def model(self, home_team, away_team):
sigma_a = pyro.sample("sigma_a", dist.HalfNormal(1.0))
sigma_b = pyro.sample("sigma_b", dist.HalfNormal(1.0))
mu_b = pyro.sample("mu_b", dist.Normal(0.0, 1.0))
rho_raw = pyro.sample("rho_raw", dist.Beta(2, 2))
rho = 2.0 * rho_raw - 1.0
log_gamma = pyro.sample("log_gamma", dist.Normal(0, 1))
with pyro.plate("teams", self.n_teams):
abilities = pyro.sample(
"abilities",
dist.MultivariateNormal(
np.array([0.0, mu_b]),
covariance_matrix=np.array([
[sigma_a**2.0, rho * sigma_a * sigma_b],
[rho * sigma_a * sigma_b, sigma_b**2.0],
]),
),
)
log_a = abilities[:, 0]
log_b = abilities[:, 1]
home_inds = np.array([self.team_to_index[team] for team in home_team])
away_inds = np.array([self.team_to_index[team] for team in away_team])
home_rate = np.exp(log_a[home_inds] + log_b[away_inds] + log_gamma)
away_rate = np.exp(log_a[away_inds] + log_b[home_inds])
pyro.sample("home_goals", dist.Poisson(home_rate).to_event(1))
pyro.sample("away_goals", dist.Poisson(away_rate).to_event(1))
def seir_model(initial_seir_state,
num_days,
infection_data,
recovery_data,
step_size=0.1):
if infection_data is not None:
assert num_days == infection_data.shape[0]
if recovery_data is not None:
assert num_days == recovery_data.shape[0]
beta = numpyro.sample('beta', dist.HalfCauchy(scale=1000.))
gamma = numpyro.sample('gamma', dist.HalfCauchy(scale=1000.))
sigma = numpyro.sample('sigma', dist.HalfCauchy(scale=1000.))
mu = numpyro.sample('mu', dist.HalfCauchy(scale=1000.))
nu = np.array(0.0) # No vaccine yet
def seir_update(day, seir_state):
s = seir_state[..., 0]
e = seir_state[..., 1]
i = seir_state[..., 2]
r = seir_state[..., 3]
n = s + e + i + r
s_upd = mu * (n - s) - beta * (s * i / n) - nu * s
e_upd = beta * (s * i / n) - (mu + sigma) * e
i_upd = sigma * e - (mu + gamma) * i
r_upd = gamma * i - mu * r + nu * s
return np.stack((s_upd, e_upd, i_upd, r_upd), axis=-1)
num_steps = int(num_days / step_size)
sim = runge_kutta_4(seir_update, initial_seir_state, step_size, num_steps)
sim = np.reshape(sim, (num_days, int(1 / step_size), 4))[:, -1, :] + 1e-3
with numpyro.plate('data', num_days):
numpyro.sample('infections',
dist.Poisson(sim[:, 2]),
obs=infection_data)
numpyro.sample('recovery', dist.Poisson(sim[:, 3]), obs=recovery_data)
def model(home_id, away_id, score1_obs=None, score2_obs=None):
# priors
alpha = numpyro.sample("alpha", dist.Normal(0.0, 1.0))
sd_att = numpyro.sample(
"sd_att",
dist.FoldedDistribution(dist.StudentT(3.0, 0.0, 2.5)),
)
sd_def = numpyro.sample(
"sd_def",
dist.FoldedDistribution(dist.StudentT(3.0, 0.0, 2.5)),
)
home = numpyro.sample("home", dist.Normal(0.0, 1.0)) # home advantage
nt = len(np.unique(home_id))
# team-specific model parameters
with numpyro.plate("plate_teams", nt):
attack = numpyro.sample("attack", dist.Normal(0, sd_att))
defend = numpyro.sample("defend", dist.Normal(0, sd_def))
# likelihood
theta1 = jnp.exp(alpha + home + attack[home_id] - defend[away_id])
theta2 = jnp.exp(alpha + attack[away_id] - defend[home_id])
with numpyro.plate("data", len(home_id)):
