293 lines
10 KiB
Python
293 lines
10 KiB
Python
r"""
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PyTorch provides two global :class:`ConstraintRegistry` objects that link
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:class:`~torch.distributions.constraints.Constraint` objects to
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:class:`~torch.distributions.transforms.Transform` objects. These objects both
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input constraints and return transforms, but they have different guarantees on
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bijectivity.
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1. ``biject_to(constraint)`` looks up a bijective
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:class:`~torch.distributions.transforms.Transform` from ``constraints.real``
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to the given ``constraint``. The returned transform is guaranteed to have
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``.bijective = True`` and should implement ``.log_abs_det_jacobian()``.
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2. ``transform_to(constraint)`` looks up a not-necessarily bijective
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:class:`~torch.distributions.transforms.Transform` from ``constraints.real``
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to the given ``constraint``. The returned transform is not guaranteed to
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implement ``.log_abs_det_jacobian()``.
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The ``transform_to()`` registry is useful for performing unconstrained
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optimization on constrained parameters of probability distributions, which are
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indicated by each distribution's ``.arg_constraints`` dict. These transforms often
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overparameterize a space in order to avoid rotation; they are thus more
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suitable for coordinate-wise optimization algorithms like Adam::
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loc = torch.zeros(100, requires_grad=True)
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unconstrained = torch.zeros(100, requires_grad=True)
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scale = transform_to(Normal.arg_constraints['scale'])(unconstrained)
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loss = -Normal(loc, scale).log_prob(data).sum()
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The ``biject_to()`` registry is useful for Hamiltonian Monte Carlo, where
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samples from a probability distribution with constrained ``.support`` are
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propagated in an unconstrained space, and algorithms are typically rotation
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invariant.::
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dist = Exponential(rate)
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unconstrained = torch.zeros(100, requires_grad=True)
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sample = biject_to(dist.support)(unconstrained)
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potential_energy = -dist.log_prob(sample).sum()
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.. note::
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An example where ``transform_to`` and ``biject_to`` differ is
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``constraints.simplex``: ``transform_to(constraints.simplex)`` returns a
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:class:`~torch.distributions.transforms.SoftmaxTransform` that simply
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exponentiates and normalizes its inputs; this is a cheap and mostly
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coordinate-wise operation appropriate for algorithms like SVI. In
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contrast, ``biject_to(constraints.simplex)`` returns a
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:class:`~torch.distributions.transforms.StickBreakingTransform` that
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bijects its input down to a one-fewer-dimensional space; this a more
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expensive less numerically stable transform but is needed for algorithms
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like HMC.
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The ``biject_to`` and ``transform_to`` objects can be extended by user-defined
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constraints and transforms using their ``.register()`` method either as a
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function on singleton constraints::
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transform_to.register(my_constraint, my_transform)
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or as a decorator on parameterized constraints::
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@transform_to.register(MyConstraintClass)
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def my_factory(constraint):
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assert isinstance(constraint, MyConstraintClass)
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return MyTransform(constraint.param1, constraint.param2)
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You can create your own registry by creating a new :class:`ConstraintRegistry`
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object.
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"""
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import numbers
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from torch.distributions import constraints, transforms
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__all__ = [
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"ConstraintRegistry",
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"biject_to",
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"transform_to",
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]
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class ConstraintRegistry:
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"""
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Registry to link constraints to transforms.
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"""
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def __init__(self):
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self._registry = {}
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super().__init__()
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def register(self, constraint, factory=None):
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"""
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Registers a :class:`~torch.distributions.constraints.Constraint`
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subclass in this registry. Usage::
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@my_registry.register(MyConstraintClass)
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def construct_transform(constraint):
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assert isinstance(constraint, MyConstraint)
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return MyTransform(constraint.arg_constraints)
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Args:
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constraint (subclass of :class:`~torch.distributions.constraints.Constraint`):
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A subclass of :class:`~torch.distributions.constraints.Constraint`, or
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a singleton object of the desired class.
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factory (Callable): A callable that inputs a constraint object and returns
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a :class:`~torch.distributions.transforms.Transform` object.
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"""
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# Support use as decorator.
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if factory is None:
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return lambda factory: self.register(constraint, factory)
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# Support calling on singleton instances.
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if isinstance(constraint, constraints.Constraint):
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constraint = type(constraint)
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if not isinstance(constraint, type) or not issubclass(
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constraint, constraints.Constraint
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):
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raise TypeError(
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f"Expected constraint to be either a Constraint subclass or instance, but got {constraint}"
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)
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self._registry[constraint] = factory
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return factory
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def __call__(self, constraint):
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"""
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Looks up a transform to constrained space, given a constraint object.
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Usage::
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constraint = Normal.arg_constraints['scale']
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scale = transform_to(constraint)(torch.zeros(1)) # constrained
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u = transform_to(constraint).inv(scale) # unconstrained
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Args:
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constraint (:class:`~torch.distributions.constraints.Constraint`):
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A constraint object.
