def sample(self, conv_rate, relative_copy_chrc, depth):
relative_copy_chrc = relative_copy_chrc.repeat(self.n_sample,1)
depth = depth.repeat(self.n_sample, 1)
num_nulcear = dist.Binomial(depth, 1 / (1 + relative_copy_chrc) ).sample()
num_non_conv = dist.Binomial(depth - num_nulcear, conv_rate).sample()
return(num_nulcear + num_non_conv)
def reparameterized_discrete_model(args, data):
# Sample global parameters.
rate_s, prob_i, rho = global_model(args.population)
# Sequentially sample time-local variables.
S_curr = torch.tensor(args.population - 1.0)
I_curr = torch.tensor(1.0)
for t, datum in enumerate(data):
# Sample reparameterizing variables.
# When reparameterizing to a factor graph, we ignored density via
# .mask(False). Thus distributions are used only for initialization.
S_prev, I_prev = S_curr, I_curr
S_curr = pyro.sample("S_{}".format(t),
dist.Binomial(args.population, 0.5).mask(False))
I_curr = pyro.sample("I_{}".format(t),
dist.Binomial(args.population, 0.5).mask(False))
# Now we reverse the computation.
S2I = S_prev - S_curr
I2R = I_prev - I_curr + S2I
pyro.sample(
"S2I_{}".format(t),
dist.ExtendedBinomial(S_prev, -(rate_s * I_prev).expm1()),
obs=S2I,
)
pyro.sample("I2R_{}".format(t),
dist.ExtendedBinomial(I_prev, prob_i),
obs=I2R)
pyro.sample("obs_{}".format(t),
dist.ExtendedBinomial(S2I, rho),
obs=datum)
def model(data, params):
# initialize data
data = {k: torch.tensor(v).float() for k, v in data.items()}
n1 = data["n1"]
n2 = data["n2"]
k1 = data["k1"]
k2 = data["k2"]
# init parameters
theta = pyro.sample("theta", dist.Beta(1., 1.))
pyro.sample("k1", dist.Binomial(n1, theta), obs=k1)
pyro.sample("k2", dist.Binomial(n2, theta), obs=k2)
def test_beta_binomial_dependent_sample():
total = 10
counts = dist.Binomial(total, 0.3).sample()
concentration1 = torch.tensor(0.5)
concentration0 = torch.tensor(1.5)
prior = dist.Beta(concentration1, concentration0)
posterior = dist.Beta(concentration1 + counts,
concentration0 + total - counts)
def model(counts):
prob = pyro.sample("prob", prior)
pyro.sample("counts", dist.Binomial(total, prob), obs=counts)
reparam_model = poutine.reparam(
model,
{
"prob":
ConjugateReparam(
lambda counts: dist.Beta(1 + counts, 1 + total - counts)),
},
)
with poutine.trace() as tr, pyro.plate("particles", 10000):
reparam_model(counts)
samples = tr.trace.nodes["prob"]["value"]
assert_close(samples.mean(), posterior.mean, atol=0.01)
assert_close(samples.std(), posterior.variance.sqrt(), atol=0.01)
def test_beta_binomial_hmc():
num_samples = 1000
total = 10
counts = dist.Binomial(total, 0.3).sample()
concentration1 = torch.tensor(0.5)
concentration0 = torch.tensor(1.5)
prior = dist.Beta(concentration1, concentration0)
likelihood = dist.Beta(1 + counts, 1 + total - counts)
posterior = dist.Beta(concentration1 + counts,
concentration0 + total - counts)
def model():
prob = pyro.sample("prob", prior)
