def test_reuse_mcmc_pe_gen():
y1 = onp.random.normal(3, 0.1, (100, ))
y2 = onp.random.normal(-3, 0.1, (100, ))
def model(y_obs):
mu = numpyro.sample('mu', dist.Normal(0., 1.))
sigma = numpyro.sample("sigma", dist.HalfCauchy(3.))
numpyro.sample("y", dist.Normal(mu, sigma), obs=y_obs)
init_params, potential_fn, constrain_fn = initialize_model(
random.PRNGKey(0), model, y1, dynamic_args=True)
init_kernel, sample_kernel = hmc(potential_fn_gen=potential_fn)
init_state = init_kernel(init_params, num_warmup=300, model_args=(y1, ))
@jit
def _sample(state_and_args):
hmc_state, model_args = state_and_args
return sample_kernel(hmc_state, (model_args, )), model_args
samples = fori_collect(0,
500,
_sample, (init_state, y1),
transform=lambda state: constrain_fn(y1)
(state[0].z))
assert_allclose(samples['mu'].mean(), 3., atol=0.1)
# Run on data, re-using `mcmc` - this should be much faster.
init_state = init_kernel(init_params, num_warmup=300, model_args=(y2, ))
samples = fori_collect(0,
500,
_sample, (init_state, y2),
transform=lambda state: constrain_fn(y2)
(state[0].z))
assert_allclose(samples['mu'].mean(), -3., atol=0.1)
def test_functional_beta_bernoulli_x64(algo):
warmup_steps, num_samples = 500, 20000
def model(data):
alpha = np.array([1.1, 1.1])
beta = np.array([1.1, 1.1])
p_latent = numpyro.sample('p_latent', dist.Beta(alpha, beta))
numpyro.sample('obs', dist.Bernoulli(p_latent), obs=data)
return p_latent
true_probs = np.array([0.9, 0.1])
data = dist.Bernoulli(true_probs).sample(random.PRNGKey(1), (1000, 2))
init_params, potential_fn, constrain_fn = initialize_model(
random.PRNGKey(2), model, model_args=(data, ))
init_kernel, sample_kernel = hmc(potential_fn, algo=algo)
hmc_state = init_kernel(init_params,
trajectory_length=1.,
num_warmup=warmup_steps)
samples = fori_collect(0,
num_samples,
sample_kernel,
hmc_state,
transform=lambda x: constrain_fn(x.z))
assert_allclose(np.mean(samples['p_latent'], 0), true_probs, atol=0.05)
if 'JAX_ENABLE_X64' in os.environ:
assert samples['p_latent'].dtype == np.float64
def run(
self,
rng_key,
num_steps,
*args,
progress_bar=True,
init_state=None,
collect_fn=lambda val: val[1], # TODO: refactor
**kwargs,
):
def bodyfn(_i, info):
body_state = info[0]
return (*self.update(body_state, *info[2:], **kwargs), *info[2:])
if init_state is None:
state = self.init(rng_key, *args, **kwargs)
else:
state = init_state
loss = self.evaluate(state, *args, **kwargs)
auxiliaries, last_res = fori_collect(
0,
num_steps,
lambda info: bodyfn(0, info),
(state, loss, *args),
progbar=progress_bar,
transform=collect_fn,
return_last_val=True,
)
state = last_res[0]
return SteinVIRunResult(self.get_params(state), state, auxiliaries)
def test_dirichlet_categorical(algo, dense_mass):
warmup_steps, num_samples = 100, 20000
def model(data):
concentration = np.array([1.0, 1.0, 1.0])
p_latent = sample('p_latent', dist.Dirichlet(concentration))
sample('obs', dist.Categorical(p_latent), obs=data)
return p_latent
true_probs = np.array([0.1, 0.6, 0.3])
data = dist.Categorical(true_probs).sample(random.PRNGKey(1), (2000,))
init_params, potential_fn, constrain_fn = initialize_model(random.PRNGKey(2), model, data)
init_kernel, sample_kernel = hmc(potential_fn, algo=algo)
hmc_state = init_kernel(init_params,
trajectory_length=1.,
num_warmup=warmup_steps,
progbar=False,
dense_mass=dense_mass)
hmc_states = fori_collect(num_samples, sample_kernel, hmc_state,
transform=lambda x: constrain_fn(x.z),
progbar=False)
assert_allclose(np.mean(hmc_states['p_latent'], 0), true_probs, atol=0.02)
if 'JAX_ENABLE_x64' in os.environ:
assert hmc_states['p_latent'].dtype == np.float64
def single_chain_mcmc(rng, init_params):
hmc_state = init_kernel(init_params, num_warmup, run_warmup=False, rng=rng,
**sampler_kwargs)
samples = fori_collect(num_warmup, num_warmup + num_samples, sample_kernel, hmc_state,
transform=lambda x: constrain_fn(x.z),
progbar=progbar)
return samples
def test_binomial_stable(with_logits):
# Ref: https://github.com/pyro-ppl/pyro/issues/1706
warmup_steps, num_samples = 200, 200
def model(data):
p = numpyro.sample('p', dist.Beta(1., 1.))