numpyro.sample("s1", dist.Poisson(theta1), obs=score1_obs)
numpyro.sample("s2", dist.Poisson(theta2), obs=score2_obs)
def model(self, home_team, away_team, gameweek):
n_gameweeks = max(gameweek) + 1
sigma_0 = pyro.sample("sigma_0", dist.HalfNormal(5))
sigma_b = pyro.sample("sigma_b", dist.HalfNormal(5))
gamma = pyro.sample("gamma", dist.LogNormal(0, 1))
b = pyro.sample("b", dist.Normal(0, 1))
loc_mu_b = pyro.sample("loc_mu_b", dist.Normal(0, 1))
scale_mu_b = pyro.sample("scale_mu_b", dist.HalfNormal(1))
with pyro.plate("teams", self.n_teams):
log_a0 = pyro.sample("log_a0", dist.Normal(0, sigma_0))
mu_b = pyro.sample(
"mu_b",
dist.TransformedDistribution(
dist.Normal(0, 1),
dist.transforms.AffineTransform(loc_mu_b, scale_mu_b),
),
)
sigma_rw = pyro.sample("sigma_rw", dist.HalfNormal(0.1))
with pyro.plate("random_walk", n_gameweeks - 1):
diffs = pyro.sample(
"diff",
dist.TransformedDistribution(
dist.Normal(0, 1),
dist.transforms.AffineTransform(0, sigma_rw)),
)
diffs = np.vstack((log_a0, diffs))
log_a = np.cumsum(diffs, axis=-2)
with pyro.plate("weeks", n_gameweeks):
log_b = pyro.sample(
"log_b",
dist.TransformedDistribution(
dist.Normal(0, 1),
dist.transforms.AffineTransform(
mu_b + b * log_a, sigma_b),
),
)
pyro.sample("log_a", dist.Delta(log_a), obs=log_a)
home_inds = np.array([self.team_to_index[team] for team in home_team])
away_inds = np.array([self.team_to_index[team] for team in away_team])
home_rate = np.clip(
log_a[gameweek, home_inds] - log_b[gameweek, away_inds] + gamma,
-7, 2)
away_rate = np.clip(
log_a[gameweek, away_inds] - log_b[gameweek, home_inds], -7, 2)
pyro.sample("home_goals", dist.Poisson(np.exp(home_rate)))
pyro.sample("away_goals", dist.Poisson(np.exp(away_rate)))
def sample_y(dist_y, theta, y, sigma_obs=None):
if not sigma_obs:
if dist_y == 'gamma':
sigma_obs = numpyro.sample('sigma_obs', dist.Exponential(1))
else:
sigma_obs = numpyro.sample('sigma_obs', dist.HalfNormal(1))
if dist_y == 'student':
numpyro.sample('y', dist.StudentT(numpyro.sample('nu_y', dist.Gamma(1, .1)), theta, sigma_obs), obs=y)
elif dist_y == 'normal':
numpyro.sample('y', dist.Normal(theta, sigma_obs), obs=y)
elif dist_y == 'lognormal':
numpyro.sample('y', dist.LogNormal(theta, sigma_obs), obs=y)
elif dist_y == 'gamma':
numpyro.sample('y', dist.Gamma(jnp.exp(theta), sigma_obs), obs=y)
elif dist_y == 'gamma_raw':
numpyro.sample('y', dist.Gamma(theta, sigma_obs), obs=y)
elif dist_y == 'poisson':
numpyro.sample('y', dist.Poisson(theta), obs=y)
elif dist_y == 'exponential':
numpyro.sample('y', dist.Exponential(jnp.exp(theta)), obs=y)
elif dist_y == 'exponential_raw':
numpyro.sample('y', dist.Exponential(theta), obs=y)
elif dist_y == 'uniform':
numpyro.sample('y', dist.Uniform(0, 1), obs=y)
else:
raise NotImplementedError
def _load_data(num_seasons: int = 10,
batch: int = 1,
x_dim: int = 1) -> Tuple[jnp.ndarray, jnp.ndarray]:
"""Load sequential data with peaky noize.
ref) http://docs.pyro.ai/en/stable/_modules/pyro/contrib/examples/bart.html
Returns:
Time series data with shape of `(seq_len, batch, data_dim)`.
