def test_linear_model_sigma(kernel_cls,
N=90,
P=40,
sigma=0.07,
warmup_steps=500,
num_samples=500):
np.random.seed(1)
X = np.random.randn(N * P).reshape((N, P))
XX = np.matmul(np.transpose(X), X)
Y = X[:, 0] + sigma * np.random.randn(N)
XY = np.sum(X * Y[:, None], axis=0)
def model(X, Y):
N, P = X.shape
sigma = numpyro.sample("sigma", dist.HalfCauchy(1.0))
beta = numpyro.sample("beta", dist.Normal(jnp.zeros(P), jnp.ones(P)))
mean = jnp.sum(beta * X, axis=-1)
numpyro.sample("obs", dist.Normal(mean, sigma), obs=Y)
gibbs_fn = partial(_linear_regression_gibbs_fn, X, XX, XY, Y)
hmc_kernel = kernel_cls(model)
kernel = HMCGibbs(hmc_kernel, gibbs_fn=gibbs_fn, gibbs_sites=['beta'])
mcmc = MCMC(kernel, warmup_steps, num_samples, progress_bar=False)
mcmc.run(random.PRNGKey(0), X, Y)
beta_mean = np.mean(mcmc.get_samples()['beta'], axis=0)
assert_allclose(beta_mean, np.array([1.0] + [0.0] * (P - 1)), atol=0.05)
sigma_mean = np.mean(mcmc.get_samples()['sigma'], axis=0)
assert_allclose(sigma_mean, sigma, atol=0.25)
def test_linear_model_log_sigma(
kernel_cls, N=100, P=50, sigma=0.11, num_warmup=500, num_samples=500
):
np.random.seed(0)
X = np.random.randn(N * P).reshape((N, P))
XX = np.matmul(np.transpose(X), X)
Y = X[:, 0] + sigma * np.random.randn(N)
XY = np.sum(X * Y[:, None], axis=0)
def model(X, Y):
N, P = X.shape
log_sigma = numpyro.sample("log_sigma", dist.Normal(1.0))
sigma = jnp.exp(log_sigma)
beta = numpyro.sample("beta", dist.Normal(jnp.zeros(P), jnp.ones(P)))
mean = jnp.sum(beta * X, axis=-1)
numpyro.deterministic("mean", mean)
numpyro.sample("obs", dist.Normal(mean, sigma), obs=Y)
gibbs_fn = partial(_linear_regression_gibbs_fn, X, XX, XY, Y)
hmc_kernel = kernel_cls(model)
kernel = HMCGibbs(hmc_kernel, gibbs_fn=gibbs_fn, gibbs_sites=["beta"])
mcmc = MCMC(
kernel, num_warmup=num_warmup, num_samples=num_samples, progress_bar=False
)
mcmc.run(random.PRNGKey(0), X, Y)
beta_mean = np.mean(mcmc.get_samples()["beta"], axis=0)
assert_allclose(beta_mean, np.array([1.0] + [0.0] * (P - 1)), atol=0.05)
sigma_mean = np.exp(np.mean(mcmc.get_samples()["log_sigma"], axis=0))
assert_allclose(sigma_mean, sigma, atol=0.25)
def test_gaussian_model(kernel_cls, D=2, num_warmup=5000, num_samples=5000):
np.random.seed(0)
cov = np.random.randn(4 * D * D).reshape((2 * D, 2 * D))
cov = jnp.matmul(jnp.transpose(cov), cov) + 0.25 * jnp.eye(2 * D)
cov00 = cov[:D, :D]
cov01 = cov[:D, D:]
cov10 = cov[D:, :D]
cov11 = cov[D:, D:]
cov_01_cov11_inv = jnp.matmul(cov01, inv(cov11))
cov_10_cov00_inv = jnp.matmul(cov10, inv(cov00))
posterior_cov0 = cov00 - jnp.matmul(cov_01_cov11_inv, cov10)
posterior_cov1 = cov11 - jnp.matmul(cov_10_cov00_inv, cov01)
# we consider a model in which (x0, x1) ~ MVN(0, cov)
def gaussian_gibbs_fn(rng_key, hmc_sites, gibbs_sites):
x1 = hmc_sites["x1"]
posterior_loc0 = jnp.matmul(cov_01_cov11_inv, x1)
x0_proposal = dist.MultivariateNormal(
loc=posterior_loc0,
covariance_matrix=posterior_cov0).sample(rng_key)
return {"x0": x0_proposal}
def model():
x0 = numpyro.sample(
"x0",
dist.MultivariateNormal(loc=jnp.zeros(D), covariance_matrix=cov00))
posterior_loc1 = jnp.matmul(cov_10_cov00_inv, x0)
numpyro.sample(
"x1",
dist.MultivariateNormal(loc=posterior_loc1,
covariance_matrix=posterior_cov1),
)