if with_logits:
logits = logit(p)
numpyro.sample('obs',
dist.Binomial(data['n'], logits=logits),
obs=data['x'])
else:
numpyro.sample('obs',
dist.Binomial(data['n'], probs=p),
obs=data['x'])
data = {'n': 5000000, 'x': 3849}
init_params, potential_fn, constrain_fn = initialize_model(
random.PRNGKey(2), model, data)
init_kernel, sample_kernel = hmc(potential_fn)
hmc_state = init_kernel(init_params, num_warmup=warmup_steps)
samples = fori_collect(0,
num_samples,
sample_kernel,
hmc_state,
transform=lambda x: constrain_fn(x.z))
assert_allclose(np.mean(samples['p'], 0), data['x'] / data['n'], rtol=0.05)
if 'JAX_ENABLE_x64' in os.environ:
assert samples['p'].dtype == np.float64
def _single_chain_mcmc(self,
init,
collect_fields=('z', ),
collect_warmup=False,
args=(),
kwargs={}):
rng_key, init_params = init
init_state, constrain_fn = self.sampler.init(rng_key,
self.num_warmup,
init_params,
model_args=args,
model_kwargs=kwargs)
if self.constrain_fn is None:
constrain_fn = identity if constrain_fn is None else constrain_fn
else:
constrain_fn = self.constrain_fn
collect_fn = attrgetter(*collect_fields)
lower = 0 if collect_warmup else self.num_warmup
states = fori_collect(
lower,
self.num_warmup + self.num_samples,
self.sampler.sample,
init_state,
transform=collect_fn,
progbar=self.progress_bar,
progbar_desc=functools.partial(get_progbar_desc_str,
self.num_warmup),
diagnostics_fn=get_diagnostics_str if rng_key.ndim == 1 else None)
if len(collect_fields) == 1:
states = (states, )
states = dict(zip(collect_fields, states))
states['z'] = vmap(constrain_fn)(
states['z']) if len(tree_flatten(states)[0]) > 0 else states['z']
return states
def main(args):
_, fetch = load_dataset(SP500, shuffle=False)
dates, returns = fetch()
init_rng_key, sample_rng_key = random.split(random.PRNGKey(args.rng_seed))
model_info = initialize_model(init_rng_key, model, model_args=(returns,))
init_kernel, sample_kernel = hmc(model_info.potential_fn, algo='NUTS')
hmc_state = init_kernel(model_info.param_info, args.num_warmup, rng_key=sample_rng_key)
hmc_states = fori_collect(args.num_warmup, args.num_warmup + args.num_samples, sample_kernel, hmc_state,
transform=lambda hmc_state: model_info.postprocess_fn(hmc_state.z),
progbar=False if "NUMPYRO_SPHINXBUILD" in os.environ else True)
print_results(hmc_states, dates)
fig, ax = plt.subplots(figsize=(8, 6), constrained_layout=True)
dates = mdates.num2date(mdates.datestr2num(dates))
ax.plot(dates, returns, lw=0.5)
# format the ticks
ax.xaxis.set_major_locator(mdates.YearLocator())
ax.xaxis.set_major_formatter(mdates.DateFormatter('%Y'))
ax.xaxis.set_minor_locator(mdates.MonthLocator())
ax.plot(dates, jnp.exp(hmc_states['s'].T), 'r', alpha=0.01)
legend = ax.legend(['returns', 'volatility'], loc='upper right')
legend.legendHandles[1].set_alpha(0.6)
ax.set(xlabel='time', ylabel='returns', title='Volatility of S&P500 over time')
plt.savefig("stochastic_volatility_plot.pdf")
def test_change_point():
# Ref: https://forum.pyro.ai/t/i-dont-understand-why-nuts-code-is-not-working-bayesian-hackers-mail/696
warmup_steps, num_samples = 500, 3000
def model(data):
alpha = 1 / np.mean(data)
lambda1 = sample('lambda1', dist.Exponential(alpha))
lambda2 = sample('lambda2', dist.Exponential(alpha))
tau = sample('tau', dist.Uniform(0, 1))