pyro.sample("counts", dist.Binomial(total, prob), obs=counts)
reparam_model = poutine.reparam(model,
{"prob": ConjugateReparam(likelihood)})
kernel = HMC(reparam_model)
samples = MCMC(kernel, num_samples, warmup_steps=0).run()
pred = Predictive(reparam_model, samples, num_samples=num_samples)
trace = pred.get_vectorized_trace()
samples = trace.nodes["prob"]["value"]
assert_close(samples.mean(), posterior.mean, atol=0.01)
assert_close(samples.std(), posterior.variance.sqrt(), atol=0.01)
def model(self, n_samples=None, anwser_mask=True):
"""p(x) for BigFiveModel
Keyword Arguments:
n_samples {int} -- Number of samples to generate (default: {None})
anwser_mask {bool or list of booleans} -- Mask with shape of anwsers. 1.0 represent observed value and False represent unobserved (default: {True})
Returns:
(anwser, trait) -- Anwsers and traits that were generated by the model
"""
if n_samples is None:
n_samples = len(self._observations)
with pyro.plate("person", n_samples):
# Draw a trait value from Beta. We assume a Gaussian-shaped Beta with mean 0.5 as a prior
with pyro.plate('traits', 5):
trait = pyro.sample(
'trait',
dist.Beta(torch.tensor(self.ALPHA_PRIOR),
torch.tensor(self.BETA_PRIOR)))
with pyro.plate("question", 10):
anwser = pyro.sample(
'anwser',
dist.Binomial(4, trait).mask(anwser_mask))
return anwser, trait
def model(data, params):
# initialize data
n = torch.tensor(data["n"]).float()
k = torch.tensor(data["k"]).float()
theta = pyro.sample("theta", dist.Beta(1., 1.))
pyro.sample("k", dist.Binomial(n, theta), obs=k)
def discrete_model(args, data):
# Sample global parameters.
rate_s, prob_i, rho = global_model(args.population)
# Sequentially sample time-local variables.
S = torch.tensor(args.population - 1.0)
I = torch.tensor(1.0)
for t, datum in enumerate(data):
S2I = pyro.sample("S2I_{}".format(t),
dist.Binomial(S, -(rate_s * I).expm1()))
I2R = pyro.sample("I2R_{}".format(t), dist.Binomial(I, prob_i))
S = pyro.deterministic("S_{}".format(t), S - S2I)
I = pyro.deterministic("I_{}".format(t), I + S2I - I2R)
pyro.sample("obs_{}".format(t),
dist.ExtendedBinomial(S2I, rho),
obs=datum)
def test_extended_binomial(tol):
with set_approx_log_prob_tol(tol):
total_count = torch.tensor([0.0, 1.0, 2.0, 10.0])
probs = torch.tensor([0.5, 0.5, 0.4, 0.2]).requires_grad_()
d1 = dist.Binomial(total_count, probs)
d2 = dist.ExtendedBinomial(total_count, probs)
# Check on good data.
data = d1.sample((100, ))
assert_equal(d1.log_prob(data), d2.log_prob(data))
# Check on extended data.
data = torch.arange(-10.0, 20.0).unsqueeze(-1)
with pytest.raises(ValueError):
d1.log_prob(data)
log_prob = d2.log_prob(data)
valid = d1.support.check(data)
assert ((log_prob > -math.inf) == valid).all()
check_grad(log_prob, probs)
# Check on shape error.
with pytest.raises(ValueError):
d2.log_prob(torch.tensor([0.0, 0.0]))
# Check on value error.
with pytest.raises(ValueError):
d2.log_prob(torch.tensor(0.5))
