def test_saasbo_sample(self):
for use_saas, use_input_warping in product((False, True),
repeat=2):
with torch.random.fork_rng():
torch.manual_seed(0)
X = torch.randn(3, 2)
Y = torch.randn(3, 1)
Yvar = torch.randn(3, 1)
kernel = NUTS(pyro_model, max_tree_depth=1)
mcmc = MCMC(kernel, warmup_steps=0, num_samples=1)
mcmc.run(
X,
Y,
Yvar,
use_input_warping=use_input_warping,
use_saas=use_saas,
)
samples = mcmc.get_samples()
if use_saas:
self.assertTrue("kernel_tausq" in samples)
self.assertTrue("_kernel_inv_length_sq" in samples)
self.assertTrue("lengthscale" not in samples)
else:
self.assertTrue("kernel_tausq" not in samples)
self.assertTrue("_kernel_inv_length_sq" not in samples)
self.assertTrue("lengthscale" in samples)
if use_input_warping:
self.assertIn("c0", samples)
self.assertIn("c1", samples)
else:
self.assertNotIn("c0", samples)
self.assertNotIn("c1", samples)
def test_structured_mass():
def model(cov):
w = pyro.sample("w", dist.Normal(0, 1000).expand([2]).to_event(1))
x = pyro.sample("x", dist.Normal(0, 1000).expand([1]).to_event(1))
y = pyro.sample("y", dist.Normal(0, 1000).expand([1]).to_event(1))
z = pyro.sample("z", dist.Normal(0, 1000).expand([1]).to_event(1))
wxyz = torch.cat([w, x, y, z])
pyro.sample("obs", dist.MultivariateNormal(torch.zeros(5), cov), obs=wxyz)
w_cov = torch.tensor([[1.5, 0.5], [0.5, 1.5]])
xy_cov = torch.tensor([[2., 1.], [1., 3.]])
z_var = torch.tensor([2.5])
cov = torch.zeros(5, 5)
cov[:2, :2] = w_cov
cov[2:4, 2:4] = xy_cov
cov[4, 4] = z_var
# smoke tests
for dense_mass in [True, False]:
kernel = NUTS(model, jit_compile=True, ignore_jit_warnings=True, full_mass=dense_mass)
mcmc = MCMC(kernel, num_samples=1, warmup_steps=1)
mcmc.run(cov)
assert kernel.inverse_mass_matrix[("w", "x", "y", "z")].dim() == 1 + int(dense_mass)
kernel = NUTS(model, jit_compile=True, ignore_jit_warnings=True, full_mass=[("w",), ("x", "y")])
mcmc = MCMC(kernel, num_samples=1, warmup_steps=1000)
mcmc.run(cov)
assert_close(kernel.inverse_mass_matrix[("w",)], w_cov, atol=0.5, rtol=0.5)
assert_close(kernel.inverse_mass_matrix[("x", "y")], xy_cov, atol=0.5, rtol=0.5)
assert_close(kernel.inverse_mass_matrix[("z",)], z_var, atol=0.5, rtol=0.5)
def test_arrowhead_mass():
def model(prec):
w = pyro.sample("w", dist.Normal(0, 1000).expand([2]).to_event(1))
x = pyro.sample("x", dist.Normal(0, 1000).expand([1]).to_event(1))
y = pyro.sample("y", dist.Normal(0, 1000).expand([1]).to_event(1))
z = pyro.sample("z", dist.Normal(0, 1000).expand([2]).to_event(1))
wyxz = torch.cat([w, y, x, z])
pyro.sample("obs", dist.MultivariateNormal(torch.zeros(6), precision_matrix=prec), obs=wyxz)
A = torch.randn(6, 12)
prec = A @ A.t() * 0.1
# smoke tests
for dense_mass in [True, False]:
kernel = NUTS(model, jit_compile=True, ignore_jit_warnings=True, full_mass=dense_mass)
mcmc = MCMC(kernel, num_samples=1, warmup_steps=1)
mcmc.run(prec)
assert kernel.inverse_mass_matrix[("w", "x", "y", "z")].dim() == 1 + int(dense_mass)
kernel = NUTS(model, jit_compile=True, ignore_jit_warnings=True, full_mass=[("w",), ("y", "x")])
kernel.mass_matrix_adapter = ArrowheadMassMatrix()
mcmc = MCMC(kernel, num_samples=1, warmup_steps=1000)
mcmc.run(prec)
assert ("w", "y", "x", "z") in kernel.inverse_mass_matrix
mass_matrix = kernel.mass_matrix_adapter.mass_matrix[("w", "y", "x", "z")]
assert mass_matrix.top.shape == (4, 6)
assert mass_matrix.bottom_diag.shape == (2,)
assert_close(mass_matrix.top, prec[:4], atol=0.2, rtol=0.2)
assert_close(mass_matrix.bottom_diag, prec.diag()[4:], atol=0.2, rtol=0.2)
def test_gaussian_mixture_model(jit):
K, N = 3, 1000
def gmm(data):
mix_proportions = pyro.sample("phi", dist.Dirichlet(torch.ones(K)))
with pyro.plate("num_clusters", K):
cluster_means = pyro.sample(
"cluster_means", dist.Normal(torch.arange(float(K)), 1.0)
)
with pyro.plate("data", data.shape[0]):
assignments = pyro.sample("assignments", dist.Categorical(mix_proportions))
pyro.sample("obs", dist.Normal(cluster_means[assignments], 1.0), obs=data)
return cluster_means
true_cluster_means = torch.tensor([1.0, 5.0, 10.0])
true_mix_proportions = torch.tensor([0.1, 0.3, 0.6])
cluster_assignments = dist.Categorical(true_mix_proportions).sample(
torch.Size((N,))
)
data = dist.Normal(true_cluster_means[cluster_assignments], 1.0).sample()
nuts_kernel = NUTS(
gmm, max_plate_nesting=1, jit_compile=jit, ignore_jit_warnings=True