lambda12 = np.where(np.arange(len(data)) < tau * len(data), lambda1, lambda2)
sample('obs', dist.Poisson(lambda12), obs=data)
count_data = np.array([
13, 24, 8, 24, 7, 35, 14, 11, 15, 11, 22, 22, 11, 57,
11, 19, 29, 6, 19, 12, 22, 12, 18, 72, 32, 9, 7, 13,
19, 23, 27, 20, 6, 17, 13, 10, 14, 6, 16, 15, 7, 2,
15, 15, 19, 70, 49, 7, 53, 22, 21, 31, 19, 11, 18, 20,
12, 35, 17, 23, 17, 4, 2, 31, 30, 13, 27, 0, 39, 37,
5, 14, 13, 22,
])
init_params, potential_fn, constrain_fn = initialize_model(random.PRNGKey(4), model, count_data)
init_kernel, sample_kernel = hmc(potential_fn)
hmc_state = init_kernel(init_params, num_warmup=warmup_steps)
samples = fori_collect(num_samples, sample_kernel, hmc_state,
transform=lambda x: constrain_fn(x.z))
tau_posterior = (samples['tau'] * len(count_data)).astype("int")
tau_values, counts = onp.unique(tau_posterior, return_counts=True)
mode_ind = np.argmax(counts)
mode = tau_values[mode_ind]
assert mode == 44
if 'JAX_ENABLE_x64' in os.environ:
assert samples['lambda1'].dtype == np.float64
assert samples['lambda2'].dtype == np.float64
assert samples['tau'].dtype == np.float64
def test_beta_bernoulli(algo):
warmup_steps, num_samples = 500, 20000
def model(data):
alpha = np.array([1.1, 1.1])
beta = np.array([1.1, 1.1])
p_latent = sample('p_latent', dist.Beta(alpha, beta))
sample('obs', dist.Bernoulli(p_latent), obs=data)
return p_latent
true_probs = np.array([0.9, 0.1])
data = dist.Bernoulli(true_probs).sample(random.PRNGKey(1), size=(1000, 2))
init_params, potential_fn, constrain_fn = initialize_model(
random.PRNGKey(2), model, data)
init_kernel, sample_kernel = hmc(potential_fn, algo=algo)
hmc_state = init_kernel(init_params,
trajectory_length=1.,
num_warmup=warmup_steps,
progbar=False)
hmc_states = fori_collect(num_samples,
sample_kernel,
hmc_state,
transform=lambda x: constrain_fn(x.z),
progbar=False)
assert_allclose(np.mean(hmc_states['p_latent'], 0), true_probs, atol=0.05)
def _single_chain_mcmc(self, init, args, kwargs, collect_fields):
rng_key, init_state, init_params = init
if init_state is None:
init_state = self.sampler.init(
rng_key,
self.num_warmup,
init_params,
model_args=args,
model_kwargs=kwargs,
)
sample_fn, postprocess_fn = self._get_cached_fns()
diagnostics = (
lambda x: self.sampler.get_diagnostics_str(x[0])
if rng_key.ndim == 1
else ""
) # noqa: E731
init_val = (init_state, args, kwargs) if self._jit_model_args else (init_state,)
lower_idx = self._collection_params["lower"]
upper_idx = self._collection_params["upper"]
phase = self._collection_params["phase"]
collection_size = self._collection_params["collection_size"]
collection_size = (
collection_size
if collection_size is None
else collection_size // self.thinning
)
collect_vals = fori_collect(
lower_idx,
upper_idx,
sample_fn,
init_val,
transform=_collect_fn(collect_fields),
progbar=self.progress_bar,
return_last_val=True,
thinning=self.thinning,
collection_size=collection_size,
progbar_desc=partial(_get_progbar_desc_str, lower_idx, phase),
diagnostics_fn=diagnostics,
num_chains=self.num_chains if self.chain_method == "parallel" else 1,
)
states, last_val = collect_vals
# Get first argument of type `HMCState`
last_state = last_val[0]
if len(collect_fields) == 1:
states = (states,)
states = dict(zip(collect_fields, states))
