def codomain(self):
if self.domain is constraints.real:
return constraints.real
elif isinstance(self.domain, constraints.greater_than):
if not_jax_tracer(self.scale) and np.all(np.less(self.scale, 0)):
return constraints.less_than(self(self.domain.lower_bound))
# we suppose scale > 0 for any tracer
else:
return constraints.greater_than(self(self.domain.lower_bound))
elif isinstance(self.domain, constraints.less_than):
if not_jax_tracer(self.scale) and np.all(np.less(self.scale, 0)):
return constraints.greater_than(self(self.domain.upper_bound))
# we suppose scale > 0 for any tracer
else:
return constraints.less_than(self(self.domain.upper_bound))
elif isinstance(self.domain, constraints.interval):
if not_jax_tracer(self.scale) and np.all(np.less(self.scale, 0)):
return constraints.interval(
self(self.domain.upper_bound), self(self.domain.lower_bound)
)
else:
return constraints.interval(
self(self.domain.lower_bound), self(self.domain.upper_bound)
)
else:
raise NotImplementedError
def _support(self, *args, **kwargs):
(a, b), loc, scale = self._parse_args(*args, **kwargs)
# TODO: make constraints.less_than and support a == -np.inf
if b == np.inf:
return constraints.greater_than((a - loc) * scale)
else:
return constraints.interval((a - loc) * scale, (b - loc) * scale)
def __init__(self, base_gamma, low, validate_args=None):
assert isinstance(base_gamma, Gamma)
batch_shape = lax.broadcast_shapes(base_gamma.batch_shape,
jnp.shape(low))
self.base_gamma = tree_map(
lambda p: promote_shapes(p, shape=batch_shape)[0], base_gamma)
(self.low, ) = promote_shapes(low, shape=batch_shape)
self._support = constraints.greater_than(low)
super().__init__(batch_shape, validate_args=validate_args)
def codomain(self):
if self.domain is constraints.real:
return constraints.positive
elif isinstance(self.domain, constraints.greater_than):
return constraints.greater_than(self.__call__(self.domain.lower_bound))
elif isinstance(self.domain, constraints.interval):
return constraints.interval(self.__call__(self.domain.lower_bound),
self.__call__(self.domain.upper_bound))
else:
raise NotImplementedError
def __init__(self, base_dist, low=0.0, validate_args=None):
assert isinstance(base_dist, self.supported_types)
assert (
base_dist.support is constraints.real
), "The base distribution should be univariate and have real support."
batch_shape = lax.broadcast_shapes(base_dist.batch_shape, jnp.shape(low))
self.base_dist = tree_map(
lambda p: promote_shapes(p, shape=batch_shape)[0], base_dist
)
(self.low,) = promote_shapes(low, shape=batch_shape)
self._support = constraints.greater_than(low)
super().__init__(batch_shape, validate_args=validate_args)
class pareto_gen(jax_continuous):
arg_constraints = {'b': constraints.positive}
_support_mask = constraints.greater_than(1)
def _rvs(self, b):
return random.pareto(self._random_state, b, shape=self._size)
def _cdf(self, x, b):
return 1 - x ** (-b)
def _ppf(self, q, b):
return np.pow(1 - q, -1.0 / b)
def _sf(self, x, b):
return x ** (-b)
def _stats(self, b, moments='mv'):
mu, mu2, g1, g2 = None, None, None, None
if 'm' in moments:
mask = b > 1
bt = np.extract(mask, b)
mu = np.where(mask, bt / (bt - 1.0), np.inf)
if 'v' in moments:
mask = b > 2
bt = np.extract(mask, b)
mu2 = np.where(mask, bt / (bt - 2.0) / (bt - 1.0) ** 2, np.inf)
if 's' in moments:
mask = b > 3
bt = np.extract(mask, b)
vals = 2 * (bt + 1.0) * np.sqrt(bt - 2.0) / ((bt - 3.0) * np.sqrt(bt))
g1 = np.where(mask, vals, np.nan)
if 'k' in moments:
mask = b > 4
bt = np.extract(mask, b)
vals = (6.0 * np.polyval([1.0, 1.0, -6, -2], bt)
/ np.polyval([1.0, -7.0, 12.0, 0.0], bt))
g2 = np.where(mask, vals, np.nan)
return mu, mu2, g1, g2
def _entropy(self, c):
return 1 + 1.0 / c - np.log(c)
def _get_codomain(bijector):
if bijector.__class__.__name__ == "Sigmoid":
return constraints.interval(bijector.low, bijector.high)
elif bijector.__class__.__name__ == "Identity":
return constraints.real
elif bijector.__class__.__name__ in ["Exp", "SoftPlus"]:
return constraints.positive
elif bijector.__class__.__name__ == "GeneralizedPareto":
loc, scale, concentration = bijector.loc, bijector.scale, bijector.concentration