)
mcmc = MCMC(nuts_kernel, num_samples=300, warmup_steps=100)
mcmc.run(data)
samples = mcmc.get_samples()
assert_equal(samples["phi"].mean(0).sort()[0], true_mix_proportions, prec=0.05)
assert_equal(
samples["cluster_means"].mean(0).sort()[0], true_cluster_means, prec=0.2
)
def test_gaussian_hmm(num_steps):
dim = 4
def model(data):
initialize = pyro.sample("initialize", dist.Dirichlet(torch.ones(dim)))
with pyro.plate("states", dim):
transition = pyro.sample("transition", dist.Dirichlet(torch.ones(dim, dim)))
emission_loc = pyro.sample(
"emission_loc", dist.Normal(torch.zeros(dim), torch.ones(dim))
)
emission_scale = pyro.sample(
"emission_scale", dist.LogNormal(torch.zeros(dim), torch.ones(dim))
)
x = None
with ignore_jit_warnings([("Iterating over a tensor", RuntimeWarning)]):
for t, y in pyro.markov(enumerate(data)):
x = pyro.sample(
"x_{}".format(t),
dist.Categorical(initialize if x is None else transition[x]),
infer={"enumerate": "parallel"},
)
pyro.sample(
"y_{}".format(t),
dist.Normal(emission_loc[x], emission_scale[x]),
obs=y,
)
def _get_initial_trace():
guide = AutoDelta(
poutine.block(
model,
expose_fn=lambda msg: not msg["name"].startswith("x")
and not msg["name"].startswith("y"),
)
)
elbo = TraceEnum_ELBO(max_plate_nesting=1)
svi = SVI(model, guide, optim.Adam({"lr": 0.01}), elbo)
for _ in range(100):
svi.step(data)
return poutine.trace(guide).get_trace(data)
def _generate_data():
transition_probs = torch.rand(dim, dim)
emissions_loc = torch.arange(dim, dtype=torch.Tensor().dtype)
emissions_scale = 1.0
state = torch.tensor(1)
obs = [dist.Normal(emissions_loc[state], emissions_scale).sample()]
for _ in range(num_steps):
state = dist.Categorical(transition_probs[state]).sample()
obs.append(dist.Normal(emissions_loc[state], emissions_scale).sample())
return torch.stack(obs)
data = _generate_data()
nuts_kernel = NUTS(
model, max_plate_nesting=1, jit_compile=True, ignore_jit_warnings=True
)
if num_steps == 30:
nuts_kernel.initial_trace = _get_initial_trace()
mcmc = MCMC(nuts_kernel, num_samples=5, warmup_steps=5)
mcmc.run(data)
def test_beta_binomial(hyperpriors):
def model(data):
with pyro.plate("plate_0", data.shape[-1]):
alpha = pyro.sample(
"alpha", dist.HalfCauchy(1.)) if hyperpriors else torch.tensor(
[1., 1.])
beta = pyro.sample(
"beta", dist.HalfCauchy(1.)) if hyperpriors else torch.tensor(
[1., 1.])
beta_binom = BetaBinomialPair()
with pyro.plate("plate_1", data.shape[-2]):
probs = pyro.sample("probs", beta_binom.latent(alpha, beta))
with pyro.plate("data", data.shape[0]):
pyro.sample("binomial",
beta_binom.conditional(
probs=probs, total_count=total_count),
obs=data)
true_probs = torch.tensor([[0.7, 0.4], [0.6, 0.4]])
total_count = torch.tensor([[1000, 600], [400, 800]])
num_samples = 80
data = dist.Binomial(
total_count=total_count,
probs=true_probs).sample(sample_shape=(torch.Size((10, ))))
hmc_kernel = NUTS(collapse_conjugate(model),
jit_compile=True,
ignore_jit_warnings=True)
mcmc = MCMC(hmc_kernel, num_samples=num_samples, warmup_steps=50)
mcmc.run(data)
samples = mcmc.get_samples()
posterior = posterior_replay(model, samples, data, num_samples=num_samples)
assert_equal(posterior["probs"].mean(0), true_probs, prec=0.05)
def test_gamma_poisson(hyperpriors):
def model(data):
with pyro.plate("latent_dim", data.shape[1]):
alpha = (
pyro.sample("alpha", dist.HalfCauchy(1.0))
if hyperpriors
else torch.tensor([1.0, 1.0])
)
beta = (
pyro.sample("beta", dist.HalfCauchy(1.0))
if hyperpriors
else torch.tensor([1.0, 1.0])
)
gamma_poisson = GammaPoissonPair()
rate = pyro.sample("rate", gamma_poisson.latent(alpha, beta))
with pyro.plate("data", data.shape[0]):
pyro.sample("obs", gamma_poisson.conditional(rate), obs=data)
true_rate = torch.tensor([3.0, 10.0])
num_samples = 100
data = dist.Poisson(rate=true_rate).sample(sample_shape=(torch.Size((100,))))
hmc_kernel = NUTS(
collapse_conjugate(model), jit_compile=True, ignore_jit_warnings=True
)
mcmc = MCMC(hmc_kernel, num_samples=num_samples, warmup_steps=50)
mcmc.run(data)
samples = mcmc.get_samples()
posterior = posterior_replay(model, samples, data, num_samples=num_samples)
assert_equal(posterior["rate"].mean(0), true_rate, prec=0.3)
def sample(draws=500,
model=None,
warmup_steps=None,
num_chains=1,
kernel='nuts'):
"""Markov-chain Monte Carlo sampling.
