,
control_variate_from_function):
"""Check that the gradients are consistent between estimators."""
weights = jnp.array([1., 2., 3.], dtype=jnp.float32)
data_dims = len(weights)
mean = effective_mean * jnp.ones(shape=(data_dims), dtype=jnp.float32)
log_scale = effective_log_scale * jnp.ones(
shape=(data_dims), dtype=jnp.float32)
params = [mean, log_scale]
function = lambda x: jnp.sum(weights * x)
rng = jax.random.PRNGKey(1)
cv_rng, ge_rng = jax.random.split(rng)
jacobians = _cv_jac_variant(self.variant)(
function,
control_variate_from_function,
grad_estimator,
params,
utils.multi_normal, # dist_builder
cv_rng, # rng
num_samples,
(0., 0), # control_variate_state
False)[0]
mean_jacobians = jacobians[0]
chex.assert_shape(mean_jacobians, (num_samples, data_dims))
mean_grads = jnp.mean(mean_jacobians, axis=0)
log_scale_jacobians = jacobians[1]
chex.assert_shape(log_scale_jacobians, (num_samples, data_dims))
log_scale_grads = jnp.mean(log_scale_jacobians, axis=0)
# We use a different random number generator for the gradient estimator
# without the control variate.
no_cv_jacobians = grad_estimator(
function, [mean, log_scale],
utils.multi_normal, ge_rng, num_samples=num_samples)
no_cv_mean_jacobians = no_cv_jacobians[0]
chex.assert_shape(no_cv_mean_jacobians, (num_samples, data_dims))
no_cv_mean_grads = jnp.mean(no_cv_mean_jacobians, axis=0)
no_cv_log_scale_jacobians = no_cv_jacobians[1]
chex.assert_shape(no_cv_log_scale_jacobians, (num_samples, data_dims))
no_cv_log_scale_grads = jnp.mean(no_cv_log_scale_jacobians, axis=0)
_assert_equal(mean_grads, no_cv_mean_grads, rtol=1e-1, atol=5e-2)
_assert_equal(log_scale_grads, no_cv_log_scale_grads, rtol=1, atol=5e-2)
@chex.all_variants
@parameterized.named_parameters(
chex.params_product([
('_score_function_jacobians', 1, 1, sge.score_function_jacobians,
10**5),
('_pathwise_jacobians', 1, 1, sge.pathwise_jacobians, 10**5),
('_measure_valued_jacobians', 1, 1, sge.measure_valued_jacobians,
10**5),
], [
('control_delta_method', control_variates.control_delta_method),
('moving_avg_baseline', control_variates.moving_avg_baseline),
],
named=True))
def testNonPolynomialFunction(
self, effective_mean, effective_log_scale,
grad_estimator, num_samples, control_variate_from_function):
"""Check that the gradients are consistent between estimators."""
data_dims = 3
mean = effective_mean * jnp.ones(shape=(data_dims), dtype=jnp.float32)
log_scale = effective_log_scale * jnp.ones(
shape=(data_dims), dtype=jnp.float32)
params = [mean, log_scale]
function = lambda x: jnp.log(jnp.sum(x**2))
rng = jax.random.PRNGKey(1)
cv_rng, ge_rng = jax.random.split(rng)
jacobians = _cv_jac_variant(self.variant)(
function,
control_variate_from_function,
grad_estimator,
params,
utils.multi_normal,
cv_rng,
num_samples,
(0., 0), # control_variate_state
False)[0]
mean_jacobians = jacobians[0]
chex.assert_shape(mean_jacobians, (num_samples, data_dims))
mean_grads = jnp.mean(mean_jacobians, axis=0)
log_scale_jacobians = jacobians[1]
chex.assert_shape(log_scale_jacobians, (num_samples, data_dims))
log_scale_grads = jnp.mean(log_scale_jacobians, axis=0)