# Apply constraints if number of samples is non-zero
site_values = tree_flatten(states[self._sample_field])[0]
# XXX: lax.map still works if some arrays have 0 size
# so we only need to filter out the case site_value.shape[0] == 0
# (which happens when lower_idx==upper_idx)
if len(site_values) > 0 and jnp.shape(site_values[0])[0] > 0:
if self._jit_model_args:
states[self._sample_field] = postprocess_fn(
states[self._sample_field], args, kwargs
)
else:
states[self._sample_field] = postprocess_fn(states[self._sample_field])
return states, last_state
def test_fori_collect():
def f(x):
return {"i": x["i"] + x["j"], "j": x["i"] - x["j"]}
a = {"i": jnp.array([0.0]), "j": jnp.array([1.0])}
expected_tree = {"i": jnp.array([[0.0], [2.0]])}
actual_tree = fori_collect(1, 3, f, a, transform=lambda a: {"i": a["i"]})
check_eq(actual_tree, expected_tree)
def run_inference(dept, male, applications, admit, rng, args):
init_params, potential_fn, constrain_fn = initialize_model(
rng, glmm, dept, male, applications, admit)
init_kernel, sample_kernel = hmc(potential_fn, algo='NUTS')
hmc_state = init_kernel(init_params, args.num_warmup_steps)
hmc_states = fori_collect(args.num_samples, sample_kernel, hmc_state,
transform=lambda hmc_state: constrain_fn(hmc_state.z))
return hmc_states
def test_fori_collect():
def f(x):
return {'i': x['i'] + x['j'], 'j': x['i'] - x['j']}
a = {'i': jnp.array([0.]), 'j': jnp.array([1.])}
expected_tree = {'i': jnp.array([[0.], [2.]])}
actual_tree = fori_collect(1, 3, f, a, transform=lambda a: {'i': a['i']})
check_eq(actual_tree, expected_tree)
def test_fori_collect_thinning():
def f(x):
return x + 1.0
actual2 = fori_collect(0, 9, f, jnp.array([-1]), thinning=2)
expected2 = jnp.array([[2], [4], [6], [8]])
check_eq(actual2, expected2)
actual3 = fori_collect(0, 9, f, jnp.array([-1]), thinning=3)
expected3 = jnp.array([[2], [5], [8]])
check_eq(actual3, expected3)
actual4 = fori_collect(0, 9, f, jnp.array([-1]), thinning=4)
expected4 = jnp.array([[4], [8]])
check_eq(actual4, expected4)
actual5 = fori_collect(12, 37, f, jnp.array([-1]), thinning=5)
expected5 = jnp.array([[16], [21], [26], [31], [36]])
check_eq(actual5, expected5)
def mcmc(num_warmup,
num_samples,
init_params,
sampler='hmc',
constrain_fn=None,
print_summary=True,
**sampler_kwargs):
"""
Convenience wrapper for MCMC samplers -- runs warmup, prints
diagnostic summary and returns a collections of samples
from the posterior.
:param num_warmup: Number of warmup steps.
:param num_samples: Number of samples to generate from the Markov chain.
:param init_params: Initial parameters to begin sampling. The type can
must be consistent with the input type to `potential_fn`.
:param sampler: currently, only `hmc` is implemented (default).
:param constrain_fn: Callable that converts a collection of unconstrained
sample values returned from the sampler to constrained values that
lie within the support of the sample sites.
:param print_summary: Whether to print diagnostics summary for
each sample site. Default is ``True``.
:param `**sampler_kwargs`: Sampler specific keyword arguments.
- *HMC*: Refer to :func:`~numpyro.mcmc.hmc` and
:func:`~numpyro.mcmc.hmc.init_kernel` for accepted arguments. Note
that all arguments must be provided as keywords.
:return: collection of samples from the posterior.