Sampling should be run within the context of a model or the model should be passed as an argument `model` explicitly.
Number of samples is given by `draws` which defaults to `500`.
Warm-up steps are assumed to be 30% of sample count.
MCMC kernel can be selected by setting `kernel`. `hmc` and `nuts` are available.
`pmpyro.inference.sample` returns a trace of samples
"""
# get model from context
if model is None:
model = Context.get_context()
stfn = model.stfn # get stochastic function from model
data = model.args # get data
# make nuts kernel
kernels = {'nuts': NUTS(stfn, adapt_step_size=True), 'hmc': HMC(stfn)}
# if not num_chains: # figure out number of chains
# num_chains = max(os.cpu_count() -1, 2)
if not warmup_steps: # figure out warm-up steps
warmup_steps = int(0.3 * draws)
# run MCMC
mcmc = MCMC(kernels[kernel],
num_samples=draws,
warmup_steps=warmup_steps,
num_chains=num_chains)
mcmc.run(*data)
# get num samples
num_samples = num_chains * draws
return mcmc.get_samples()
def test_nuts_conjugate_gaussian(
fixture,
num_samples,
warmup_steps,
expected_means,
expected_precs,
mean_tol,
std_tol,
):
pyro.get_param_store().clear()
nuts_kernel = NUTS(fixture.model)
mcmc = MCMC(nuts_kernel, num_samples, warmup_steps)
mcmc.run(fixture.data)
samples = mcmc.get_samples()
for i in range(1, fixture.chain_len + 1):
param_name = "loc_" + str(i)
latent = samples[param_name]
latent_loc = latent.mean(0)
latent_std = latent.std(0)
expected_mean = torch.ones(fixture.dim) * expected_means[i - 1]
expected_std = 1 / torch.sqrt(torch.ones(fixture.dim) * expected_precs[i - 1])
# Actual vs expected posterior means for the latents
logger.debug("Posterior mean (actual) - {}".format(param_name))
logger.debug(latent_loc)
logger.debug("Posterior mean (expected) - {}".format(param_name))
logger.debug(expected_mean)
assert_equal(rmse(latent_loc, expected_mean).item(), 0.0, prec=mean_tol)
# Actual vs expected posterior precisions for the latents
logger.debug("Posterior std (actual) - {}".format(param_name))
logger.debug(latent_std)
logger.debug("Posterior std (expected) - {}".format(param_name))
logger.debug(expected_std)
assert_equal(rmse(latent_std, expected_std).item(), 0.0, prec=std_tol)
def numpyro_schools_model(data, draws, chains):
"""Centered eight schools implementation in NumPyro."""
import jax
import numpyro
import numpyro.distributions as dist
from numpyro.mcmc import MCMC, NUTS
def model():
mu = numpyro.sample("mu", dist.Normal(0, 5))
tau = numpyro.sample("tau", dist.HalfCauchy(5))
# TODO: use numpyro.plate or `sample_shape` kwargs instead of # pylint: disable=fixme
# multiplying with np.ones(J) in future versions of NumPyro
theta = numpyro.sample("theta",
dist.Normal(mu * np.ones(data["J"]), tau))
numpyro.sample("obs", dist.Normal(theta, data["sigma"]), obs=data["y"])
mcmc = MCMC(
NUTS(model),
num_warmup=draws,
num_samples=draws,
num_chains=chains,
chain_method="sequential",
)
mcmc.run(jax.random.PRNGKey(0), collect_fields=("z", "diverging"))
return mcmc
class BinomialQuadraticApproximator():
def __init__(self, X, N, n_steps, learning_rate, prior_type, infer_type):
self.X = X
self.N = N
self.n_steps = n_steps
self.prior_type = prior_type
self.infer_type = infer_type
self.optimiser = pyro.optim.Adam({'lr': learning_rate})
self.map_guide = AutoLaplaceApproximation(self.model)
def plot(self):
plt.subplot(3, 1, 1)
plt.plot(self.losses)
plt.title('losses')
plt.subplot(3, 1, 2)
plt.plot(self._posterior_approximate_mean)
plt.title('Posterior Mean')
plt.subplot(3, 1, 3)
plt.plot(self._posterior_approximate_scale)
plt.title('Posterior Scale (Variance)')
def train(self, **kwargs):
pyro.clear_param_store()
if self.infer_type == 'svi':
self._svi_trainer(**kwargs)
elif self.infer_type == 'mcmc':
