def step(self, state, t, i):
obs = lambda value: full((state._num_particles, ), value)
n = state[f"s{t-1}"] + state[f"i{t-1}"] + state[f"r{t-1}"]
τ = sample(
f"τ{t}",
Binomial(state[f"s{t-1}"],
1.0 - exp(-state["λ"] * state[f"i{t-1}"] / n)))
Δi = sample(f"Δi{t}", Binomial(τ, state["δ"]))
Δr = sample(f"Δr{t}", Binomial(state[f"i{t-1}"], state["γ"]))
state[f"s{t}"] = sample(f"s{t}", Delta(state[f"s{t-1}"] - Δi))
state[f"i{t}"] = sample(f"i{t}",
Delta(state[f"i{t-1}"] + Δi - Δr),
obs=obs(i))
state[f"r{t}"] = sample(f"r{t}", Delta(state[f"r{t-1}"] + Δr))
def log_reg(x_data=None, y_data=None):
w = pyro.sample("w", Normal(torch.zeros(d), torch.ones(d)))
w0 = pyro.sample("w0", Normal(0., 1.))
with pyro.plate("map", N):
x = pyro.sample("x", Normal(torch.zeros(d), 2).to_event(1), obs=x_data)
logits = (w0 + x @ torch.FloatTensor(w)).squeeze(-1)
y = pyro.sample("pred", Binomial(logits=logits), obs=y_data)
return x, y
def fully_pooled(at_bats):
"""
Number of hits in $K$ at bats for each player has a Binomial
distribution with a common probability of success, $\phi$.
:param (torch.Tensor) at_bats: Number of at bats for each player.
:return: Number of hits predicted by the model.
"""
phi_prior = Uniform(at_bats.new_tensor(0), at_bats.new_tensor(1))
phi = pyro.sample("phi", phi_prior)
return pyro.sample("obs", Binomial(at_bats, phi))
def not_pooled(at_bats):
"""
Number of hits in $K$ at bats for each player has a Binomial
distribution with independent probability of success, $\phi_i$.
:param (torch.Tensor) at_bats: Number of at bats for each player.
:return: Number of hits predicted by the model.
"""
num_players = at_bats.shape[0]
phi_prior = Uniform(at_bats.new_tensor(0), at_bats.new_tensor(1)).expand_by([num_players]).independent(1)
phi = pyro.sample("phi", phi_prior)
return pyro.sample("obs", Binomial(at_bats, phi))
def not_pooled(at_bats, hits):
r"""
Number of hits in $K$ at bats for each player has a Binomial
distribution with independent probability of success, $\phi_i$.
:param (torch.Tensor) at_bats: Number of at bats for each player.
:param (torch.Tensor) hits: Number of hits for the given at bats.
:return: Number of hits predicted by the model.
"""
num_players = at_bats.shape[0]
with pyro.plate("num_players", num_players):
phi_prior = Uniform(scalar_like(at_bats, 0), scalar_like(at_bats, 1))
phi = pyro.sample("phi", phi_prior)
return pyro.sample("obs", Binomial(at_bats, phi), obs=hits)
def partially_pooled(at_bats):
"""
Number of hits has a Binomial distribution with a logit link function.
The logits $\alpha$ for each player is normally distributed with the
mean and scale parameters sharing a common prior.
:param (torch.Tensor) at_bats: Number of at bats for each player.
:return: Number of hits predicted by the model.
"""
num_players = at_bats.shape[0]
loc = pyro.sample("loc", Normal(at_bats.new_tensor(-1), at_bats.new_tensor(1)))
scale = pyro.sample("scale", HalfCauchy(at_bats.new_tensor(0), at_bats.new_tensor(1)))
alpha = pyro.sample("alpha", Normal(loc, scale).expand_by([num_players]).independent(1))
return pyro.sample("obs", Binomial(at_bats, logits=alpha))
def model(data):
# whether new topic or not; prior=0.5; random choice whether old/new
with pyro.plate("new_topic_plate", T):
new_topic = pyro.sample("new_topic", Binomial(probs=0.5))
# if new topic, if linked to old topic, prior=0.5
with pyro.plate("linked_plate", T):
linked = pyro.sample("linked", Binomial(probs=0.5))
# if old topic, which old topic
with pyro.plate("old_topic_plate", T):
which_old_topic = pyro.sample("which_old_topic",
Multinomial(probs=prev_topic_freq))
# beta sampling for topic weights
with pyro.plate("beta_plate", T - 1):
beta = pyro.sample("beta", Beta(1, alpha))
with pyro.plate("theta_plate", T): # shape [T,C]
# Dirichlet distribution (conjugate prior of Mult); symmetric prior
theta = pyro.sample("theta", Dirichlet(torch.ones(C) / C))
with pyro.plate("gamma_plate", T_prev):
gamma = pyro.sample("gamma", Dirichlet(prev_taus))
with pyro.plate("data", N):
z = pyro.sample("z", Categorical(probs=mix_weights(beta)))
old = get_old_topics(which_old_topic)
a = (new_topic) * (linked)
b = (1 - new_topic)
c = (new_topic) * (1 - linked)
a = a[z].reshape(N, 1)
b = b[z].reshape(N, 1)
c = c[z].reshape(N, 1)
mult_probs = a * gamma[old[z]] + b * prev_theta[old[z]] + c * theta[z]
pyro.sample("obs", Multinomial(probs=mult_probs), obs=data)
def model(n_ice, n_obs, floe_size, cover_subp):
a_floe = pyro.sample("a_floe", dist.Normal(1., 1.))