if not_jax_tracer(concentration) and jnp.all(concentration < 0):
return constraints.interval(loc, loc + scale / jnp.abs(concentration))
# XXX: here we suppose concentration > 0
# which is not true in general, but should cover enough usage cases
else:
return constraints.greater_than(loc)
elif bijector.__class__.__name__ == "SoftmaxCentered":
return constraints.simplex
elif bijector.__class__.__name__ == "Chain":
return _get_codomain(bijector.bijectors[-1])
else:
return constraints.real
def support(self):
return constraints.greater_than(self.scale)
@pytest.mark.parametrize(
'constraint, x, expected',
[
(constraints.boolean, np.array([True, False]), np.array([True, True])),
(constraints.boolean, np.array([1, 1]), np.array([True, True])),
(constraints.boolean, np.array([-1, 1]), np.array([False, True])),
(constraints.corr_cholesky,
np.array([[[1, 0], [0, 1]], [[1, 0.1], [0, 1]]
]), np.array([True, False])), # NB: not lower_triangular
(constraints.corr_cholesky,
np.array([[[1, 0], [1, 0]], [[1, 0], [0.5, 0.5]]]),
np.array([False, False
])), # NB: not positive_diagonal & not unit_norm_row
(constraints.greater_than(1), 3, True),
(constraints.greater_than(1), np.array(
[-1, 1, 5]), np.array([False, False, True])),
(constraints.integer_interval(-3, 5), 0, True),
(constraints.integer_interval(-3, 5), np.array([-5, -3, 0, 1.1, 5, 7]),
np.array([False, True, True, False, True, False])),
(constraints.interval(-3, 5), 0, True),
(constraints.interval(-3, 5), np.array(
[-5, -3, 0, 5, 7]), np.array([False, False, True, False, False])),
(constraints.lower_cholesky, np.array([[1., 0.], [-2., 0.1]]), True),
(constraints.lower_cholesky,
np.array([[[1., 0.], [-2., -0.1]], [[1., 0.1], [2., 0.2]]
]), np.array([False, False])),
(constraints.nonnegative_integer, 3, True),
(constraints.nonnegative_integer, np.array(
[-1., 0., 5.]), np.array([False, True, True])),
def model():
a = numpyro.param("a", a_init, constraint=constraints.greater_than(a_minval))
b = numpyro.param("b", b_init, constraint=constraints.positive)
numpyro.sample("x", dist.Normal(a, b))
def model():
a = numpyro.param('a',
a_init,
constraint=constraints.greater_than(a_minval))
b = numpyro.param('b', b_init, constraint=constraints.positive)
numpyro.sample('x', dist.Normal(a, b), obs=obs)
########################################
@pytest.mark.parametrize('constraint, x, expected', [
(constraints.boolean, np.array([True, False]), np.array([True, True])),
(constraints.boolean, np.array([1, 1]), np.array([True, True])),
(constraints.boolean, np.array([-1, 1]), np.array([False, True])),
(constraints.corr_cholesky, np.array([[[1, 0], [0, 1]], [[1, 0.1], [0, 1]]]),
np.array([True, False])), # NB: not lower_triangular
(constraints.corr_cholesky, np.array([[[1, 0], [1, 0]], [[1, 0], [0.5, 0.5]]]),
np.array([False, False])), # NB: not positive_diagonal & not unit_norm_row
(constraints.corr_matrix, np.array([[[1, 0], [0, 1]], [[1, 0.1], [0, 1]]]),
np.array([True, False])), # NB: not lower_triangular
(constraints.corr_matrix, np.array([[[1, 0], [1, 0]], [[1, 0], [0.5, 0.5]]]),
np.array([False, False])), # NB: not unit diagonal
(constraints.greater_than(1), 3, True),
(constraints.greater_than(1), np.array([-1, 1, 5]), np.array([False, False, True])),
(constraints.integer_interval(-3, 5), 0, True),
(constraints.integer_interval(-3, 5), np.array([-5, -3, 0, 1.1, 5, 7]),
np.array([False, True, True, False, True, False])),
(constraints.interval(-3, 5), 0, True),
(constraints.interval(-3, 5), np.array([-5, -3, 0, 5, 7]),
np.array([False, False, True, False, False])),
(constraints.lower_cholesky, np.array([[1., 0.], [-2., 0.1]]), True),
(constraints.lower_cholesky, np.array([[[1., 0.], [-2., -0.1]], [[1., 0.1], [2., 0.2]]]),
np.array([False, False])),
(constraints.nonnegative_integer, 3, True),
(constraints.nonnegative_integer, np.array([-1., 0., 5.]), np.array([False, True, True])),
(constraints.positive, 3, True),
(constraints.positive, np.array([-1, 0, 5]), np.array([False, False, True])),
(constraints.positive_definite, np.array([[1., 0.3], [0.3, 1.]]), True),
def tree_unflatten(cls, aux_data, params):
d = cls(*params)
if aux_data is not None:
d._support = constraints.greater_than(aux_data)
return d