self._mcmc_trainer(**kwargs)
def _svi_trainer(self):
svi = SVI(self.model, self.map_guide, self.optimiser, Trace_ELBO())
self.losses = []
self._posterior_approximate_mean = []
self._posterior_approximate_scale = []
for step in range(self.n_steps):
loss = svi.step(self.X)
self.losses.append(loss)
quadratic_approximation = self.map_guide.laplace_approximation(self.X).get_posterior()
self._posterior_approximate_mean.append(quadratic_approximation.loc.item())
self._posterior_approximate_scale.append(quadratic_approximation.scale_tril.item())
if step % 50 == 0:
print('[iter {}] loss: {:.4f}'.format(step, loss))
def _mcmc_trainer(self, step_size=0.1, num_samples=1000, warmup_steps=100):
mcmc_kernel = NUTS(self.model, step_size=step_size)
self.mcmc = MCMC(mcmc_kernel, num_samples=num_samples, warmup_steps=warmup_steps)
self.mcmc.run(self.X)
def model(self, data):
if self.prior_type == 'uniform':
p = pyro.sample('p', dist.Uniform(0, 1))
elif self.prior_type == 'beta':
p = pyro.sample('p', dist.Beta(10.0, 10.0))
return pyro.sample('obs', dist.Binomial(total_count=self.N, probs=p), obs=self.X)
def train_nuts(model, data, num_warmup, num_samples, num_chains=1, **kwargs):
_kwargs = dict(adapt_step_size=True, adapt_mass_matrix=True, jit_compile=True)
_kwargs.update(kwargs)
print(_kwargs)
kernel = NUTS(model, **_kwargs)
engine = MCMC(kernel, num_samples, num_warmup, num_chains=num_chains)
engine.run(data, training=True)
return engine
def run_inference(
pyro_model: Callable[[Tensor, Tensor, Tensor, bool, str, float], None],
X: Tensor,
Y: Tensor,
Yvar: Tensor,
num_samples: int = 512,
warmup_steps: int = 1024,
thinning: int = 16,
use_input_warping: bool = False,
max_tree_depth: int = 6,
use_saas: bool = False,
disable_progbar: bool = False,
) -> Tensor:
start = time.time()
try:
from pyro.infer.mcmc import NUTS, MCMC
except ImportError: # pragma: no cover
raise RuntimeError("Cannot call run_inference without pyro installed!")
kernel = NUTS(
pyro_model,
jit_compile=True,
full_mass=True,
ignore_jit_warnings=True,
max_tree_depth=max_tree_depth,
)
mcmc = MCMC(
kernel,
warmup_steps=warmup_steps,
num_samples=num_samples,
disable_progbar=disable_progbar,
)
mcmc.run(
# there is an issue with jit-compilation and cuda
# for now, we run MCMC on the CPU.
X.cpu(),
Y.cpu(),
Yvar.cpu(),
use_input_warping=use_input_warping,
use_saas=use_saas,
)
# this prints the summary
orig_std_out = sys.stdout.write
sys.stdout.write = logger.info
mcmc.summary()
sys.stdout.write = orig_std_out
logger.info(f"MCMC elapsed time: {time.time() - start}")
samples = mcmc.get_samples()
if use_saas: # compute the lengthscale for saas and throw away everything else
inv_length_sq = (samples["kernel_tausq"].unsqueeze(-1) *
samples["_kernel_inv_length_sq"])
samples["lengthscale"] = (1.0 /
inv_length_sq).sqrt() # pyre-ignore [16]
del samples["kernel_tausq"], samples["_kernel_inv_length_sq"]
# thin
for k, v in samples.items():
# apply thinning and move back to X's device
samples[k] = v[::thinning].to(device=X.device)
return samples
def fit_fully_bayesian_model_nuts(
model: SaasFullyBayesianSingleTaskGP,
max_tree_depth: int = 6,
warmup_steps: int = 512,
num_samples: int = 256,
thinning: int = 16,
disable_progbar: bool = False,
) -> None:
r"""Fit a fully Bayesian model using the No-U-Turn-Sampler (NUTS)
Args:
model: SaasFullyBayesianSingleTaskGP to be fitted.
max_tree_depth: Maximum tree depth for NUTS
warmup_steps: The number of burn-in steps for NUTS.
num_samples: The number of MCMC samples. Note that with thinning,
num_samples / thinning samples are retained.
thinning: The amount of thinning. Every nth sample is retained.
disable_progbar: A boolean indicating whether to print the progress
bar and diagnostics during MCMC.