# We use a different random number generator for the gradient estimator
# without the control variate.
no_cv_jacobians = grad_estimator(
function, [mean, log_scale],
utils.multi_normal, ge_rng, num_samples=num_samples)
no_cv_mean_jacobians = no_cv_jacobians[0]
chex.assert_shape(no_cv_mean_jacobians, (num_samples, data_dims))
no_cv_mean_grads = jnp.mean(no_cv_mean_jacobians, axis=0)
no_cv_log_scale_jacobians = no_cv_jacobians[1]
chex.assert_shape(no_cv_log_scale_jacobians, (num_samples, data_dims))
no_cv_log_scale_grads = jnp.mean(no_cv_log_scale_jacobians, axis=0)
_assert_equal(mean_grads, no_cv_mean_grads, rtol=1e-1, atol=5e-2)
_assert_equal(log_scale_grads, no_cv_log_scale_grads, rtol=1e-1, atol=5e-2)
class GradientEstimatorsTest(chex.TestCase):
@chex.all_variants
@parameterized.named_parameters(
chex.params_product([
('_score_function_jacobians', sge.score_function_jacobians),
('_pathwise_jacobians', sge.pathwise_jacobians),
('_measure_valued_jacobians', sge.measure_valued_jacobians),
], [
('0.1', 0.1),
('0.5', 0.5),
('0.9', 0.9),
],
named=True))
def testConstantFunction(self, estimator, constant):
data_dims = 3
num_samples = _estimator_to_num_samples[estimator]
effective_mean = 1.5
mean = effective_mean * _ones(data_dims)
effective_log_scale = 0.0
log_scale = effective_log_scale * _ones(data_dims)
rng = jax.random.PRNGKey(1)
jacobians = _estimator_variant(self.variant, estimator)(
lambda x: jnp.array(constant), [mean, log_scale],
utils.multi_normal, rng, num_samples)
# Average over the number of samples.
mean_jacobians = jacobians[0]
chex.assert_shape(mean_jacobians, (num_samples, data_dims))
mean_grads = np.mean(mean_jacobians, axis=0)
expected_mean_grads = np.zeros(data_dims, dtype=np.float32)
log_scale_jacobians = jacobians[1]
chex.assert_shape(log_scale_jacobians, (num_samples, data_dims))
log_scale_grads = np.mean(log_scale_jacobians, axis=0)
expected_log_scale_grads = np.zeros(data_dims, dtype=np.float32)
_assert_equal(mean_grads, expected_mean_grads, atol=5e-3)
_assert_equal(log_scale_grads, expected_log_scale_grads, atol=5e-3)
@chex.all_variants
@parameterized.named_parameters(
chex.params_product([
('_score_function_jacobians', sge.score_function_jacobians),
('_pathwise_jacobians', sge.pathwise_jacobians),
('_measure_valued_jacobians', sge.measure_valued_jacobians),
], [
('0.5_-1.', 0.5, -1.),
('0.7_0.0)', 0.7, 0.0),
('0.8_0.1', 0.8, 0.1),
],
named=True))
def testLinearFunction(self, estimator, effective_mean,
effective_log_scale):
data_dims = 3
num_samples = _estimator_to_num_samples[estimator]
rng = jax.random.PRNGKey(1)
mean = effective_mean * _ones(data_dims)
log_scale = effective_log_scale * _ones(data_dims)
jacobians = _estimator_variant(self.variant,
estimator)(np.sum, [mean, log_scale],
utils.multi_normal, rng,
num_samples)
mean_jacobians = jacobians[0]
chex.assert_shape(mean_jacobians, (num_samples, data_dims))
mean_grads = np.mean(mean_jacobians, axis=0)
expected_mean_grads = np.ones(data_dims, dtype=np.float32)
log_scale_jacobians = jacobians[1]
chex.assert_shape(log_scale_jacobians, (num_samples, data_dims))
log_scale_grads = np.mean(log_scale_jacobians, axis=0)
expected_log_scale_grads = np.zeros(data_dims, dtype=np.float32)
_assert_equal(mean_grads, expected_mean_grads)
