def logistic_random_effects(positions, annotations):
"""
This model corresponds to the plate diagram in Figure 5 of reference [1].
"""
num_annotators = int(np.max(positions)) + 1
num_classes = int(np.max(annotations)) + 1
num_items, num_positions = annotations.shape
with numpyro.plate("class", num_classes):
zeta = numpyro.sample("zeta", dist.Normal(0, 1).expand([num_classes - 1]).to_event(1))
omega = numpyro.sample("Omega", dist.HalfNormal(1).expand([num_classes - 1]).to_event(1))
chi = numpyro.sample("Chi", dist.HalfNormal(1).expand([num_classes - 1]).to_event(1))
with numpyro.plate("annotator", num_annotators, dim=-2):
with numpyro.plate("class", num_classes):
with handlers.reparam(config={"beta": LocScaleReparam(0)}):
beta = numpyro.sample("beta", dist.Normal(zeta, omega).to_event(1))
beta = jnp.pad(beta, [(0, 0)] * (jnp.ndim(beta) - 1) + [(0, 1)])
pi = numpyro.sample("pi", dist.Dirichlet(jnp.ones(num_classes)))
with numpyro.plate("item", num_items, dim=-2):
c = numpyro.sample("c", dist.Categorical(pi))
with handlers.reparam(config={"theta": LocScaleReparam(0)}):
theta = numpyro.sample("theta", dist.Normal(0, chi[c]).to_event(1))
theta = jnp.pad(theta, [(0, 0)] * (jnp.ndim(theta) - 1) + [(0, 1)])
with numpyro.plate("position", num_positions):
logits = Vindex(beta)[positions, c, :] - theta
numpyro.sample("y", dist.Categorical(logits=logits), obs=annotations)
def transition_fn(x, y):
probs = transition_probs[x]
x = numpyro.sample("x", dist.Categorical(probs))
with numpyro.plate("D", D, dim=-1):
w = numpyro.sample("w", dist.Bernoulli(0.6))
numpyro.sample("y", dist.Normal(Vindex(locs)[x, w], 1), obs=y)
return x, None
def hierarchical_dawid_skene(positions, annotations):
"""
This model corresponds to the plate diagram in Figure 4 of reference [1].
"""
num_annotators = int(np.max(positions)) + 1
num_classes = int(np.max(annotations)) + 1
num_items, num_positions = annotations.shape
with numpyro.plate("class", num_classes):
# NB: we define `beta` as the `logits` of `y` likelihood; but `logits` is
# invariant up to a constant, so we'll follow [1]: fix the last term of `beta`
# to 0 and only define hyperpriors for the first `num_classes - 1` terms.
zeta = numpyro.sample("zeta", dist.Normal(0, 1).expand([num_classes - 1]).to_event(1))
omega = numpyro.sample("Omega", dist.HalfNormal(1).expand([num_classes - 1]).to_event(1))
with numpyro.plate("annotator", num_annotators, dim=-2):
with numpyro.plate("class", num_classes):
# non-centered parameterization
with handlers.reparam(config={"beta": LocScaleReparam(0)}):
beta = numpyro.sample("beta", dist.Normal(zeta, omega).to_event(1))
# pad 0 to the last item
beta = jnp.pad(beta, [(0, 0)] * (jnp.ndim(beta) - 1) + [(0, 1)])
pi = numpyro.sample("pi", dist.Dirichlet(jnp.ones(num_classes)))
with numpyro.plate("item", num_items, dim=-2):
c = numpyro.sample("c", dist.Categorical(pi))
with numpyro.plate("position", num_positions):
logits = Vindex(beta)[positions, c, :]
numpyro.sample("y", dist.Categorical(logits=logits), obs=annotations)
def test_value(x_shape, i_shape, j_shape, event_shape):
x = jnp.array(np.random.rand(*(x_shape + (5, 6) + event_shape)))