Example:
>>> gp = SaasFullyBayesianSingleTaskGP(train_X, train_Y)
>>> fit_fully_bayesian_model_nuts(gp)
"""
model.train()
# Do inference with NUTS
nuts = NUTS(
model.pyro_model.sample,
jit_compile=True,
full_mass=True,
ignore_jit_warnings=True,
max_tree_depth=max_tree_depth,
)
mcmc = MCMC(
nuts,
warmup_steps=warmup_steps,
num_samples=num_samples,
disable_progbar=disable_progbar,
)
mcmc.run()
# Get final MCMC samples from the Pyro model
mcmc_samples = model.pyro_model.postprocess_mcmc_samples(
mcmc_samples=mcmc.get_samples())
for k, v in mcmc_samples.items():
mcmc_samples[k] = v[::thinning]
# Load the MCMC samples back into the BoTorch model
model.load_mcmc_samples(mcmc_samples)
model.eval()
def test_pyro_sampling(self):
try:
import pyro # noqa
from pyro.infer.mcmc import NUTS, MCMC
except ImportError:
return
train_x, test_x, train_y, test_y = self._get_data(cuda=False)
likelihood = GaussianLikelihood(
noise_constraint=gpytorch.constraints.Positive())
gp_model = ExactGPModel(train_x, train_y, likelihood)
# Register normal GPyTorch priors
gp_model.mean_module.register_prior("mean_prior", UniformPrior(-1, 1),
"constant")
gp_model.covar_module.base_kernel.register_prior(
"lengthscale_prior", UniformPrior(0.01, 0.5), "lengthscale")
gp_model.covar_module.register_prior("outputscale_prior",
UniformPrior(1, 2), "outputscale")
likelihood.register_prior("noise_prior", UniformPrior(0.05, 0.3),
"noise")
def pyro_model(x, y):
with gpytorch.settings.fast_computations(False, False, False):
sampled_model = gp_model.pyro_sample_from_prior()
output = sampled_model.likelihood(sampled_model(x))
pyro.sample("obs", output, obs=y)
return y
nuts_kernel = NUTS(pyro_model, adapt_step_size=True)
mcmc_run = MCMC(nuts_kernel,
num_samples=3,
warmup_steps=20,
disable_progbar=True)
mcmc_run.run(train_x, train_y)
gp_model.pyro_load_from_samples(mcmc_run.get_samples())
gp_model.eval()
expanded_test_x = test_x.unsqueeze(-1).repeat(3, 1, 1)
output = gp_model(expanded_test_x)
self.assertEqual(output.mean.size(0), 3)
# All 3 samples should do reasonably well on a noiseless dataset.
self.assertLess(
torch.norm(output.mean[0] - test_y) / test_y.norm(), 0.2)
self.assertLess(
torch.norm(output.mean[1] - test_y) / test_y.norm(), 0.2)
self.assertLess(
torch.norm(output.mean[2] - test_y) / test_y.norm(), 0.2)
def test_gp_kernels(self):
torch.manual_seed(0)
X = torch.randn(3, 2)
Y = torch.randn(3, 1)
Yvar = torch.randn(3, 1)
kernel = NUTS(single_task_pyro_model, max_tree_depth=1)
with self.assertRaises(ValueError):
mcmc = MCMC(kernel, warmup_steps=0, num_samples=1)
mcmc.run(
X,
Y,
Yvar,
gp_kernel="some_kernel_we_dont_support",
)
def test_dirichlet_categorical(jit):
def model(data):
concentration = torch.tensor([1.0, 1.0, 1.0])
p_latent = pyro.sample("p_latent", dist.Dirichlet(concentration))
pyro.sample("obs", dist.Categorical(p_latent), obs=data)
return p_latent
true_probs = torch.tensor([0.1, 0.6, 0.3])
data = dist.Categorical(true_probs).sample(sample_shape=(torch.Size((2000,))))
nuts_kernel = NUTS(model, jit_compile=jit, ignore_jit_warnings=True)
mcmc = MCMC(nuts_kernel, num_samples=200, warmup_steps=100)
mcmc.run(data)
samples = mcmc.get_samples()
posterior = samples["p_latent"]
assert_equal(posterior.mean(0), true_probs, prec=0.02)
def test_gamma_beta(jit):
def model(data):
alpha_prior = pyro.sample('alpha', dist.Gamma(concentration=1., rate=1.))
beta_prior = pyro.sample('beta', dist.Gamma(concentration=1., rate=1.))
pyro.sample('x', dist.Beta(concentration1=alpha_prior, concentration0=beta_prior), obs=data)
true_alpha = torch.tensor(5.)
true_beta = torch.tensor(1.)
data = dist.Beta(concentration1=true_alpha, concentration0=true_beta).sample(torch.Size((5000,)))
nuts_kernel = NUTS(model, jit_compile=jit, ignore_jit_warnings=True)
mcmc = MCMC(nuts_kernel, num_samples=500, warmup_steps=200)
mcmc.run(data)
samples = mcmc.get_samples()
assert_equal(samples["alpha"].mean(0), true_alpha, prec=0.08)
assert_equal(samples["beta"].mean(0), true_beta, prec=0.05)
def test_pyro_sampling(self):
try:
import pyro
from pyro.infer.mcmc import NUTS, MCMC
except:
return
train_x, test_x, train_y, test_y = self._get_data(cuda=False)
likelihood = GaussianLikelihood(
noise_constraint=gpytorch.constraints.Positive())
gp_model = ExactGPModel(train_x, train_y, likelihood)
# Register normal GPyTorch priors
gp_model.mean_module.register_prior("mean_prior", UniformPrior(-1, 1),
"constant")
gp_model.covar_module.base_kernel.register_prior(
"lengthscale_prior", UniformPrior(0.01, 0.2), "lengthscale")
gp_model.covar_module.register_prior("outputscale_prior",
UniformPrior(1, 2), "outputscale")
likelihood.register_prior("noise_prior", LogNormalPrior(-1.5, 0.1),
"noise")
mll = gpytorch.mlls.ExactMarginalLogLikelihood(likelihood, gp_model)
def pyro_model(x, y):
gp_model.pyro_sample_from_prior()
output = gp_model(x)
loss = mll.pyro_factor(output, y)
return y
nuts_kernel = NUTS(pyro_model, adapt_step_size=True)
mcmc_run = MCMC(nuts_kernel, num_samples=3, warmup_steps=20)
mcmc_run.run(train_x, train_y)
gp_model.pyro_load_from_samples(mcmc_run.get_samples())
gp_model.eval()
expanded_test_x = test_x.unsqueeze(-1).repeat(3, 1, 1)
output = gp_model(expanded_test_x)
self.assertEqual(output.mean.size(0), 3)