"""
rng_key = random.PRNGKey(1234)
rng_key_0, rng_key_1 = random.split(rng_key, 2)
x = dist.Poisson(100).sample(rng_key_0, (70 * num_seasons, batch, x_dim))
x += jnp.array(
([1] * 65 + [50] * 5) * num_seasons)[:, None, None] * random.normal(
rng_key_1, (70 * num_seasons, batch, x_dim))
t = jnp.arange(len(x))[:, None, None]
t = t.repeat(batch, axis=1)
assert isinstance(x, jnp.ndarray)
assert isinstance(t, jnp.ndarray)
assert x.shape[0] == t.shape[0]
assert x.shape[1] == t.shape[1]
return x, t
def model(data):
alpha = 1 / jnp.mean(data.astype(np.float32))
lambda1 = numpyro.sample("lambda1", dist.Exponential(alpha))
lambda2 = numpyro.sample("lambda2", dist.Exponential(alpha))
tau = numpyro.sample("tau", dist.Uniform(0, 1))
lambda12 = jnp.where(jnp.arange(len(data)) < tau * len(data), lambda1, lambda2)
numpyro.sample("obs", dist.Poisson(lambda12), obs=data)
def model(data):
alpha = 1 / jnp.mean(data)
lambda1 = numpyro.sample('lambda1', dist.Exponential(alpha))
lambda2 = numpyro.sample('lambda2', dist.Exponential(alpha))
tau = numpyro.sample('tau', dist.Uniform(0, 1))
lambda12 = jnp.where(jnp.arange(len(data)) < tau * len(data), lambda1, lambda2)
numpyro.sample('obs', dist.Poisson(lambda12), obs=data)
def model(count_data):
n_count_data = count_data.shape[0]
alpha = 1 / jnp.mean(count_data.astype(np.float32))
lambda_1 = numpyro.sample('lambda_1', dist.Exponential(alpha))
lambda_2 = numpyro.sample('lambda_2', dist.Exponential(alpha))
# this is the same as DiscreteUniform(0, 69)
tau = numpyro.sample('tau', dist.Categorical(logits=jnp.zeros(70)))
idx = jnp.arange(n_count_data)
lambda_ = jnp.where(tau > idx, lambda_1, lambda_2)
with numpyro.plate("data", n_count_data):
numpyro.sample('obs', dist.Poisson(lambda_), obs=count_data)
def test_gamma_poisson_log_prob(shape):
gamma_conc = onp.exp(onp.random.normal(size=shape))
gamma_rate = onp.exp(onp.random.normal(size=shape))
value = np.arange(15)
num_samples = 300000
poisson_rate = onp.random.gamma(gamma_conc, 1 / gamma_rate, size=(num_samples,) + shape)
log_probs = dist.Poisson(poisson_rate).log_prob(value)
expected = logsumexp(log_probs, 0) - np.log(num_samples)
actual = dist.GammaPoisson(gamma_conc, gamma_rate).log_prob(value)
assert_allclose(actual, expected, rtol=0.05)
def test_ZIP_log_prob(rate):
# if gate is 0 ZIP is Poisson
zip_ = dist.ZeroInflatedPoisson(0., rate)
pois = dist.Poisson(rate)
s = zip_.sample(random.PRNGKey(0), (20,))
zip_prob = zip_.log_prob(s)
pois_prob = pois.log_prob(s)
assert_allclose(zip_prob, pois_prob)
# if gate is 1 ZIP is Delta(0)
zip_ = dist.ZeroInflatedPoisson(1., rate)
delta = dist.Delta(0.)
s = np.array([0., 1.])
zip_prob = zip_.log_prob(s)
delta_prob = delta.log_prob(s)
assert_allclose(zip_prob, delta_prob)
def observe_poisson(name, latent, det_prob, obs=None):
mask = True
if obs is not None:
mask = np.isfinite(obs) & (obs >= 0)
obs = np.where(mask, obs, 0.0)
det_prob = np.broadcast_to(det_prob, latent.shape)
mean = det_prob * latent
d = dist.Poisson(mean)
numpyro.deterministic("mean_" + name, mean)
with numpyro.handlers.mask(mask_array=mask):
y = numpyro.sample(name, d, obs=obs)
return y
def _load_data(num_seasons: int = 100,
batch: int = 1,
x_dim: int = 1) -> Tuple[jnp.ndarray, jnp.ndarray]:
"""Load sequential data with seasonality and trend."""