# Check on negative total_count.
total_count = torch.arange(-10, 0.0)
probs = torch.tensor(0.5).requires_grad_()
d = dist.ExtendedBinomial(total_count, probs)
log_prob = d.log_prob(data)
assert (log_prob == -math.inf).all()
check_grad(log_prob, probs)
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 nested():
true_probs = torch.ones(5) * 0.7
num_trials = torch.ones(5) * 1000
num_success = dist.Binomial(num_trials, true_probs).sample()
conditioned_model = poutine.condition(model, data={"obs": num_success})
nuts_kernel = NUTS(conditioned_model, adapt_step_size=True)
mcmc_run = MCMC(nuts_kernel, num_samples=10, warmup_steps=2).run(num_trials)
return mcmc_run
def _model_(self):
control_prior = pyro.sample('control_p', dist.Beta(1, 1))
treatment_prior = pyro.sample('treatment_p', dist.Beta(1, 1))
return pyro.sample(
'obs',
dist.Binomial(self.traffic_size,
torch.stack([control_prior, treatment_prior])),
obs=self.outcome)
def model_current(data):
# define the hyperparameters that control the beta prior
alpha0 = torch.tensor(10.0)
beta0 = torch.tensor(10.0)
f = pyro.sample("prior_current", dist.Beta(alpha0, beta0))
# Determine the binomial likelihood of the observed data, assuming each hypothesis is true
for i in range(len(data)):
pyro.sample(f'obs_prop_{i}', dist.Binomial(probs=f), obs=data[i])
def model(data, params):
# initialize data
data = {k: torch.tensor(v).float() for k, v in data.items()}
n = data["n"]
k = data["k"]
# model block
theta = pyro.sample("theta", dist.Beta(1., 1.))
thetaprior = pyro.sample("thetaprior", dist.Beta(1., 1.))
k = pyro.sample("k", dist.Binomial(n, theta), obs=k)
def test_binomial_approx_sample(total_count, prob):
sample_shape = (10000, )
d = dist.Binomial(total_count, prob)
expected = d.sample(sample_shape)
with set_approx_sample_thresh(200):
actual = d.sample(sample_shape)
assert_close(expected.mean(), actual.mean(), rtol=0.05)
assert_close(expected.std(), actual.std(), rtol=0.05)
def model():
# define the hyperparameters that control the beta prior
alpha0 = torch.tensor(10.0)
beta0 = torch.tensor(10.0)
f = pyro.sample("latent_fairness", dist.Beta(alpha0, beta0))
# Determine the binomial likelihood of the observed data, assuming each hypothesis is true
lkl = pyro.sample('obs', dist.Binomial(probs=f))
return lkl
def model1():
c1 = pyro.param("c1",
torch.tensor(0.5),
constraint=constraints.positive)
c0 = pyro.param("c0",
torch.tensor(1.5),
constraint=constraints.positive)
with poutine.collapse():
probs = pyro.sample("probs", dist.Beta(c1, c0))
pyro.sample("obs", dist.Binomial(total_count, probs), obs=data)
def test_binomial_approx_log_prob(tol):
logits = torch.linspace(-10.0, 10.0, 100)
k = torch.arange(100.0).unsqueeze(-1)
n_minus_k = torch.arange(100.0).unsqueeze(-1).unsqueeze(-1)
n = k + n_minus_k
expected = torch.distributions.Binomial(n, logits=logits).log_prob(k)
with set_approx_log_prob_tol(tol):
actual = dist.Binomial(n, logits=logits).log_prob(k)
assert_close(actual, expected, atol=tol)
def test_posterior_predictive_svi_auto_delta_guide(parallel):
true_probs = torch.ones(5) * 0.7
num_trials = torch.ones(5) * 1000
num_success = dist.Binomial(num_trials, true_probs).sample()
conditioned_model = poutine.condition(model, data={"obs": num_success})
guide = AutoDelta(conditioned_model)
svi = SVI(conditioned_model, guide, optim.Adam(dict(lr=1.0)), Trace_ELBO())
for i in range(1000):
svi.step(num_trials)
posterior_predictive = Predictive(model, guide=guide, num_samples=10000, parallel=parallel)
marginal_return_vals = posterior_predictive.get_samples(num_trials)["obs"]
assert_close(marginal_return_vals.mean(dim=0), torch.ones(5) * 700, rtol=0.05)
def model(data):
param = pyro.sample("var1", dist.Uniform(20, 50))
Recruiters = pyro.sample("var2", dist.Poisson(param))
percentile = pyro.sample("var3", dist.Uniform(0, 1))
if (percentile > 0.95):
GPA = 4
else:
GPA = pyro.sample("var4", dist.Normal(2.75, 0.5))
if (GPA == 4):
Interviews = dist.Binomial(Recruiters, 0.9).sample()
if (GPA < 4):
Interviews = dist.Binomial(Recruiters, 0.6).sample()
for n in range(1, 2):
with pyro.iarange("data"):
pyro.sample("obs",
dist.Binomial(Interviews, 0.4),
obs=data['offers'][n])
def test_beta_binomial(sample_shape, batch_shape):
concentration1 = torch.randn(batch_shape).exp()
concentration0 = torch.randn(batch_shape).exp()
total = 10
obs = dist.Binomial(total, 0.2).sample(sample_shape + batch_shape)
f = dist.Beta(concentration1, concentration0)
g = dist.Beta(1 + obs, 1 + total - obs)
fg, log_normalizer = f.conjugate_update(g)
x = fg.sample(sample_shape)
assert_close(f.log_prob(x) + g.log_prob(x), fg.log_prob(x) + log_normalizer)
def model(data):
# define the hyperparameters that control the beta prior
alpha0 = torch.tensor(10.0)
beta0 = torch.tensor(10.0)
