def test_hmcecs_normal_normal(kernel_cls, num_block, subsample_size):
true_loc = jnp.array([0.3, 0.1, 0.9])
num_warmup, num_samples = 200, 200
data = true_loc + dist.Normal(jnp.zeros(3, ), jnp.ones(3, )).sample(
random.PRNGKey(1), (10000, ))
def model(data, subsample_size):
mean = numpyro.sample('mean', dist.Normal().expand((3, )).to_event(1))
with numpyro.plate('batch',
data.shape[0],
dim=-2,
subsample_size=subsample_size):
sub_data = numpyro.subsample(data, 0)
numpyro.sample("obs", dist.Normal(mean, 1), obs=sub_data)
ref_params = {
'mean':
true_loc + dist.Normal(true_loc, 5e-2).sample(random.PRNGKey(0))
}
proxy_fn = HMCECS.taylor_proxy(ref_params)
kernel = HMCECS(kernel_cls(model), proxy=proxy_fn)
mcmc = MCMC(kernel, num_warmup, num_samples)
mcmc.run(random.PRNGKey(0), data, subsample_size)
samples = mcmc.get_samples()
assert_allclose(np.mean(mcmc.get_samples()['mean'], axis=0),
true_loc,
atol=0.1)
assert len(samples['mean']) == num_samples
def test_subsample_gibbs_partitioning(kernel_cls, num_blocks):
def model(obs):
with plate('N', obs.shape[0], subsample_size=100) as idx:
numpyro.sample('x', dist.Normal(0, 1), obs=obs[idx])
obs = random.normal(random.PRNGKey(0), (10000, )) / 100
kernel = HMCECS(kernel_cls(model), num_blocks=num_blocks)
state = kernel.init(random.PRNGKey(1),
10,
None,
model_args=(obs, ),
model_kwargs=None)
gibbs_sites = {'N': jnp.arange(100)}
def potential_fn(z_gibbs, z_hmc):
return kernel.inner_kernel._potential_fn_gen(
obs, _gibbs_sites=z_gibbs)(z_hmc)
gibbs_fn = numpyro.infer.hmc_gibbs._subsample_gibbs_fn(
potential_fn, kernel._plate_sizes, num_blocks)
new_gibbs_sites, _ = gibbs_fn(
random.PRNGKey(2), gibbs_sites, state.hmc_state.z,
state.hmc_state.potential_energy) # accept_prob > .999
block_size = 100 // num_blocks
for name in gibbs_sites:
assert block_size == jnp.not_equal(gibbs_sites[name],
new_gibbs_sites[name]).sum()
def test_estimate_likelihood(kernel_cls):
data_key, tr_key, sub_key, rng_key = random.split(random.PRNGKey(0), 4)
ref_params = jnp.array([0.1, 0.5, -0.2])
sigma = 0.1
data = ref_params + dist.Normal(jnp.zeros(3), jnp.ones(3)).sample(
data_key, (10_000,)
)
n, _ = data.shape
num_warmup = 200
num_samples = 200
num_blocks = 20
def model(data):
mean = numpyro.sample(
"mean", dist.Normal(ref_params, jnp.ones_like(ref_params))
)
with numpyro.plate("N", data.shape[0], subsample_size=100, dim=-2) as idx:
numpyro.sample("obs", dist.Normal(mean, sigma), obs=data[idx])
proxy_fn = HMCECS.taylor_proxy({"mean": ref_params})
kernel = HMCECS(kernel_cls(model), proxy=proxy_fn, num_blocks=num_blocks)
mcmc = MCMC(kernel, num_warmup=num_warmup, num_samples=num_samples)
mcmc.run(random.PRNGKey(0), data, extra_fields=["hmc_state.potential_energy"])
pes = mcmc.get_extra_fields()["hmc_state.potential_energy"]
samples = mcmc.get_samples()
pes_full = vmap(
lambda sample: log_density(
model, (data,), {}, {**sample, **{"N": jnp.arange(n)}}
)[0]
)(samples)
assert jnp.var(jnp.exp(-pes - pes_full)) < 1.0
def run_hmcecs(hmcecs_key, args, data, obs, inner_kernel):
svi_key, mcmc_key = random.split(hmcecs_key)