"""
if sampler == 'hmc':
if constrain_fn is None:
constrain_fn = identity
potential_fn = sampler_kwargs.pop('potential_fn')
kinetic_fn = sampler_kwargs.pop('kinetic_fn', None)
algo = sampler_kwargs.pop('algo', 'NUTS')
progbar = sampler_kwargs.pop('progbar', True)
init_kernel, sample_kernel = hmc(potential_fn, kinetic_fn, algo)
hmc_state = init_kernel(init_params,
num_warmup,
progbar=progbar,
**sampler_kwargs)
samples = fori_collect(num_samples,
sample_kernel,
hmc_state,
transform=lambda x: constrain_fn(x.z),
progbar=progbar,
diagnostics_fn=get_diagnostics_str,
progbar_desc='sample')
if print_summary:
summary(samples)
return samples
else:
raise ValueError('sampler: {} not recognized'.format(sampler))
def main(args):
jax_config.update('jax_platform_name', args.device)
_, fetch = load_dataset(SP500, shuffle=False)
dates, returns = fetch()
init_rng, sample_rng = random.split(random.PRNGKey(args.rng))
init_params, potential_fn, constrain_fn = initialize_model(init_rng, model, returns)
init_kernel, sample_kernel = hmc(potential_fn, algo='NUTS')
hmc_state = init_kernel(init_params, args.num_warmup, rng=sample_rng)
hmc_states = fori_collect(0, args.num_samples, sample_kernel, hmc_state,
transform=lambda hmc_state: constrain_fn(hmc_state.z))
print_results(hmc_states, dates)
def test_construct():
import bellini
from bellini import Quantity, Species, Substance, Story
import pint
ureg = pint.UnitRegistry()
s = Story()
water = Species(name='water')
s.one_water_quantity = bellini.distributions.Normal(
loc=Quantity(3.0, ureg.mole),
scale=Quantity(0.01, ureg.mole),
name="first_normal",
)
s.another_water_quantity = bellini.distributions.Normal(
loc=Quantity(3.0, ureg.mole),
scale=Quantity(0.01, ureg.mole),
name="second_normal",
)
s.combined_water = s.one_water_quantity + s.another_water_quantity
# s.combined_water.observed = True
s.combined_water.name = "combined_water"
s.combined_water_with_nose = bellini.distributions.Normal(
loc=s.combined_water,
scale=Quantity(0.01, ureg.mole),
name="combined_with_noise")
s.combined_water_with_nose.observed = True
from bellini.api._numpyro import graph_to_numpyro_model
model = graph_to_numpyro_model(s.g)
from numpyro.infer.util import initialize_model
import jax
model_info = initialize_model(
jax.random.PRNGKey(2666),
model,
)
from numpyro.infer.hmc import hmc
from numpyro.util import fori_collect
init_kernel, sample_kernel = hmc(model_info.potential_fn, algo='NUTS')
hmc_state = init_kernel(model_info.param_info,
trajectory_length=10,
num_warmup=300)
samples = fori_collect(
0,
500,
sample_kernel,
hmc_state,
transform=lambda state: model_info.postprocess_fn(state.z))
print(samples)
def test_fori_collect_return_last(progbar):
def f(x):
x['i'] = x['i'] + 1
return x
tree, init_state = fori_collect(2, 4, f, {'i': 0},
transform=lambda a: {'i': a['i']},
return_last_val=True,
progbar=progbar)
expected_tree = {'i': jnp.array([3, 4])}
expected_last_state = {'i': jnp.array(4)}
check_eq(init_state, expected_last_state)
check_eq(tree, expected_tree)
def test_unnormalized_normal(algo):
true_mean, true_std = 1., 2.
warmup_steps, num_samples = 1000, 8000
def potential_fn(z):
return 0.5 * np.sum(((z - true_mean) / true_std)**2)
init_kernel, sample_kernel = hmc(potential_fn, algo=algo)
init_params = np.array(0.)
hmc_state = init_kernel(init_params,
trajectory_length=9,
num_warmup=warmup_steps)
hmc_states = fori_collect(num_samples,
sample_kernel,
hmc_state,
transform=lambda x: x.z)
assert_allclose(np.mean(hmc_states), true_mean, rtol=0.05)
assert_allclose(np.std(hmc_states), true_std, rtol=0.05)
def run_inference(transition_prior, emission_prior, supervised_categories,
supervised_words, unsupervised_words, rng, args):
init_params, potential_fn, constrain_fn = initialize_model(
rng,
semi_supervised_hmm,
transition_prior,
emission_prior,
supervised_categories,
supervised_words,
unsupervised_words,
)
init_kernel, sample_kernel = hmc(potential_fn, algo='NUTS')
hmc_state = init_kernel(init_params, args.num_warmup)
hmc_states = fori_collect(args.num_samples,
sample_kernel,
hmc_state,
transform=lambda state: constrain_fn(state.z))
return hmc_states
def _single_chain_mcmc(self,
rng_key,
init_state,
init_params,
args,
kwargs,
collect_fields=('z', )):
if init_state is None:
init_state = self.sampler.init(rng_key,
self.num_warmup,
init_params,
model_args=args,
model_kwargs=kwargs)
if self.constrain_fn is None:
self.constrain_fn = self.sampler.constrain_fn(args, kwargs)
diagnostics = lambda x: get_diagnostics_str(x[
0]) if rng_key.ndim == 1 else None # noqa: E731
init_val = (init_state, args,
kwargs) if self._jit_model_args else (init_state, )
lower_idx = self._collection_params["lower"]
upper_idx = self._collection_params["upper"]
collect_vals = fori_collect(
lower_idx,
upper_idx,
self._get_cached_fn(),
init_val,
transform=_collect_fn(collect_fields),
progbar=self.progress_bar,
return_last_val=True,
collection_size=self._collection_params["collection_size"],
progbar_desc=functools.partial(get_progbar_desc_str, lower_idx),
diagnostics_fn=diagnostics)
states, last_val = collect_vals
# Get first argument of type `HMCState`
last_state = last_val[0]
if len(collect_fields) == 1:
states = (states, )
states = dict(zip(collect_fields, states))
# Apply constraints if number of samples is non-zero
site_values = tree_flatten(states['z'])[0]
if len(site_values) > 0 and site_values[0].size > 0:
states['z'] = lax.map(self.constrain_fn, states['z'])
return states, last_state
def benchmark_hmc(args, features, labels):
trajectory_length = step_size * args.num_steps
_, potential_fn, _ = initialize_model(random.PRNGKey(1), model, features, labels)
init_kernel, sample_kernel = hmc(potential_fn, algo=args.algo)
t0 = time.time()