# register a distribution named ”latent_fairness” as a learnable value for Pyro.
f = pyro.sample("latent_fairness", dist.Beta(alpha0, beta0))
# Condition the model on the observed data
# Determine the binomial likelihood of the observed data, assuming each hypothesis is true
# Register every observation as a learnable value
for i in range(len(data)):
sensor = pyro.sample(f'obs_{i}', dist.Binomial(probs=f), obs=data[i])
def test_posterior_predictive():
true_probs = torch.ones(5) * 0.7
num_trials = torch.ones(5) * 1000
num_success = dist.Binomial(num_trials, true_probs).sample()
conditioned_model = poutine.condition(model, data={"obs": num_success})
nuts_kernel = NUTS(conditioned_model, adapt_step_size=True)
mcmc_run = MCMC(nuts_kernel, num_samples=1000,
warmup_steps=200).run(num_trials)
posterior_predictive = TracePredictive(model, mcmc_run,
num_samples=10000).run(num_trials)
marginal_return_vals = EmpiricalMarginal(posterior_predictive)
assert_equal(marginal_return_vals.mean, torch.ones(5) * 700, prec=30)
def test_beta_binomial_log_prob(total_count, shape):
concentration0 = torch.randn(shape).exp()
concentration1 = torch.randn(shape).exp()
value = torch.arange(1. + total_count)
num_samples = 100000
probs = dist.Beta(concentration1, concentration0).sample((num_samples, ))
log_probs = dist.Binomial(total_count, probs).log_prob(value)
expected = log_probs.logsumexp(0) - math.log(num_samples)
actual = BetaBinomial(concentration1, concentration0,
total_count).log_prob(value)
assert_close(actual, expected, rtol=0.02)
def test_init():
total = 10
counts = dist.Binomial(total, 0.3).sample()
concentration1 = torch.tensor(0.5)
concentration0 = torch.tensor(1.5)
prior = dist.Beta(concentration1, concentration0)
likelihood = dist.Beta(1 + counts, 1 + total - counts)
def model():
x = pyro.sample("x", prior)
pyro.sample("counts", dist.Binomial(total, x), obs=counts)
return x
check_init_reparam(model, ConjugateReparam(likelihood))
def test_posterior_predictive_svi_auto_diag_normal_guide(return_trace):
true_probs = torch.ones(5) * 0.7
num_trials = torch.ones(5) * 1000
num_success = dist.Binomial(num_trials, true_probs).sample()
conditioned_model = poutine.condition(model, data={"obs": num_success})
guide = AutoDiagonalNormal(conditioned_model)
svi = SVI(conditioned_model, guide, optim.Adam(dict(lr=0.1)), Trace_ELBO())
for i in range(1000):
svi.step(num_trials)
posterior_predictive = Predictive(model, guide=guide, num_samples=10000, parallel=True)
if return_trace:
marginal_return_vals = posterior_predictive.get_vectorized_trace(num_trials).nodes["obs"]["value"]
else:
marginal_return_vals = posterior_predictive.get_samples(num_trials)["obs"]
assert_close(marginal_return_vals.mean(dim=0), torch.ones(5) * 700, rtol=0.05)
def model(data, params):
# initialize data
N = data["N"]
n = data["n"]
r = data["r"]
x = data["x"]
# initialize transformed data
centered_x = data["centered_x"]