i = dist.Categorical(jnp.ones((5,))).sample(random.PRNGKey(1), i_shape)
j = dist.Categorical(jnp.ones((6,))).sample(random.PRNGKey(2), j_shape)
if event_shape:
actual = Vindex(x)[..., i, j, :]
else:
actual = Vindex(x)[..., i, j]
shape = lax.broadcast_shapes(x_shape, i_shape, j_shape)
x = jnp.broadcast_to(x, shape + (5, 6) + event_shape)
i = jnp.broadcast_to(i, shape)
j = jnp.broadcast_to(j, shape)
expected = np.empty(shape + event_shape, dtype=x.dtype)
for ind in itertools.product(*map(range, shape)) if shape else [()]:
expected[ind] = x[ind + (i[ind].item(), j[ind].item())]
assert jnp.all(actual == jnp.array(expected, dtype=x.dtype))
def model(data):
x = 0
D_plate = numpyro.plate("D", D, dim=-1)
for i, y in markov(enumerate(data)):
probs = transition_probs[x]
x = numpyro.sample(f"x_{i}", dist.Categorical(probs))
with D_plate:
w = numpyro.sample(f"w_{i}", dist.Bernoulli(0.6))
numpyro.sample(f"y_{i}", dist.Normal(Vindex(locs)[x, w], 1), obs=y)
def transition_fn(carry, y):
x_prev, x_curr, t = carry
with numpyro.plate("sequences", num_sequences, dim=-2):
with mask(mask=(t < lengths)[..., None]):
probs_x_t = Vindex(probs_x)[x_prev, x_curr]
x_prev, x_curr = x_curr, numpyro.sample(
"x", dist.Categorical(probs_x_t))
with numpyro.plate("tones", data_dim, dim=-1):
probs_y_t = probs_y[x_curr.squeeze(-1)]
numpyro.sample("y", dist.Bernoulli(probs_y_t), obs=y)
return (x_prev, x_curr, t + 1), None
def transition_fn(carry, y):
w_prev, x_prev, t = carry
with numpyro.plate("sequences", num_sequences, dim=-2):
with mask(mask=(t < lengths)[..., None]):
w = numpyro.sample("w", dist.Categorical(probs_w[w_prev]))
x = numpyro.sample("x", dist.Categorical(Vindex(probs_x)[w, x_prev]))
with numpyro.plate("tones", data_dim, dim=-1) as tones:
numpyro.sample("y",
dist.Bernoulli(probs_y[w, x, tones]),
obs=y)
return (w, x, t + 1), None
def test_hmm_example(prev_enum_dim, curr_enum_dim):
hidden_dim = 8
probs_x = jnp.array(np.random.rand(hidden_dim, hidden_dim, hidden_dim))
x_prev = jnp.arange(hidden_dim).reshape((-1,) + (1,) * (-1 - prev_enum_dim))
x_curr = jnp.arange(hidden_dim).reshape((-1,) + (1,) * (-1 - curr_enum_dim))
expected = probs_x[
x_prev.reshape(x_prev.shape + (1,)),
x_curr.reshape(x_curr.shape + (1,)),
jnp.arange(hidden_dim),
]
actual = Vindex(probs_x)[x_prev, x_curr, :]
assert jnp.all(actual == expected)
def dawid_skene(positions, annotations):
"""
This model corresponds to the plate diagram in Figure 2 of reference [1].
"""
num_annotators = int(np.max(positions)) + 1
num_classes = int(np.max(annotations)) + 1
num_items, num_positions = annotations.shape
with numpyro.plate("annotator", num_annotators, dim=-2):
with numpyro.plate("class", num_classes):
beta = numpyro.sample("beta", dist.Dirichlet(jnp.ones(num_classes)))
pi = numpyro.sample("pi", dist.Dirichlet(jnp.ones(num_classes)))
with numpyro.plate("item", num_items, dim=-2):
c = numpyro.sample("c", dist.Categorical(pi))
# here we use Vindex to allow broadcasting for the second index `c`
# ref: http://num.pyro.ai/en/latest/utilities.html#numpyro.contrib.indexing.vindex
with numpyro.plate("position", num_positions):
numpyro.sample("y", dist.Categorical(Vindex(beta)[positions, c, :]), obs=annotations)