# TODO: Use init_params from `initialize_model` instead of fixed params.
hmc_state, _, _ = init_kernel(init_params, num_warmup=0, step_size=step_size,
trajectory_length=trajectory_length,
adapt_step_size=False, run_warmup=False)
t1 = time.time()
print("time for hmc_init: ", t1 - t0)
def transform(state): return {'coefs': state.z['coefs'],
'num_steps': state.num_steps}
hmc_states = fori_collect(args.num_samples, sample_kernel, hmc_state, transform=transform)
num_leapfrogs = np.sum(hmc_states['num_steps'])
print('number of leapfrog steps: ', num_leapfrogs)
print('avg. time for each step: ', (time.time() - t1) / num_leapfrogs)
def test_functional_map(algo, map_fn):
if map_fn is pmap and jax.device_count() == 1:
pytest.skip("pmap test requires device_count greater than 1.")
true_mean, true_std = 1.0, 2.0
num_warmup, num_samples = 1000, 8000
def potential_fn(z):
return 0.5 * jnp.sum(((z - true_mean) / true_std)**2)
init_kernel, sample_kernel = hmc(potential_fn, algo=algo)
init_params = jnp.array([0.0, -1.0])
rng_keys = random.split(random.PRNGKey(0), 2)
init_kernel_map = map_fn(
lambda init_param, rng_key: init_kernel(init_param,
trajectory_length=9,
num_warmup=num_warmup,
rng_key=rng_key))
init_states = init_kernel_map(init_params, rng_keys)
fori_collect_map = map_fn(lambda hmc_state: fori_collect(
0,
num_samples,
sample_kernel,
hmc_state,
transform=lambda x: x.z,
progbar=False,
))
chain_samples = fori_collect_map(init_states)
assert_allclose(jnp.mean(chain_samples, axis=1),
jnp.repeat(true_mean, 2),
rtol=0.06)
assert_allclose(jnp.std(chain_samples, axis=1),
jnp.repeat(true_std, 2),
rtol=0.06)
def test_map(algo, map_fn):
if map_fn is pmap and xla_bridge.device_count() == 1:
pytest.skip('pmap test requires device_count greater than 1.')
true_mean, true_std = 1., 2.
warmup_steps, num_samples = 1000, 8000
def potential_fn(z):
return 0.5 * np.sum(((z - true_mean) / true_std)**2)
init_kernel, sample_kernel = hmc(potential_fn, algo=algo)
init_params = np.array([0., -1.])
rngs = random.split(random.PRNGKey(0), 2)
init_kernel_map = map_fn(
lambda init_param, rng: init_kernel(init_param,
trajectory_length=9,
num_warmup=warmup_steps,
progbar=False,
rng=rng))
init_states = init_kernel_map(init_params, rngs)
fori_collect_map = map_fn(
lambda hmc_state: fori_collect(0,
num_samples,
sample_kernel,
hmc_state,
transform=lambda x: x.z,
progbar=False))
chain_samples = fori_collect_map(init_states)
assert_allclose(np.mean(chain_samples, axis=1),
np.repeat(true_mean, 2),
rtol=0.05)
assert_allclose(np.std(chain_samples, axis=1),
np.repeat(true_std, 2),
rtol=0.05)
def mcmc(num_warmup, num_samples, init_params, sampler='hmc',
constrain_fn=None, print_summary=True, **sampler_kwargs):
"""
Convenience wrapper for MCMC samplers -- runs warmup, prints
diagnostic summary and returns a collections of samples
from the posterior.
:param num_warmup: Number of warmup steps.
:param num_samples: Number of samples to generate from the Markov chain.