_assert_equal(log_scale_grads, expected_log_scale_grads)
@chex.all_variants
@parameterized.named_parameters(
chex.params_product([
('_score_function_jacobians', sge.score_function_jacobians),
('_pathwise_jacobians', sge.pathwise_jacobians),
('_measure_valued_jacobians', sge.measure_valued_jacobians),
], [
('1.0_0.3', 1.0, 0.3),
],
named=True))
def testQuadraticFunction(self, estimator, effective_mean,
effective_log_scale):
data_dims = 3
num_samples = _estimator_to_num_samples[estimator]
rng = jax.random.PRNGKey(1)
mean = effective_mean * _ones(data_dims)
log_scale = effective_log_scale * _ones(data_dims)
jacobians = _estimator_variant(self.variant,
estimator)(lambda x: np.sum(x**2) / 2,
[mean, log_scale],
utils.multi_normal, rng,
num_samples)
mean_jacobians = jacobians[0]
chex.assert_shape(mean_jacobians, (num_samples, data_dims))
mean_grads = np.mean(mean_jacobians, axis=0)
expected_mean_grads = effective_mean * np.ones(data_dims,
dtype=np.float32)
log_scale_jacobians = jacobians[1]
chex.assert_shape(log_scale_jacobians, (num_samples, data_dims))
log_scale_grads = np.mean(log_scale_jacobians, axis=0)
expected_log_scale_grads = np.exp(2 * effective_log_scale) * np.ones(
data_dims, dtype=np.float32)
_assert_equal(mean_grads, expected_mean_grads, atol=5e-2)
_assert_equal(log_scale_grads, expected_log_scale_grads, atol=5e-2)
@chex.all_variants
@parameterized.named_parameters(
chex.params_product([
('_score_function_jacobians', sge.score_function_jacobians),
('_pathwise_jacobians', sge.pathwise_jacobians),
('_measure_valued_jacobians', sge.measure_valued_jacobians),
], [
('case_1', [1.0, 2.0, 3.], [-1., 0.3, -2.], [1., 1., 1.]),
('case_2', [1.0, 2.0, 3.], [-1., 0.3, -2.], [4., 2., 3.]),
('case_3', [1.0, 2.0, 3.], [0.1, 0.2, 0.1], [10., 5., 1.]),
],
named=True))
def testWeightedLinear(self, estimator, effective_mean,
effective_log_scale, weights):
num_samples = _weighted_estimator_to_num_samples[estimator]
rng = jax.random.PRNGKey(1)
mean = jnp.array(effective_mean)
log_scale = jnp.array(effective_log_scale)
weights = jnp.array(weights)
data_dims = len(effective_mean)
function = lambda x: jnp.sum(x * weights)
jacobians = _estimator_variant(self.variant,
estimator)(function, [mean, log_scale],
utils.multi_normal, rng,
num_samples)
mean_jacobians = jacobians[0]
chex.assert_shape(mean_jacobians, (num_samples, data_dims))
mean_grads = np.mean(mean_jacobians, axis=0)
log_scale_jacobians = jacobians[1]
chex.assert_shape(log_scale_jacobians, (num_samples, data_dims))
log_scale_grads = np.mean(log_scale_jacobians, axis=0)
expected_mean_grads = weights
expected_log_scale_grads = np.zeros(data_dims, dtype=np.float32)
_assert_equal(mean_grads, expected_mean_grads, atol=5e-2)
_assert_equal(log_scale_grads, expected_log_scale_grads, atol=5e-2)
@chex.all_variants
@parameterized.named_parameters(
chex.params_product([
('_score_function_jacobians', sge.score_function_jacobians),
('_pathwise_jacobians', sge.pathwise_jacobians),
('_measure_valued_jacobians', sge.measure_valued_jacobians),
], [
('case_1', [1.0, 2.0, 3.], [-1., 0.3, -2.], [1., 1., 1.]),
('case_2', [1.0, 2.0, 3.], [-1., 0.3, -2.], [4., 2., 3.]),
('case_3', [1.0, 2.0, 3.], [0.1, 0.2, 0.1], [3., 5., 1.]),
],
named=True))
def testWeightedQuadratic(self, estimator, effective_mean,