hmc_kernel = kernel_cls(model, dense_mass=True)
kernel = HMCGibbs(hmc_kernel,
gibbs_fn=gaussian_gibbs_fn,
gibbs_sites=["x0"])
mcmc = MCMC(kernel,
num_warmup=num_warmup,
num_samples=num_samples,
progress_bar=False)
mcmc.run(random.PRNGKey(0))
x0_mean = np.mean(mcmc.get_samples()["x0"], axis=0)
x1_mean = np.mean(mcmc.get_samples()["x1"], axis=0)
x0_std = np.std(mcmc.get_samples()["x0"], axis=0)
x1_std = np.std(mcmc.get_samples()["x1"], axis=0)
assert_allclose(x0_mean, np.zeros(D), atol=0.2)
assert_allclose(x1_mean, np.zeros(D), atol=0.2)
assert_allclose(x0_std, np.sqrt(np.diagonal(cov00)), rtol=0.05)
assert_allclose(x1_std, np.sqrt(np.diagonal(cov11)), rtol=0.1)
def test_discrete_gibbs_enum():
def model():
numpyro.sample("x", dist.Bernoulli(0.7))
y = numpyro.sample("y", dist.Binomial(10, 0.3))
numpyro.deterministic("y2", y**2)
kernel = HMCGibbs(NUTS(model), discrete_gibbs_fn(model), gibbs_sites=["y"])
mcmc = MCMC(kernel, 1000, 10000, progress_bar=False)
mcmc.run(random.PRNGKey(0))
samples = mcmc.get_samples()
assert_allclose(jnp.mean(samples["y"], 0), 0.3 * 10, atol=0.1)
def test_discrete_gibbs_bernoulli(random_walk, modified):
def model():
numpyro.sample("c", dist.Bernoulli(0.8))
gibbs_fn = discrete_gibbs_fn(model,
random_walk=random_walk,
modified=modified)
kernel = HMCGibbs(NUTS(model), gibbs_fn, gibbs_sites=["c"])
mcmc = MCMC(kernel, 1000, 200000, progress_bar=False)
mcmc.run(random.PRNGKey(0))
samples = mcmc.get_samples()["c"]
assert_allclose(jnp.mean(samples), 0.8, atol=0.05)
def test_discrete_gibbs_multiple_sites():
def model():
numpyro.sample("x", dist.Bernoulli(0.7).expand([3]))
numpyro.sample("y", dist.Binomial(10, 0.3))
kernel = HMCGibbs(NUTS(model),
discrete_gibbs_fn(model),
gibbs_sites=["x", "y"])
mcmc = MCMC(kernel, 1000, 10000, progress_bar=False)
mcmc.run(random.PRNGKey(0))
samples = mcmc.get_samples()
assert_allclose(jnp.mean(samples["x"], 0), 0.7 * jnp.ones(3), atol=0.01)
assert_allclose(jnp.mean(samples["y"], 0), 0.3 * 10, atol=0.1)
def test_discrete_gibbs_gmm_1d(modified):
def model(probs, locs):
c = numpyro.sample("c", dist.Categorical(probs))
numpyro.sample("x", dist.Normal(locs[c], 0.5))
probs = jnp.array([0.15, 0.3, 0.3, 0.25])
locs = jnp.array([-2, 0, 2, 4])
gibbs_fn = discrete_gibbs_fn(model, (probs, locs), modified=modified)
kernel = HMCGibbs(NUTS(model), gibbs_fn, gibbs_sites=["c"])
mcmc = MCMC(kernel, 1000, 200000, progress_bar=False)
mcmc.run(random.PRNGKey(0), probs, locs)
samples = mcmc.get_samples()
assert_allclose(jnp.mean(samples["x"]), 1.3, atol=0.1)
assert_allclose(jnp.var(samples["x"]), 4.36, atol=0.1)
assert_allclose(jnp.mean(samples["c"]), 1.65, atol=0.1)
assert_allclose(jnp.var(samples["c"]), 1.03, atol=0.1)
def sample_posterior_gibbs(rng_key: random.PRNGKey,
model,
data: np.ndarray,
Nsamples: int = 1000,
alpha: float = 1,
sigma: float = 0,
T: int = 10,
gibbs_fn=None,
gibbs_sites=None):
assert gibbs_fn is not None
assert gibbs_sites is not None
Npoints = len(data)
inner_kernel = NUTS(model)
kernel = HMCGibbs(inner_kernel, gibbs_fn=gibbs_fn, gibbs_sites=gibbs_sites)
mcmc = MCMC(kernel, num_samples=Nsamples, num_warmup=NUM_WARMUP)
mcmc.run(rng_key, data=data, alpha=alpha, sigma=sigma, T=T)
samples = mcmc.get_samples()
z = samples['z']
assert z.shape == (Nsamples, Npoints)
return z