:param init_params: Initial parameters to begin sampling. The type can
must be consistent with the input type to `potential_fn`.
:param sampler: currently, only `hmc` is implemented (default).
:param constrain_fn: Callable that converts a collection of unconstrained
sample values returned from the sampler to constrained values that
lie within the support of the sample sites.
:param print_summary: Whether to print diagnostics summary for
each sample site. Default is ``True``.
:param `**sampler_kwargs`: Sampler specific keyword arguments.
- *HMC*: Refer to :func:`~numpyro.mcmc.hmc` and
:func:`~numpyro.mcmc.hmc.init_kernel` for accepted arguments. Note
that all arguments must be provided as keywords.
:return: collection of samples from the posterior.
.. testsetup::
import jax
from jax import random
import jax.numpy as np
import numpyro.distributions as dist
from numpyro.handlers import sample
from numpyro.hmc_util import initialize_model
from numpyro.mcmc import hmc
from numpyro.util import fori_collect
.. doctest::
>>> true_coefs = np.array([1., 2., 3.])
>>> data = random.normal(random.PRNGKey(2), (2000, 3))
>>> dim = 3
>>> labels = dist.Bernoulli(logits=(true_coefs * data).sum(-1)).sample(random.PRNGKey(3))
>>>
>>> def model(data, labels):
... coefs_mean = np.zeros(dim)
... coefs = sample('beta', dist.Normal(coefs_mean, np.ones(3)))
... intercept = sample('intercept', dist.Normal(0., 10.))
... return sample('y', dist.Bernoulli(logits=(coefs * data + intercept).sum(-1)), obs=labels)
>>>
>>> init_params, potential_fn, constrain_fn = initialize_model(random.PRNGKey(0), model,
... data, labels)
>>> num_warmup, num_samples = 1000, 1000
>>> samples = mcmc(num_warmup, num_samples, init_params,
... potential_fn=potential_fn,
... constrain_fn=constrain_fn) # doctest: +SKIP
warmup: 100%|██████████| 1000/1000 [00:09<00:00, 109.40it/s, 1 steps of size 5.83e-01. acc. prob=0.79]
sample: 100%|██████████| 1000/1000 [00:00<00:00, 1252.39it/s, 1 steps of size 5.83e-01. acc. prob=0.85]
mean sd 5.5% 94.5% n_eff Rhat
coefs[0] 0.96 0.07 0.85 1.07 455.35 1.01
coefs[1] 2.05 0.09 1.91 2.20 332.00 1.01
coefs[2] 3.18 0.13 2.96 3.37 320.27 1.00
intercept -0.03 0.02 -0.06 0.00 402.53 1.00
"""
if sampler == 'hmc':
if constrain_fn is None:
constrain_fn = identity
potential_fn = sampler_kwargs.pop('potential_fn')
kinetic_fn = sampler_kwargs.pop('kinetic_fn', None)
algo = sampler_kwargs.pop('algo', 'NUTS')
progbar = sampler_kwargs.pop('progbar', True)
init_kernel, sample_kernel = hmc(potential_fn, kinetic_fn, algo)
hmc_state = init_kernel(init_params, num_warmup, progbar=progbar, **sampler_kwargs)
samples = fori_collect(num_samples, sample_kernel, hmc_state,
transform=lambda x: constrain_fn(x.z),
progbar=progbar,
diagnostics_fn=get_diagnostics_str,
progbar_desc='sample')
if print_summary:
summary(samples)
return samples
else:
raise ValueError('sampler: {} not recognized'.format(sampler))
def mcmc(num_warmup, num_samples, init_params, num_chains=1, sampler='hmc',
constrain_fn=None, print_summary=True, **sampler_kwargs):
"""
Convenience wrapper for MCMC samplers -- runs warmup, prints
diagnostic summary and returns a collections of samples
from the posterior.
:param num_warmup: Number of warmup steps.
:param num_samples: Number of samples to generate from the Markov chain.
:param init_params: Initial parameters to begin sampling. The type can
must be consistent with the input type to `potential_fn`.
:param sampler: currently, only `hmc` is implemented (default).
:param constrain_fn: Callable that converts a collection of unconstrained
sample values returned from the sampler to constrained values that
lie within the support of the sample sites.
:param print_summary: Whether to print diagnostics summary for
each sample site. Default is ``True``.
:param `**sampler_kwargs`: Sampler specific keyword arguments.
- *HMC*: Refer to :func:`~numpyro.mcmc.hmc` and
:func:`~numpyro.mcmc.hmc.init_kernel` for accepted arguments. Note
that all arguments must be provided as keywords.