# find reference parameters for second order taylor expansion to estimate likelihood (taylor_proxy)
optimizer = numpyro.optim.Adam(step_size=1e-3)
guide = autoguide.AutoDelta(model)
svi = SVI(model, guide, optimizer, loss=Trace_ELBO())
svi_result = svi.run(svi_key, args.num_svi_steps, data, obs,
args.subsample_size)
params, losses = svi_result.params, svi_result.losses
ref_params = {"theta": params["theta_auto_loc"]}
# taylor proxy estimates log likelihood (ll) by
# taylor_expansion(ll, theta_curr) +
# sum_{i in subsample} ll_i(theta_curr) - taylor_expansion(ll_i, theta_curr) around ref_params
proxy = HMCECS.taylor_proxy(ref_params)
kernel = HMCECS(inner_kernel, num_blocks=args.num_blocks, proxy=proxy)
mcmc = MCMC(kernel,
num_warmup=args.num_warmup,
num_samples=args.num_samples)
mcmc.run(mcmc_key, data, obs, args.subsample_size)
mcmc.print_summary()
return losses, mcmc.get_samples()
def test_enum_subsample_smoke():
def model(data):
x = numpyro.sample("x", dist.Bernoulli(0.5))
with numpyro.plate("N", data.shape[0], subsample_size=100, dim=-1):
batch = numpyro.subsample(data, event_dim=0)
numpyro.sample("obs", dist.Normal(x, 1), obs=batch)
data = random.normal(random.PRNGKey(0), (10000, )) + 1
kernel = HMCECS(NUTS(model), num_blocks=10)
mcmc = MCMC(kernel, 10, 10)
mcmc.run(random.PRNGKey(0), data)
def test_subsample_gibbs_partitioning(kernel_cls, num_blocks):
def model(obs):
with plate('N', obs.shape[0], subsample_size=100) as idx:
numpyro.sample('x', dist.Normal(0, 1), obs=obs[idx])
obs = random.normal(random.PRNGKey(0), (10000,)) / 100
kernel = HMCECS(kernel_cls(model), num_blocks=num_blocks)
hmc_state = kernel.init(random.PRNGKey(1), 10, None, model_args=(obs,), model_kwargs=None)
gibbs_sites = {'N': jnp.arange(100)}
gibbs_fn = kernel._gibbs_fn
new_gibbs_sites = gibbs_fn(random.PRNGKey(2), gibbs_sites, hmc_state.z) # accept_prob > .999
block_size = 100 // num_blocks
for name in gibbs_sites:
assert block_size == jnp.not_equal(gibbs_sites[name], new_gibbs_sites[name]).sum()
def test_hmcecs_multiple_plates():
true_loc = jnp.array([0.3, 0.1, 0.9])
num_warmup, num_samples = 2, 2
data = true_loc + dist.Normal(jnp.zeros(3), jnp.ones(3)).sample(
random.PRNGKey(1), (1000,)
)
def model(data):
mean = numpyro.sample("mean", dist.Normal().expand((3,)).to_event(1))
with numpyro.plate("batch", data.shape[0], dim=-2, subsample_size=10):
sub_data = numpyro.subsample(data, 0)
with numpyro.plate("dim", 3):
numpyro.sample("obs", dist.Normal(mean, 1), obs=sub_data)
ref_params = {
"mean": true_loc + dist.Normal(true_loc, 5e-2).sample(random.PRNGKey(0))
}
proxy_fn = HMCECS.taylor_proxy(ref_params)
kernel = HMCECS(NUTS(model), proxy=proxy_fn)
mcmc = MCMC(kernel, num_warmup=num_warmup, num_samples=num_samples)
mcmc.run(random.PRNGKey(0), data)
def benchmark_hmc(args, features, labels):
rng_key = random.PRNGKey(1)
start = time.time()
# a MAP estimate at the following source
# https://github.com/google/edward2/blob/master/examples/no_u_turn_sampler/logistic_regression.py#L117
ref_params = {
"coefs":
jnp.array([
+2.03420663e00,
-3.53567265e-02,
-1.49223924e-01,
-3.07049364e-01,
-1.00028366e-01,
-1.46827862e-01,
-1.64167881e-01,
-4.20344204e-01,
+9.47479829e-02,
-1.12681836e-02,