t = jnp.sin(jnp.arange(0, 6 * jnp.pi, step=6 * jnp.pi / 700))[:, None,
None]
x = dist.Poisson(100).sample(random.PRNGKey(1234),
(7 * num_seasons, batch, x_dim))
x += jnp.array(np.random.rand(7 * num_seasons).cumsum(0)[:, None, None])
x += jnp.array(([50] * 5 + [1] * 2) * num_seasons)[:, None, None]
x = jnp.log1p(x)
x += t * 2
assert isinstance(x, jnp.ndarray)
assert isinstance(t, jnp.ndarray)
assert x.shape[0] == t.shape[0]
assert x.shape[1] == t.shape[1]
return x, t
def likelihood_func(self, yhat):
"""Return a poisson likelihood."""
return dist.Poisson(yhat)
def model():
a = numpyro.sample("a", dist.Dirichlet(jnp.ones(3)))
b = numpyro.sample("b", dist.Categorical(a))
c = numpyro.sample("c", dist.Normal(jnp.zeros(3), 1).to_event(1))
d = numpyro.sample("d", dist.Poisson(jnp.exp(c[b])))
numpyro.sample("e", dist.Normal(d, 1), obs=jnp.ones(()))
def poisson_regression(x, N):
rate = numpyro.sample("param", dist.Gamma(1.0, 1.0))
batch_size = len(x) if x is not None else None
with numpyro.plate("batch", N, batch_size):
numpyro.sample("x", dist.Poisson(rate), obs=x)
def model_hierarchical(y, condition=None, group=None, treatment=None, dist_y='normal', add_group_slope=False,
add_group_intercept=True,
add_condition_slope=True, group2=None, add_group2_slope=False,
center_intercept=True, center_slope=False, robust_slopes=False,
add_condition_intercept=False,
dist_slope=dist.Normal
):
n_subjects = np.unique(group).shape[0]
n_conditions = np.unique(condition).shape[0]
if (condition is None) or not n_conditions:
add_condition_slope = False # Override
add_condition_intercept = False
if center_intercept:
intercept = numpyro.sample('intercept', dist.Normal(0, 100))
else:
intercept = 0
if (group is not None) and add_group_intercept:
if dist_y == 'poisson':
print('poisson intercepts')
a_group = numpyro.sample(f'mu_intercept_per_group', dist.Poisson(jnp.tile(0, n_subjects)))
intercept += a_group
else:
sigma_a_group = numpyro.sample('sigma_intercept_per_group', dist.HalfNormal(100))
a_group = numpyro.sample(f'mu_intercept_per_group', dist.Normal(jnp.tile(0, n_subjects), 10))
intercept += (a_group[group] * sigma_a_group)
if add_condition_intercept:
intercept_per_condition = numpyro.sample('intercept_per_condition',
dist.Normal(jnp.tile(0, n_conditions), 100))
sigma_intercept_per_condition = numpyro.sample('sigma_intercept_per_condition', dist.HalfNormal(100))
intercept += intercept_per_condition[condition] * sigma_intercept_per_condition
if not add_condition_slope:
center_slope = True # override center_slope
if center_slope:
slope = numpyro.sample('slope', dist_slope(0, 100))
else:
slope = 0
if add_condition_slope:
if robust_slopes:
# Robust slopes:
b_per_condition = numpyro.sample('slope_per_condition',
dist.StudentT(1, jnp.tile(0, n_conditions), 100))
else:
b_per_condition = numpyro.sample('slope_per_condition',
dist_slope(jnp.tile(0, n_conditions), 100))
sigma_b_condition = numpyro.sample('sigma_slope_per_condition', dist.HalfNormal(100))
slope = slope + b_per_condition[condition] * sigma_b_condition
if (group is not None) and add_group_slope:
sigma_b_group = numpyro.sample('sigma_slope_per_group', dist.HalfNormal(100))
b_per_group = numpyro.sample('slope_per_group', dist_slope(jnp.tile(0, n_subjects), 100))
slope = slope + b_per_group[group] * sigma_b_group
if (group2 is not None) and add_group2_slope:
sigma_b_group = numpyro.sample('sigma_slope_per_group2', dist.HalfNormal(100))
b_per_group = numpyro.sample('slope_per_group2', dist_slope(jnp.tile(0, n_subjects), 100))
slope = slope + b_per_group[group] * sigma_b_group
if type(intercept) is int:
print('Caution: No intercept')
if treatment is not None:
slope = slope * treatment
sample_y(dist_y=dist_y, theta=intercept + slope, y=y)
def sample(self, key, sample_shape=()):
key_gamma, key_poisson = random.split(key)
rate = self._gamma.sample(key_gamma, sample_shape)
return dist.Poisson(rate).sample(key_poisson)