:return: collection of samples from the posterior.
.. testsetup::
import jax
from jax import random
import jax.numpy as np
import numpyro.distributions as dist
from numpyro.handlers import sample
from numpyro.hmc_util import initialize_model
from numpyro.mcmc import hmc
from numpyro.util import fori_collect
.. doctest::
>>> true_coefs = np.array([1., 2., 3.])
>>> data = random.normal(random.PRNGKey(2), (2000, 3))
>>> dim = 3
>>> labels = dist.Bernoulli(logits=(true_coefs * data).sum(-1)).sample(random.PRNGKey(3))
>>>
>>> def model(data, labels):
... coefs_mean = np.zeros(dim)
... coefs = sample('beta', dist.Normal(coefs_mean, np.ones(3)))
... intercept = sample('intercept', dist.Normal(0., 10.))
... return sample('y', dist.Bernoulli(logits=(coefs * data + intercept).sum(-1)), obs=labels)
>>>
>>> init_params, potential_fn, constrain_fn = initialize_model(random.PRNGKey(0), model,
... data, labels)
>>> num_warmup, num_samples = 1000, 1000
>>> samples = mcmc(num_warmup, num_samples, init_params,
... potential_fn=potential_fn,
... constrain_fn=constrain_fn) # doctest: +SKIP
warmup: 100%|██████████| 1000/1000 [00:09<00:00, 109.40it/s, 1 steps of size 5.83e-01. acc. prob=0.79]
sample: 100%|██████████| 1000/1000 [00:00<00:00, 1252.39it/s, 1 steps of size 5.83e-01. acc. prob=0.85]
mean sd 5.5% 94.5% n_eff Rhat
coefs[0] 0.96 0.07 0.85 1.07 455.35 1.01
coefs[1] 2.05 0.09 1.91 2.20 332.00 1.01
coefs[2] 3.18 0.13 2.96 3.37 320.27 1.00
intercept -0.03 0.02 -0.06 0.00 402.53 1.00
"""
sequential_chain = False
if xla_bridge.device_count() < num_chains:
sequential_chain = True
warnings.warn('There are not enough devices to run parallel chains: expected {} but got {}.'
' Chains will be drawn sequentially. If you are running `mcmc` in CPU,'
' consider to disable XLA intra-op parallelism by setting the environment'
' flag "XLA_FLAGS=--xla_force_host_platform_device_count={}".'
.format(num_chains, xla_bridge.device_count(), num_chains))
progbar = sampler_kwargs.pop('progbar', True)
if num_chains > 1:
progbar = False
if sampler == 'hmc':
if constrain_fn is None:
constrain_fn = identity
potential_fn = sampler_kwargs.pop('potential_fn')
kinetic_fn = sampler_kwargs.pop('kinetic_fn', None)
algo = sampler_kwargs.pop('algo', 'NUTS')
if num_chains > 1:
rngs = sampler_kwargs.pop('rng', vmap(PRNGKey)(np.arange(num_chains)))
else:
rng = sampler_kwargs.pop('rng', PRNGKey(0))
init_kernel, sample_kernel = hmc(potential_fn, kinetic_fn, algo)
if progbar:
hmc_state = init_kernel(init_params, num_warmup, progbar=progbar, rng=rng,
**sampler_kwargs)
samples_flat = fori_collect(0, num_samples, sample_kernel, hmc_state,
transform=lambda x: constrain_fn(x.z),
progbar=progbar,
diagnostics_fn=get_diagnostics_str,
progbar_desc='sample')
samples = tree_map(lambda x: x[np.newaxis, ...], samples_flat)
else:
def single_chain_mcmc(rng, init_params):
hmc_state = init_kernel(init_params, num_warmup, run_warmup=False, rng=rng,
**sampler_kwargs)
samples = fori_collect(num_warmup, num_warmup + num_samples, sample_kernel, hmc_state,
transform=lambda x: constrain_fn(x.z),
progbar=progbar)
return samples
if num_chains == 1:
samples_flat = single_chain_mcmc(rng, init_params)
samples = tree_map(lambda x: x[np.newaxis, ...], samples_flat)
else:
if sequential_chain:
samples = lax.map(lambda args: single_chain_mcmc(*args), (rngs, init_params))
else:
samples = pmap(single_chain_mcmc)(rngs, init_params)
samples_flat = tree_map(lambda x: np.reshape(x, (-1,) + x.shape[2:]), samples)
if print_summary:
summary(samples)
return samples_flat
else:
raise ValueError('sampler: {} not recognized'.format(sampler))