b_floe = pyro.sample("b_floe", dist.Normal(0., 1.))
a_cover = pyro.sample("a_cover", dist.Normal(1., 1.))
b_cover = pyro.sample("b_cover", dist.Normal(0., 1.))
a_cover_b = pyro.sample("a_cover_b", dist.Normal(1., 1.))
b_cover_b = pyro.sample("b_cover_b", dist.Normal(0., 1.))
lambda_ice = sigmoid((a_floe * floe_size + b_floe))
alpha_det = sigmoid((a_cover * cover_subp + b_cover))
beta_det = sigmoid((a_cover_b * cover_subp + b_cover_b))
with pyro.plate('subp', size=len(floe_size)):
N_ice = pyro.sample('N_ice', Poisson(lambda_ice), obs=n_ice)
phi_det = pyro.sample('phi_det', Beta(alpha_det,
beta_det)) * (N_ice > 0).float()
N_obs = pyro.sample('N_obs', Binomial(N_ice, phi_det), obs=n_obs)
def partially_pooled_with_logit(at_bats, hits):
r"""
Number of hits has a Binomial distribution with a logit link function.
The logits $\alpha$ for each player is normally distributed with the
mean and scale parameters sharing a common prior.
:param (torch.Tensor) at_bats: Number of at bats for each player.
:param (torch.Tensor) hits: Number of hits for the given at bats.
:return: Number of hits predicted by the model.
"""
num_players = at_bats.shape[0]
loc = pyro.sample("loc", Normal(scalar_like(at_bats, -1), scalar_like(at_bats, 1)))
scale = pyro.sample("scale", HalfCauchy(scale=scalar_like(at_bats, 1)))
with pyro.plate("num_players", num_players):
alpha = pyro.sample("alpha", Normal(loc, scale))
return pyro.sample("obs", Binomial(at_bats, logits=alpha), obs=hits)
def partially_pooled(at_bats, hits):
r"""
Number of hits has a Binomial distribution with independent
probability of success, $\phi_i$. Each $\phi_i$ follows a Beta
distribution with concentration parameters $c_1$ and $c_2$, where
$c_1 = m * kappa$, $c_2 = (1 - m) * kappa$, $m ~ Uniform(0, 1)$,
and $kappa ~ Pareto(1, 1.5)$.
:param (torch.Tensor) at_bats: Number of at bats for each player.
:param (torch.Tensor) hits: Number of hits for the given at bats.
:return: Number of hits predicted by the model.
"""
num_players = at_bats.shape[0]
m = pyro.sample("m", Uniform(scalar_like(at_bats, 0), scalar_like(at_bats, 1)))
kappa = pyro.sample("kappa", Pareto(scalar_like(at_bats, 1), scalar_like(at_bats, 1.5)))
with pyro.plate("num_players", num_players):
phi_prior = Beta(m * kappa, (1 - m) * kappa)
phi = pyro.sample("phi", phi_prior)
return pyro.sample("obs", Binomial(at_bats, phi), obs=hits)
def guide(data):
# pyro params
new_topic_prob = pyro.param("new_topic_prob",
lambda: Uniform(0, 1).sample([T]),
constraint=constraints.unit_interval)
linked_prob = pyro.param("linked_prob",
lambda: Uniform(0, 1).sample([T]),
constraint=constraints.unit_interval)
which_topic_probs = pyro.param("which_topic_probs",
lambda: Uniform(0, 1).sample([T_prev]),
constraint=constraints.simplex)
kappa = pyro.param('kappa',
lambda: Uniform(0, 2).sample([T - 1]),
constraint=constraints.positive)
tau = pyro.param('tau',
lambda: MultivariateNormal(0.5 * torch.ones(C), 0.25 *
torch.eye(C)).sample([T]),
constraint=constraints.unit_interval)
# N params for categorical dist; topic weights; symmetric prior
phi = pyro.param('phi',
lambda: Dirichlet(1 / T * torch.ones(T)).sample([N]),
constraint=constraints.simplex)
# model params
with pyro.plate("new_topic_plate", T):
# print(new_topic_prob)
new_topic = pyro.sample("new_topic", Binomial(probs=new_topic_prob))
# if new topic, if linked to old topic, prior=0.5
with pyro.plate("linked_plate", T):
linked = pyro.sample("linked", Binomial(probs=linked_prob))
# if old topic, which old topic
with pyro.plate("old_topic_plate", T):
which_old_topic = pyro.sample("which_old_topic",
Multinomial(probs=which_topic_probs))
with pyro.plate("beta_plate", T - 1):
q_beta = 0
q_beta += pyro.sample("beta", Beta(torch.ones(T - 1), kappa))
# new topic with symmetric prior
with pyro.plate("theta_plate", T):
theta = pyro.sample("theta", Dirichlet(tau))
# new topic linked to old topic
with pyro.plate("gamma_plate", T_prev):
gamma = pyro.sample("gamma", Dirichlet(prev_taus))
with pyro.plate("data", N):
z = pyro.sample("z", Categorical(phi))
old = get_old_topics(which_old_topic)
a = ((new_topic) * (linked))
b = (1 - new_topic)
c = ((new_topic) * (1 - linked))
a = a[z].reshape(N, 1)
b = b[z].reshape(N, 1)
c = c[z].reshape(N, 1)
mult_probs = 0
mult_probs += a * gamma[old[z]] + b * prev_theta[old[z]] + c * theta[z]
def partial_pooled(Y):
with pyro.plate(Y.shape[0]):
θ = Beta(1, 1)
return pyro.sample("y_obs", Binomial(total_count=1, probs=θ))