# All 3 samples should do reasonably well on a noiseless dataset.
self.assertLess(
torch.norm(output.mean[0] - test_y) / test_y.norm(), 0.2)
self.assertLess(
torch.norm(output.mean[1] - test_y) / test_y.norm(), 0.2)
self.assertLess(
torch.norm(output.mean[2] - test_y) / test_y.norm(), 0.2)
def test_beta_bernoulli(step_size, adapt_step_size, adapt_mass_matrix, full_mass):
def model(data):
alpha = torch.tensor([1.1, 1.1])
beta = torch.tensor([1.1, 1.1])
p_latent = pyro.sample("p_latent", dist.Beta(alpha, beta))
pyro.sample("obs", dist.Bernoulli(p_latent), obs=data)
return p_latent
true_probs = torch.tensor([0.9, 0.1])
data = dist.Bernoulli(true_probs).sample(sample_shape=(torch.Size((1000,))))
nuts_kernel = NUTS(model, step_size=step_size, adapt_step_size=adapt_step_size,
adapt_mass_matrix=adapt_mass_matrix, full_mass=full_mass)
mcmc = MCMC(nuts_kernel, num_samples=400, warmup_steps=200)
mcmc.run(data)
samples = mcmc.get_samples()
assert_equal(samples["p_latent"].mean(0), true_probs, prec=0.02)
def pyro_centered_schools(data, draws, chains):
"""Centered eight schools implementation in Pyro.
Note there is not really a deterministic node in pyro, so I do not
know how to do a non-centered implementation.
"""
import torch
from pyro.infer.mcmc import MCMC, NUTS
del chains
y = torch.Tensor(data["y"]).type(torch.Tensor)
sigma = torch.Tensor(data["sigma"]).type(torch.Tensor)
nuts_kernel = NUTS(_pyro_conditioned_model, adapt_step_size=True)
posterior = MCMC( # pylint:disable=not-callable
nuts_kernel, num_samples=draws, warmup_steps=500
).run(_pyro_centered_model, sigma, y)
# This block lets the posterior be pickled
for trace in posterior.exec_traces:
for node in trace.nodes.values():
node.pop("fn", None)
posterior.kernel = None
posterior.run = None
posterior.logger = None
if hasattr(posterior, "sampler"):
posterior.sampler = None
return posterior
def _train_hmc(self, train_loader, n_samples, warmup, step_size, num_steps,
device):
print("\n == HMC training ==")
pyro.clear_param_store()
num_batches = int(len(train_loader.dataset) / train_loader.batch_size)
batch_samples = int(n_samples / num_batches) + 1
print("\nn_batches=", num_batches, "\tbatch_samples =", batch_samples)
kernel = HMC(self.model, step_size=step_size, num_steps=num_steps)
mcmc = MCMC(kernel=kernel,
num_samples=batch_samples,
warmup_steps=warmup,
num_chains=1)
start = time.time()
for x_batch, y_batch in train_loader:
x_batch = x_batch.to(device)
labels = y_batch.to(device).argmax(-1)
mcmc.run(x_batch, labels)
execution_time(start=start, end=time.time())
self.posterior_predictive = {}
posterior_samples = mcmc.get_samples(n_samples)
state_dict_keys = list(self.basenet.state_dict().keys())
if DEBUG:
print("\n", list(posterior_samples.values())[-1])
for model_idx in range(n_samples):
net_copy = copy.deepcopy(self.basenet)
model_dict = OrderedDict({})
for weight_idx, weights in enumerate(posterior_samples.values()):
model_dict.update(
{state_dict_keys[weight_idx]: weights[model_idx]})
net_copy.load_state_dict(model_dict)
self.posterior_predictive.update({str(model_idx): net_copy})
if DEBUG:
print("\n", weights[model_idx])
self.save()
def test_gamma_normal(jit, use_multinomial_sampling):
def model(data):
rate = torch.tensor([1.0, 1.0])
concentration = torch.tensor([1.0, 1.0])
p_latent = pyro.sample('p_latent', dist.Gamma(rate, concentration))
pyro.sample("obs", dist.Normal(3, p_latent), obs=data)
return p_latent
true_std = torch.tensor([0.5, 2])
data = dist.Normal(3, true_std).sample(sample_shape=(torch.Size((2000, ))))
nuts_kernel = NUTS(model,
use_multinomial_sampling=use_multinomial_sampling,
jit_compile=jit,
ignore_jit_warnings=True)
mcmc = MCMC(nuts_kernel, num_samples=200, warmup_steps=100)
mcmc.run(data)
samples = mcmc.get_samples()
assert_equal(samples["p_latent"].mean(0), true_std, prec=0.05)
def run(param):
nn_model, p_tgt, save_fn, args = param
if (not args.overwrite) and os.path.isfile(save_fn):
print(save_fn + ' already exists!')
return
if not os.path.isfile(save_fn):
fo = open(save_fn,
'w') # write the file first to signal working on it.