+2.64442056e-01,
-1.22087866e-01,
-6.00568838e-02,
-3.79419506e-01,
-1.06668741e-01,
-2.97053963e-01,
-2.05253899e-01,
-4.69537191e-02,
-2.78072730e-02,
-1.43250525e-01,
-6.77954629e-02,
-4.34899796e-03,
+5.90927452e-02,
+7.23133609e-02,
+1.38526391e-02,
-1.24497898e-01,
-1.50733739e-02,
-2.68872194e-02,
-1.80925727e-02,
+3.47936489e-02,
+4.03552800e-02,
-9.98773426e-03,
+6.20188080e-02,
+1.15002751e-01,
+1.32145107e-01,
+2.69109547e-01,
+2.45785132e-01,
+1.19035013e-01,
-2.59744357e-02,
+9.94279515e-04,
+3.39266285e-02,
-1.44057125e-02,
-6.95222765e-02,
-7.52013028e-02,
+1.21171586e-01,
+2.29205526e-02,
+1.47308692e-01,
-8.34354162e-02,
-9.34122875e-02,
-2.97472421e-02,
-3.03937674e-01,
-1.70958012e-01,
-1.59496680e-01,
-1.88516974e-01,
-1.20889175e00,
])
}
if args.algo == "HMC":
step_size = jnp.sqrt(0.5 / features.shape[0])
trajectory_length = step_size * args.num_steps
kernel = HMC(
model,
step_size=step_size,
trajectory_length=trajectory_length,
adapt_step_size=False,
dense_mass=args.dense_mass,
)
subsample_size = None
elif args.algo == "NUTS":
kernel = NUTS(model, dense_mass=args.dense_mass)
subsample_size = None
elif args.algo == "HMCECS":
subsample_size = 1000
inner_kernel = NUTS(
model,
init_strategy=init_to_value(values=ref_params),
dense_mass=args.dense_mass,
)
# note: if num_blocks=100, we'll update 10 index at each MCMC step
# so it took 50000 MCMC steps to iterative the whole dataset
kernel = HMCECS(inner_kernel,
num_blocks=100,
proxy=HMCECS.taylor_proxy(ref_params))
elif args.algo == "SA":
# NB: this kernel requires large num_warmup and num_samples
# and running on GPU is much faster than on CPU
kernel = SA(model,
adapt_state_size=1000,
init_strategy=init_to_value(values=ref_params))
subsample_size = None
elif args.algo == "FlowHMCECS":
subsample_size = 1000
guide = AutoBNAFNormal(model, num_flows=1, hidden_factors=[8])
svi = SVI(model, guide, numpyro.optim.Adam(0.01), Trace_ELBO())
svi_result = svi.run(random.PRNGKey(2), 2000, features, labels)
params, losses = svi_result.params, svi_result.losses
plt.plot(losses)
plt.show()
neutra = NeuTraReparam(guide, params)
neutra_model = neutra.reparam(model)
neutra_ref_params = {"auto_shared_latent": jnp.zeros(55)}
# no need to adapt mass matrix if the flow does a good job
inner_kernel = NUTS(
neutra_model,
init_strategy=init_to_value(values=neutra_ref_params),
adapt_mass_matrix=False,
)
kernel = HMCECS(inner_kernel,
num_blocks=100,
proxy=HMCECS.taylor_proxy(neutra_ref_params))
else:
raise ValueError(
"Invalid algorithm, either 'HMC', 'NUTS', or 'HMCECS'.")
mcmc = MCMC(kernel,
num_warmup=args.num_warmup,
num_samples=args.num_samples)
mcmc.run(rng_key,
features,
labels,
subsample_size,
extra_fields=("accept_prob", ))
print("Mean accept prob:",
jnp.mean(mcmc.get_extra_fields()["accept_prob"]))
mcmc.print_summary(exclude_deterministic=False)
print("\nMCMC elapsed time:", time.time() - start)
def test_pickle_hmcecs():
mcmc = MCMC(HMCECS(NUTS(logistic_regression)), num_warmup=10, num_samples=10)
mcmc.run(random.PRNGKey(0))
pickled_mcmc = pickle.loads(pickle.dumps(mcmc))
test_util.check_close(mcmc.get_samples(), pickled_mcmc.get_samples())