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Returns:
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A :class:`~torch.distributions.transforms.Transform` object.
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Raises:
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`NotImplementedError` if no transform has been registered.
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"""
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# Look up by Constraint subclass.
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try:
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factory = self._registry[type(constraint)]
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except KeyError:
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raise NotImplementedError(
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f"Cannot transform {type(constraint).__name__} constraints"
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) from None
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return factory(constraint)
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biject_to = ConstraintRegistry()
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transform_to = ConstraintRegistry()
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################################################################################
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# Registration Table
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################################################################################
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@biject_to.register(constraints.real)
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@transform_to.register(constraints.real)
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def _transform_to_real(constraint):
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return transforms.identity_transform
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@biject_to.register(constraints.independent)
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def _biject_to_independent(constraint):
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base_transform = biject_to(constraint.base_constraint)
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return transforms.IndependentTransform(
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base_transform, constraint.reinterpreted_batch_ndims
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)
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@transform_to.register(constraints.independent)
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def _transform_to_independent(constraint):
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base_transform = transform_to(constraint.base_constraint)
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return transforms.IndependentTransform(
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base_transform, constraint.reinterpreted_batch_ndims
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)
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@biject_to.register(constraints.positive)
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@biject_to.register(constraints.nonnegative)
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@transform_to.register(constraints.positive)
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@transform_to.register(constraints.nonnegative)
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def _transform_to_positive(constraint):
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return transforms.ExpTransform()
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@biject_to.register(constraints.greater_than)
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@biject_to.register(constraints.greater_than_eq)
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@transform_to.register(constraints.greater_than)
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@transform_to.register(constraints.greater_than_eq)
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def _transform_to_greater_than(constraint):
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return transforms.ComposeTransform(
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[
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transforms.ExpTransform(),
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transforms.AffineTransform(constraint.lower_bound, 1),
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]
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)
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@biject_to.register(constraints.less_than)
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@transform_to.register(constraints.less_than)
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def _transform_to_less_than(constraint):
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return transforms.ComposeTransform(
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[
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transforms.ExpTransform(),
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transforms.AffineTransform(constraint.upper_bound, -1),
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]
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)
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@biject_to.register(constraints.interval)
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@biject_to.register(constraints.half_open_interval)
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@transform_to.register(constraints.interval)
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@transform_to.register(constraints.half_open_interval)
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def _transform_to_interval(constraint):
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# Handle the special case of the unit interval.
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lower_is_0 = (
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isinstance(constraint.lower_bound, numbers.Number)
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and constraint.lower_bound == 0
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)
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upper_is_1 = (
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isinstance(constraint.upper_bound, numbers.Number)
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and constraint.upper_bound == 1
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)
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if lower_is_0 and upper_is_1:
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return transforms.SigmoidTransform()
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loc = constraint.lower_bound
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scale = constraint.upper_bound - constraint.lower_bound
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return transforms.ComposeTransform(
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[transforms.SigmoidTransform(), transforms.AffineTransform(loc, scale)]
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)
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@biject_to.register(constraints.simplex)
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def _biject_to_simplex(constraint):
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return transforms.StickBreakingTransform()
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@transform_to.register(constraints.simplex)
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def _transform_to_simplex(constraint):
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return transforms.SoftmaxTransform()
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# TODO define a bijection for LowerCholeskyTransform
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@transform_to.register(constraints.lower_cholesky)
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def _transform_to_lower_cholesky(constraint):
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return transforms.LowerCholeskyTransform()
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@transform_to.register(constraints.positive_definite)
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@transform_to.register(constraints.positive_semidefinite)
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def _transform_to_positive_definite(constraint):
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return transforms.PositiveDefiniteTransform()
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@biject_to.register(constraints.corr_cholesky)
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@transform_to.register(constraints.corr_cholesky)
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def _transform_to_corr_cholesky(constraint):
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return transforms.CorrCholeskyTransform()
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@biject_to.register(constraints.cat)
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def _biject_to_cat(constraint):
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return transforms.CatTransform(
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[biject_to(c) for c in constraint.cseq], constraint.dim, constraint.lengths
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)
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@transform_to.register(constraints.cat)
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def _transform_to_cat(constraint):
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return transforms.CatTransform(
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[transform_to(c) for c in constraint.cseq], constraint.dim, constraint.lengths
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)
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@biject_to.register(constraints.stack)
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def _biject_to_stack(constraint):
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return transforms.StackTransform(
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[biject_to(c) for c in constraint.cseq], constraint.dim
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)
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@transform_to.register(constraints.stack)
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def _transform_to_stack(constraint):
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return transforms.StackTransform(
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[transform_to(c) for c in constraint.cseq], constraint.dim
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)
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