fo.write('\n')
fo.close()
nuts = NUTS(program_arbitrary)
mcmc = MCMC(nuts,
num_samples=args.num_samples,
warmup_steps=args.num_warmups,
num_chains=args.num_chains)
mcmc.run(nn_model, p_tgt)
zs = mcmc.get_samples()['z'].detach().cpu().numpy()
np.savetxt(save_fn, zs)
def test_bernoulli_latent_model(jit):
@poutine.broadcast
def model(data):
y_prob = pyro.sample("y_prob", dist.Beta(1., 1.))
with pyro.plate("data", data.shape[0]):
y = pyro.sample("y", dist.Bernoulli(y_prob))
z = pyro.sample("z", dist.Bernoulli(0.65 * y + 0.1))
pyro.sample("obs", dist.Normal(2. * z, 1.), obs=data)
N = 2000
y_prob = torch.tensor(0.3)
y = dist.Bernoulli(y_prob).sample(torch.Size((N,)))
z = dist.Bernoulli(0.65 * y + 0.1).sample()
data = dist.Normal(2. * z, 1.0).sample()
nuts_kernel = NUTS(model, max_plate_nesting=1, jit_compile=jit, ignore_jit_warnings=True)
mcmc = MCMC(nuts_kernel, num_samples=600, warmup_steps=200)
mcmc.run(data)
samples = mcmc.get_samples()
assert_equal(samples["y_prob"].mean(0), y_prob, prec=0.05)
def test_logistic_regression(jit, use_multinomial_sampling):
dim = 3
data = torch.randn(2000, dim)
true_coefs = torch.arange(1., dim + 1.)
labels = dist.Bernoulli(logits=(true_coefs * data).sum(-1)).sample()
def model(data):
coefs_mean = torch.zeros(dim)
coefs = pyro.sample('beta', dist.Normal(coefs_mean, torch.ones(dim)))
y = pyro.sample('y', dist.Bernoulli(logits=(coefs * data).sum(-1)), obs=labels)
return y
nuts_kernel = NUTS(model,
use_multinomial_sampling=use_multinomial_sampling,
jit_compile=jit,
ignore_jit_warnings=True)
mcmc = MCMC(nuts_kernel, num_samples=500, warmup_steps=100)
mcmc.run(data)
samples = mcmc.get_samples()
assert_equal(rmse(true_coefs, samples["beta"].mean(0)).item(), 0.0, prec=0.1)
def monte_carlo(y):
pyro.clear_param_store()
# create a Simple Hamiltonian Monte Carlo kernel with step_size of 0.1
hmc_kernel = HMC(conditioned_model, step_size=.1)
mcmc = MCMC(hmc_kernel, num_samples=500, warmup_steps=100)
# create a Markov Chain Monte Carlo method with:
# the hmc_kernel, 500 samples, and 100 warmup iterations
mcmc.run(model,y)
mcmc.run(model, y)
sample_dict = mcmc.get_samples(num_samples=5000)
plt.figure(figsize=(8, 6))
sns.distplot(sample_dict["p"].numpy())
plt.xlabel("Observed probability value")
plt.ylabel("Observed frequency")
plt.show()
mcmc.summary(prob=0.95)
return sample_dict
def _train_hmc(self, train_loader, n_samples, warmup, step_size, num_steps, savedir, device):
print("\n == fullBNN HMC training ==")
pyro.clear_param_store()
num_batches = int(len(train_loader.dataset)/train_loader.batch_size)
batch_samples = int(n_samples/num_batches)+1
print("\nn_batches =",num_batches,"\tbatch_samples =", batch_samples)
# kernel = HMC(self.model, step_size=step_size, num_steps=num_steps)
kernel = NUTS(self.model, adapt_step_size=True)
mcmc = MCMC(kernel=kernel, num_samples=batch_samples, warmup_steps=warmup, num_chains=1)
self.posterior_samples=[]
state_dict_keys = list(self.basenet.state_dict().keys())
start = time.time()
for x_batch, y_batch in train_loader:
x_batch = x_batch.to(device)
y_batch = y_batch.to(device).argmax(-1)
mcmc_run = mcmc.run(x_batch, y_batch)
posterior_samples = mcmc.get_samples(batch_samples)
# print('module$$$model.1.weight:\n', posterior_samples['module$$$model.1.weight'][:,0,:5])
for sample_idx in range(batch_samples):
net_copy = copy.deepcopy(self.basenet)
model_dict=OrderedDict({})
for weight_idx, weights in enumerate(posterior_samples.values()):
model_dict.update({state_dict_keys[weight_idx]:weights[sample_idx]})
net_copy.load_state_dict(model_dict)
self.posterior_samples.append(net_copy)
execution_time(start=start, end=time.time())
self.save(savedir)
def mcmc(model,
obs,
num_samples,
kernel='HMC',
kernel_params={},
mcmc_params={},
sites=['theta']):
# NOTE: requires differentiable model
model_conditioned = partial(model, obs=obs)
if kernel.upper() == 'HMC':
mcmc_kernel = HMC(model_conditioned, **kernel_params)
elif kernel.upper() == 'NUTS':
mcmc_kernel = NUTS(model_conditioned, **kernel_params)
else:
raise NotImplementedError
mcmc = MCMC(mcmc_kernel, num_samples, **mcmc_params)
mcmc_run = mcmc.run()
posterior = pyro.infer.EmpiricalMarginal(mcmc_run, sites=sites)
return posterior
class BayesianGP(object):
def __init__(self, x: np.ndarray, y: np.ndarray):
"""