mean_x = data["mean_x"]
# initialize transformed parameters
alpha_star = pyro.sample("alpha_star", dist.Normal(0., 1.0))
beta = pyro.sample("beta", dist.Normal(0., 10000.0))
with pyro.plate('data', N):
p = dist.Normal(0., 1.).cdf(alpha_star + beta * centered_x)
r = pyro.sample("r", dist.Binomial(n, p), obs=r)
def guide(self,
lengths=None,
sequences=None,
expected_string_length: int = 5):
pyro.module('gru', self.gru)
pyro.module('neural_emitter', self.neural_emitter)
binom_prob_v = pyro.param('binom_prob_v',
torch.tensor(expected_string_length /
self.smct.max_chain_length),
constraint=constraints.unit_interval)
binom_prob = pyro.sample('binom_prob', dist.Delta(binom_prob_v))
if lengths is None:
lengths = pyro.sample(
'lengths', dist.Binomial(self.smct.max_chain_length,
binom_prob)).unsqueeze(-1)
sequence_size = 1 if sequences is None else sequences.size(0)
initial_pseudocounts = pyro.param('initial_pseudocounts',
torch.ones(self.smct.alphabet_size,
dtype=torch.float,
device=lengths.device),
constraint=constraints.interval(
1, 100))
with pyro.plate('sequences', size=sequence_size, dim=-2) as batch:
for t in pyro.markov(range(self.smct.max_chain_length),
history=self.smct.order):
if t == 0:
probs_t = pyro.sample(
f'probs_{t}',
dist.Dirichlet(
initial_pseudocounts.unsqueeze(-2)).to_event())
h_t = torch.randn(self.gru.num_layers,
sequence_size,
self.gru.hidden_size,
dtype=torch.float,
device=lengths.device)
else:
if sequences is not None:
x_t = nnf.one_hot(
sequences[batch, t - 1:t],
num_classes=self.smct.alphabet_size).float()
else:
x_t = dist.OneHotCategorical(probs_t).sample()
gru_out_t, h_t = self.gru.forward(x_t, h_t)
pseudo_counts_t = self.neural_emitter.forward(gru_out_t)
probs_t = pyro.sample(f'probs_{t}',
dist.Dirichlet(pseudo_counts_t))
def model(data, params):
# XXX: this model currenty NaNs
# initialize data
G = data["G"]
N = data["N"]
r = data["r"]
n = data["n"]
# model block
with pyro.plate('a_', G, dim=-2):
mu = pyro.sample('mu', dist.Uniform(0., 1.))
a_plus_b = pyro.sample('a_plus_b', dist.Pareto(0.1, 1.5))
a = mu * a_plus_b
b = (1 - mu) * a_plus_b
with pyro.plate('data', N, dim=-1):
p = pyro.sample('p', dist.Beta(a, b))
r = pyro.sample('r', dist.Binomial(n, p), obs=r)
def test_posterior_predictive_svi_manual_guide(parallel):
true_probs = torch.ones(5) * 0.7
num_trials = torch.ones(5) * 1000
num_success = dist.Binomial(num_trials, true_probs).sample()
conditioned_model = poutine.condition(model, data={"obs": num_success})
elbo = Trace_ELBO(num_particles=100, vectorize_particles=True)
svi = SVI(conditioned_model, beta_guide, optim.Adam(dict(lr=1.0)), elbo)
for i in range(1000):
svi.step(num_trials)
posterior_predictive = Predictive(
model,
guide=beta_guide,
num_samples=10000,
parallel=parallel,
return_sites=["_RETURN"],
)
marginal_return_vals = posterior_predictive(num_trials)["_RETURN"]
assert_close(marginal_return_vals.mean(dim=0), torch.ones(5) * 700, rtol=0.05)