effective_log_scale, weights):
num_samples = _weighted_estimator_to_num_samples[estimator]
rng = jax.random.PRNGKey(1)
mean = jnp.array(effective_mean, dtype=jnp.float32)
log_scale = jnp.array(effective_log_scale, dtype=jnp.float32)
weights = jnp.array(weights, dtype=jnp.float32)
data_dims = len(effective_mean)
function = lambda x: jnp.sum(x * weights)**2
jacobians = _estimator_variant(self.variant,
estimator)(function, [mean, log_scale],
utils.multi_normal, rng,
num_samples)
mean_jacobians = jacobians[0]
chex.assert_shape(mean_jacobians, (num_samples, data_dims))
mean_grads = np.mean(mean_jacobians, axis=0)
log_scale_jacobians = jacobians[1]
chex.assert_shape(log_scale_jacobians, (num_samples, data_dims))
log_scale_grads = np.mean(log_scale_jacobians, axis=0)
expected_mean_grads = 2 * weights * np.sum(weights * mean)
effective_scale = np.exp(log_scale)
expected_scale_grads = 2 * weights**2 * effective_scale
expected_log_scale_grads = expected_scale_grads * effective_scale
_assert_equal(mean_grads, expected_mean_grads, atol=1e-1, rtol=1e-1)
_assert_equal(log_scale_grads,
expected_log_scale_grads,
atol=1e-1,
rtol=1e-1)
@chex.all_variants
@parameterized.named_parameters(
chex.params_product(
[
('_sum_cos_x', [1.0], [1.0], lambda x: jnp.sum(jnp.cos(x))),
# Need to ensure that the mean is not too close to 0.
('_sum_log_x', [10.0], [0.0], lambda x: jnp.sum(jnp.log(x))),
('_sum_cos_2x', [1.0, 2.0], [1.0, -2],
lambda x: jnp.sum(jnp.cos(2 * x))),
('_cos_sum_2x', [1.0, 2.0], [1.0, -2],
lambda x: jnp.cos(jnp.sum(2 * x))),
],
[
('coupling', True),
('nocoupling', False),
],
named=True))
def testNonPolynomialFunctionConsistencyWithPathwise(
self, effective_mean, effective_log_scale, function, coupling):
num_samples = 10**5
rng = jax.random.PRNGKey(1)
measure_rng, pathwise_rng = jax.random.split(rng)
mean = jnp.array(effective_mean, dtype=jnp.float32)
log_scale = jnp.array(effective_log_scale, dtype=jnp.float32)
data_dims = len(effective_mean)
measure_valued_jacobians = _measure_valued_variant(
self.variant)(function, [mean, log_scale], utils.multi_normal,
measure_rng, num_samples, coupling)
measure_valued_mean_jacobians = measure_valued_jacobians[0]
chex.assert_shape(measure_valued_mean_jacobians,
(num_samples, data_dims))
measure_valued_mean_grads = np.mean(measure_valued_mean_jacobians,
axis=0)
measure_valued_log_scale_jacobians = measure_valued_jacobians[1]
chex.assert_shape(measure_valued_log_scale_jacobians,
(num_samples, data_dims))
measure_valued_log_scale_grads = np.mean(
measure_valued_log_scale_jacobians, axis=0)
pathwise_jacobians = _estimator_variant(
self.variant, sge.pathwise_jacobians)(function, [mean, log_scale],
utils.multi_normal,
pathwise_rng, num_samples)
pathwise_mean_jacobians = pathwise_jacobians[0]
chex.assert_shape(pathwise_mean_jacobians, (num_samples, data_dims))
pathwise_mean_grads = np.mean(pathwise_mean_jacobians, axis=0)
pathwise_log_scale_jacobians = pathwise_jacobians[1]
chex.assert_shape(pathwise_log_scale_jacobians,
(num_samples, data_dims))
pathwise_log_scale_grads = np.mean(pathwise_log_scale_jacobians,
axis=0)
_assert_equal(pathwise_mean_grads,
measure_valued_mean_grads,
rtol=5e-1,
atol=1e-1)
_assert_equal(pathwise_log_scale_grads,
measure_valued_log_scale_grads,
rtol=5e-1,
atol=1e-1)