:param x: [N x D]
:param y: [N]
"""
x, y = TensorType(x), TensorType(y)
assert x.ndimension() == 2
assert y.ndimension() == 1
assert x.shape[0] == y.numel()
self.x = x
self.y = y
self.n_samples = 32
self._xform = ExpTransform()
# Length scales for the kernel
self.raw_scales_prior = Normal(zeros(self.dx), ones(self.dx))
# Kernel variance
self.raw_variance_prior = Normal(zeros(1), ones(1))
# Jitter, aka Gaussian likelihood's variance
self.raw_jitter_prior = Normal(-3.0 + zeros(1), ones(1))
# For the constant ("bias") mean function
self.bias_prior = Normal(zeros(1), ones(1))
self._mcmc = None
@property
def dx(self):
"""
Input dimension
"""
return self.x.shape[1]
@property
def n(self):
"""
Number of data
"""
return self.y.numel()
def fit(self):
mcmc_kernel = NUTS(self._prior_model)
self._mcmc = MCMC(mcmc_kernel,
num_samples=self.n_samples,
warmup_steps=128)
self._mcmc.run()
def predict_f(self, x_test, diag=True):
return self._predict(x_test, diag, False)
def predict_y(self, x_test, diag=True):
return self._predict(x_test, diag, True)
def append_data(self, x_new, y_new):
"""
Add new input-output pair(s) to the model
:param x_new: inputs
:type x_new: np.ndarray
:param y_new: outputs
:type y_new: np.ndarray
"""
self.x = torch.cat((self.x, TensorType(np.atleast_2d(x_new))))
self.y = torch.cat((self.y, TensorType(y_new.flatten())))
def _prior_model(self):
scales, variance, jitter, bias = self._get_samples()
if self.n > 0:
kyy = _rbf(self.x, self.x, scales, variance) + jitter * eye(self.n)
try:
ckyy = _jitchol(kyy)
sample(
"output",
MultivariateNormal(bias + zeros(self.n), scale_tril=ckyy),
obs=self.y,
)
except RuntimeError: # Cholesky fails?
# "No chance"
sample("output", Delta(zeros(1)), obs=ones(1))
def _posterior_model(self, x_test, diag, with_jitter):
"""
Return means & (co)variance samples.
"""
assert self.n > 0, "Need at least one training datum for posterior"
scales, variance, jitter, bias = self._get_samples()
kyy = _rbf(self.x, self.x, scales, variance) + jitter * eye(self.n)
ckyy = _jitchol(kyy)
kys = _rbf(self.x, x_test, scales, variance)
alpha = _trtrs(kys, ckyy)
beta = _trtrs(self.y[:, None] - bias, ckyy)
mean = (alpha.t() @ beta).flatten() + bias
if diag:
kss = _rbf_diag(x_test, variance)
cov = kss - torch.sum(alpha**2, dim=0)
if with_jitter:
cov = cov + jitter
# Guard against numerically-negative variances?
cov = cov - (torch.clamp(cov, max=0.0)).detach()
else:
kss = _rbf(x_test, x_test, scales, variance)
cov = kss - alpha.t() @ alpha
if with_jitter:
cov = cov + jitter * eye(*cov.shape)
# Numerically-negativs variances?...
sample("mean", Delta(mean))
sample("cov", Delta(cov))
def _posterior_model_no_data(self, x_test, diag, with_jitter):
"""
When the conditioning set is empty
"""
scales, variance, jitter, bias = self._get_samples()
if diag:
cov = _rbf_diag(x_test, variance)
if with_jitter:
cov = cov + jitter
else:
cov = _rbf(x_test, x_test, scales, variance)
if with_jitter:
cov = cov + jitter * eye(x_test.shape[0])
mean = torch.zeros(x_test.shape[0]) + bias
sample("mean", Delta(mean))
sample("cov", Delta(cov))
def _get_samples(self):
scales = self._xform(sample("raw_scales", self.raw_scales_prior))
variance = self._xform(sample("raw_variance", self.raw_variance_prior))
jitter = self._xform(sample("raw_jitter", self.raw_jitter_prior))
bias = sample("bias", self.bias_prior)
return scales, variance, jitter, bias
@_input_as_tensor
def _predict(self, x_test: TensorType, diag, with_jitter):
"""
Return predictive mean [N* x 1] and either predictive variance [N* x 1]
or covariance [N* x N*]
:return: (TensorType, TensorType) mean & (co)variance
"""
model = self._posterior_model if self.n > 0 else self._posterior_model_no_data
samples = Predictive(model, self._mcmc.get_samples()).get_samples(
x_test, diag, with_jitter)
means, covs = samples["mean"], samples["cov"]
mean = means.mean(dim=0)
# Law of total (co)variance:
if diag:
cov = means.var(dim=0) + covs.mean(dim=0)
else:
d_mean = (means - mean)[:, :, None]
cov_of_means = (d_mean @ torch.transpose(d_mean, 1, 2)).sum(
dim=0) / (means.shape[0] - 1)
mean_of_covs = covs.mean(dim=0)
cov = cov_of_means + mean_of_covs
# Make sure the shapes are right:
if len(mean.shape) == 1:
mean = mean[:, None]
if len(cov.shape) == 1:
cov = cov[:, None]
return mean, cov
